A&A 397, 473-486 (2003)
DOI: 10.1051/0004-6361:20021384

Clusters in the inner spiral arms of M 51: The cluster IMF and the formation history[*],[*]

A. Bik 1,2 - H. J. G. L. M. Lamers 1,3 - N. Bastian 1 - N. Panagia 4,5 - M. Romaniello 6


1 - Astronomical Institute, Utrecht University, Princetonplein 5, 3584 CC Utrecht, The Netherlands
2 - Astronomical Institute Anton Pannekoek, University of Amsterdam, Kruislaan 403, 1098 SJ Amsterdam, The Netherlands
3 - SRON Laboratory for Space Research, Sorbonnelaan 2, 3584 CA Utrecht, The Netherlands
4 - Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD21218, USA
5 - On assignment from the Space Science Department of ESA
6 - European Southern Observatory, Karl-Schwarzschild Strasse 2, Garching-bei-Muenchen 85748, Germany

Received 19 June 2002 / Accepted 16 September 2002

Abstract
We present the results of an analysis of the HST-WFPC2 observations of the interacting galaxy M 51. From the observations in 5 broadband filters (UBVRI) and two narrowband filters (H$\alpha $ and [OIII]) we study the cluster population in a region of 3.2 $\times 3.2$ kpc2 in the inner spiral arms of M 51, at a distance of about 1 to 3 kpc from the nucleus. We found 877 cluster candidates and we derived their ages, initial masses and extinctions by means of a comparison between the observed spectral energy distribution and the predictions from cluster synthesis models for instantaneous star formation and solar metallicity. The lack of [OIII] emission in even the youngest clusters with strong H$\alpha $ emission, indicates the absence of the most massive stars and suggests a mass upper limit of about 25 to 30 $M_{\odot }$. The mass versus age distribution of the clusters shows a drastic decrease in the number of clusters with age, much more severe than can be expected on the basis of evolutionary fading of the clusters. This indicates that cluster dispersion is occurring on a timescale of 10 Myr or longer. The cluster initial mass function has been derived from clusters younger than 10 Myr by a linear regression fit of the cumulative mass distribution. This results in an exponent $\alpha = -{\rm d} \log~ N(M) /{\rm d} \log~(M) =
2.1 \pm 0.3 $ in the range of $2.5\times 10^3 < M < 5\times 10^4~\mbox{$M_{\odot}$ }$ but with an overabundance of clusters with $M > 2\times 10^4$ $M_{\odot }$. In the restricted range of $2.5\times 10^3 < M < 2\times 10^4$ $M_{\odot }$ we find $\alpha = 2.0 \pm 0.05$. This exponent is very similar to the value derived for clusters in the interacting Antennae galaxies, and to the exponent of the mass distribution of the giant molecular clouds in our Galaxy. To study the possible effects of the interaction of M 51 with its companion NGC 5195 about 400 Myr ago, which triggered a huge starburst in the nucleus, we determined the cluster formation rate as a function of time for clusters with an initial mass larger than 104 $M_{\odot }$. There is no evidence for a peak in the cluster formation rate at around 200 to 400 Myr ago within 2 $\sigma$ accuracy, i.e. within a factor two. The formation rate of the detected clusters decreases strongly with age by about a factor 102 between 10 Myr and 1 Gyr. For clusters older than about 150 Myr this is due to the evolutionary fading of the clusters below the detection limit. For clusters younger than 100 Myr this is due to the dispersion of the clusters, unless one assumes that the cluster formation rate has been steadily increasing with time from 1 Gyr ago to the present time.

Key words: galaxies: individual: M 51 - galaxies: interactions - galaxies: spiral - galaxies: starburst - galaxies: star clusters


   
1 Introduction

The interaction of galaxies triggers star formation as clearly seen in the young starbursts in interacting galaxies (for reviews see Kennicutt 1998; Schweizer 1998). One of the best examples is the Antennae system where the interaction is presently going on and star formation and cluster formation occurs on a very large scale in the region between the two merging nuclei (Whitmore et al. 1999).

The way the triggered star formation progresses through an interacting galaxy is best studied from a slightly older interacting system, where the close passage of the companion is over. In such a system one can hope to derive the age distribution of clusters as a function of location in the galaxy and thus measure the time sequence of the induced star and cluster formation as a function of location in the galaxy.

One of the best systems for this purpose is the interacting sytem of the Whirlpool galaxy (M 51) at a distance of $8.4 \pm 0.6$ Mpc (Feldmeier et al. 1997). The M 51 system consists of a grand design spiral galaxy (NGC 5194) interacting with its dwarf companion (NGC 5195). The almost face-on orientation of M 51 allows the observation of its structure in great detail with minimum obscuration by interstellar dust. The interaction of these two galaxies has been modelled by various authors, starting from the fundamental paper by Toomre & Toomre (1972). These authors derived an age of the closest passage to be $2 \times 10^8$ years ago. Later refined models, e.g. by Hernquist (1990), and reviewed by Barnes (1998), have improved this time estimate. The closest approach is now believed to have occurred about 250-400 Myrs ago. The best model is found for a distance of the pericenter of 17 to 20 kpc, for a mass ratio of $M/m \approx 2$ and a relative orbit which crosses the plane of M 51 under an angle of about 15 degrees. (For a discussion of the problems with this model and possible improvements, see Barnes 1998). Recently Salo & Laurikainen (2000) suggested that on the basis of N-body simulations that the M 51 system had multiple passages, with the two last at 50-100 Myrs and 400-500 Myrs ago.

Because of its relatively small distance from us, and the fact that we see the M 51 system face one, the system is ideally suited for the study of the progression of cluster formation due to galaxy - galaxy interaction. For this reason we started a series of studies of different aspects of the M 51 system based on HST-WFPC2 observations in six broad band and two narrow band filters.

The nucleus of M 51 was studied by Scuderi et al. (2002). They found that the core contains a starburst with an age of $410 \pm 140$ Myrs and a total stellar mass of about $2 \times 10^7 ~M_{\odot}$ within the central 17 pc. This age agrees with the estimated time of closest passage of the companion, so the starburst in the core is most likely due to the interaction with the passing companion. M 51 contains an unresolved nucleus with a diameter smaller than 2 pc and a luminosity of $2\times 10^6~ L_{\odot}$ (Scuderi et al. 2002).

The bulge, i.e. the reddish region with a size of $11 \times$ 16 arcsec $^2 = 460 \times 680$ pc2, between the nucleus and the inner spiral arms, was studied by Scuderi et al. (2002) and by Lamers et al. (2002). The bulge is dominated by an old stellar population with an age in excess of 5 Gyrs. The HST-WFPC2 images of the bulge show the presence of dust lanes. The total amount of dust in the bulge is about $2.3 \times 10^3$ $M_{\odot }$ and the dust has about the same extinction law and approximately the same gas to dust ratio as our Galaxy (Lamers et al. 2002). This suggests a metallicity close to that in the solar neighbourhood. The HST-WFPC2 images of the bulge of M 51 show clearly that the dust is concentrated in structures in the forms of spiral-like dust lanes and a bar that reaches all the way down into the core. Most intriguingly is the discovery of about 30 bright and mainly blue point-like sources in the bulge that are aligned more or less along the spiral-like dust lanes. Lamers et al. (2002) have shown that these are most likely very young massive stars $20 < M_* < 150~\mbox{$M_{\odot}$ }$ with little evidence of associated clusters. This mode of star formation is the result of the peculiar conditions, in particular the destruction of CO molecules, of the interstellar clouds in the bulge of M 51.

In this study we focus on the clusters at a distance of about 1 to 3 kpc from the nucleus, i.e. near the inner spiral arms. The purpose of the paper is two-fold:
- (a) to determine the cluster intitial mass function, and
- (b) to determine the presence or absence of a starburst period that can be linked to triggering by the passage of the companion. This is not an easy task, because our data will show that the age distribution of the clusters is strongly affected by the disruption of clusters older than about 40 Myrs.

We study the clusters and their properties by identifying point-like sources in the HST-WFPC2 images and measuring their UBVRI magnitudes to obtain their energy distributions. The magnitudes indicate that the sources are clusters instead of single stars. Their energy distributions are compared to cluster evolutionary synthesis models to determine the age, mass and E(B-V) of these clusters.

In Sect. 2 we describe the observations and the data reduction. In Sect. 3 the selection of cluster candidates is discussed. In Sect. 4 we describe the cluster evolutionary synthesis models and in Sect. 5 the fitting procedure for the derivation of the cluster parameters is explained. The mass versus age distribution of the clusters is derived in Sect. 6. In Sect. 7 the initial mass function of the clusters is derived from the sample of clusters younger than 10 Myrs. The cluster formation history is studied in Sect. 8. The summary and conclusions are given in Sect. 9.

   
2 Observations and reduction

M 51 was observed with HST-WFPC2 as part of the HST Supernova INtensive Study (SINS) program (Millard et al. 1999). For this study we use the images taken in the broad band filters F336W (U), F439W (B), F555W (V), F675W (R) and F814W (I) from the SINS program and in the narrow band filters F502N $(\mbox{[OIII]})$ and F656N ( $\mbox{H$\alpha$ }$) from the GO-program of H. C. Ford. The image in U was taken on 1994 May 12, the BVRI images were taken on Jan. 15 1995 and the [OIII] and H$\alpha $ images on Jan. 25 1995. The U and B images were split into three and two exposures of 400 s and 700 s respectively. The [OIII] and H$\alpha $ images are split into two exposures of 1200 s and 500 s ( $\mbox{[OIII]}$), and 1400 s and 400 s ( $\mbox{H$\alpha$ }$). In the remaining bands one single exposure of 600 s was taken. The data was processed through the PODPS (Post Observing Data Processing System) for bias removal, flat fielding and dark frame correction.

To remove the cosmic rays from the U, B [OIII] and H$\alpha $ images, we used the STSDAS task crrej for combining the available exposures. For the VRI images, where only one exposure is available, we used a procedure called "Cosmic Eraser''. This procedure combines the IRAF tasks cosmicrays and imedit to reject as carefully as possible the cosmic rays. The automatic detection of cosmic rays with the task cosmicrays is based upon two parameters, a detection threshold and a flux ratio. The first parameter enables the detection of all the pixels with a value larger than the average value of the surrounding pixels. The flux ratio is defined as the percentage of the average value of the four neighboring pixels (excluding the second brightest pixel) to the flux of the brightest pixel. This parameter allows a classification of the detected objects: cosmic ray or star. Training objects are used to determine the flux ratio carefully. These training objects are labeled by the user to be a cosmic ray or a star. With imedit the detected cosmic rays signals are replaced by an interpolation of a third order surface fit to the surrounding pixels.

After the correction for the cosmic rays, the images were corrected for bad pixels using the hot pixel list from the STScI WFPC2 website in combination with the task warmpix. Corrections for non-optimal charge transfer efficiency on the CCD's of the WFPC2 camera were applied using the formulae by Whitmore & Heyer (1997).

With the task daofind from the DAOPHOT package Stetson (1987), we identified the point sources on the image. We performed aperture photometry on these sources, also with the DAOPHOT package. We used an aperture radius of 3 pixels. The sky background was calculated in an annulus with internal and external radius of 10 and 14 pixels respectively. We only selected the point sources with an uncertainty smaller than 0.2 in the magnitude. Photometric zeropoints were obtained from table 28.2 of the HST Data Handbook (Voit 1997), using the VEGAMAG photometric system (Holtzman et al. 1995).

The aperture correction was measured for a number of isolated, high S/N point sources on each WFPC2-chip. This output was adopted for all the other point sources on the chip. Following Holtzman et al. (1995) we have normalized the aperture correction to 1 $^{\prime\prime}$ (10 WF pixels). The aperture corrections we found are between -0.24 and -0.37 mag. This is larger than the aperture corrections for stars ${\approx}{-}0.17$ mag (Holtzman et al. 1995), which means that the detected point sources are fairly well resolved.

We adopt a distance of $d = 8.4 \pm 0.6$ Mpc (Feldmeier et al. 1997), which corresponds to a distance modulus of 29.62. At this distance, 1 $^{\prime\prime}$ corresponds to a linear distance of 40.7 pc, which means that an HST-WFC pixel of 0.1 $^{\prime\prime}$ corresponds to 4.1 pc.

   
3 Selection of the clusters

The U-band images were taken in 1994, 8 months earlier than the images in the other passbands. The orientation of HST-WFPC2 was not the same at the two epochs. In the 1995 BVRI-images the nucleus of M 51 was in the center of the PC-image. The U-image was centered on SN1994I (that was 15'' off from the nucleus) so that the nucleus was near the edge of the PC-image. The orientation of the WFPC2-images is shown in Fig. 1.


  \begin{figure}
\par\includegraphics[width=8cm,clip]{h3780f1a.ps}\hspace*{0.4cm}
\includegraphics[width=8cm,clip]{h3780f1b.eps}\end{figure} Figure 1: The location of the WFPC2 camera when the BVRI images were taken, superimposed on an optical image of M 51. Right: the orientation of the WFPC2 camera when the BVRI and the U images were taken. The grey area indicates the location of the WF2 chip, covering an area of $3.25 \times 3.25$ kpc (for an adopted distance of 8.4 Mpc), that was used in this analysis. Its exact location and orientation are given in Fig. 2. The dark grey region shows the overlap of the BVRI and U images.
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For our analysis only the part of WF4-chip of the U image that overlap with the WF2-chip of the BVRI images is used (see Fig. 1). To identify the various sources, we obtained a position of the sources in U and transformed these positions to the coordinate frame of the BVRI images. The orientation of the [OIII] and H$\alpha $ images is very similar to those of the BVRI images. We transformed these narrow band images to the same orientation as the BVRI images. We applied our analysis of the cluster energy distributions to the sources that were detected in the images of at least three of the BVRI broad-band filters with a magnitude uncertainty smaller than 0.2 in each band. To this purpose we compared the positions of all detected sources in the BVRI images. If objects occur in at least three images within a position tolerance of 2 pixels they are selected for our study. This tolerance was chosen on the basis of tests with clearly identifiable sources that were observed in most bands. For the sources detected in at least three images we then checked for the presence of a source in the U image, in the region where the U image and the BVRI images do overlap (the dark grey region in Fig. 1). If a source was not detected in a particular band, we adopted a conservative lower limit for the magnitude in that band (see below). This was not always possible for the U-magnitude, because many of the sources detected in the BVRI bands are located in an area that was not covered by the U-image. As a consequence, we have no information on the U-magnitude for many of the sources. The location of the sources in the WF2-chip is shown in Fig. 2. The overlay of the sources on the V band image clearly shows that the clusters are concentrated in or near the spiral arms at a distance of about 1.5 kpc from the nucleus of M 51. The number of sources, detected in the various bands, is listed in Table 1. The sample contains a total of 877 sources for which we have reliable photometry ( $\sigma < 0.20$ mag) in at least three bands.

Figure 3 shows the magnitude distribution of the sources in the various bands. All distributions show a slow increase in numbers towards fainter objects, a maximum and a steep decrease towards even fainter sources. The slow increase to fainter sources reflects their luminosity function. The steep decrease to high magnitudes is due to the detection limit. This detection limit is not a single value for each band, because of the variable background in the WF2 field due to the spiral arms. The maximum of the distributions are near $U \simeq 20.0$, $B \simeq 22.0$, $V\simeq 22.0$, $R \simeq 21.5$ and $I \simeq 21.0$. These values will be adopted as conservative lower limits for the magnitudes of sources that were not detected in any given band.

All the objects fall in the visual magnitude range of 16.5 <V < 23.6. For distance modulus of 29.62 this corresponds to an absolute magnitude range of -12.1 < MV <-6.0 in the case of zero extinction and -12.6 < MV<-6.5 in case of moderate extinction with $E(B-V) \simeq 0.17$. This means that the faintest objects could be either very bright stars or small clusters. The vast majority of the selected point sources are so bright that they must be clusters. (See Sect. 5.6.)


 

 
Table 1: Numbers of point sources detected in the different WFPC2-HST-images.

F336W
F439W F555W F675W F814W number
(U) (B) (V) (R) (I) objects

d
d d d d 76
l d d d d 366
n d d d d 109
d l d d d 30
l l d d d 144
n l d d d 39
d d d d l 21
l d d d l 78
n d d d l 14
          877

d means "detected", l means "lower magnitude limit" (i.e. the object is fainter than the detection limit) and n means "not observed".



  \begin{figure}
\par\includegraphics[width=7.4cm,clip]{h3780f2.eps}\end{figure} Figure 2: Left: the location of all the detected point sources in the WF2 chip superimposed on the V-band image. This image is rotated 90 degrees clockwise compared to Fig. 1. The coordinates of the lower-left and upper-right corners of the image are: pixel (1, 1): $\rm RA(2000)=13^h29^m55\hbox{$.\!\!^{\rm s}$ }90$, $\rm Dec(2000)=47^011'27\hbox{$.\!\!^{\prime\prime}$ }2.$ and pixel 800, 800: $\rm RA(2000)=13^h29^m57\hbox{$.\!\!^{\rm s}$ }94$, $\rm Dec(2000)=47^013'16\hbox{$.\!\!^{\prime\prime}$ }6$.
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  \begin{figure}
\par\includegraphics[width=8.8cm,height=8.8cm,clip]{h3780f3.ps}\end{figure} Figure 3: The histogram of the magnitudes in the different bands. The slow increase at bright magnitudes is due to the luminosity function and the steep decrease at fainter magnitudes is due to the detection limit.
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3.1 The $\mathsfsl{H{\alpha}}$ and [OIII] magnitudes

The magnitudes in the narrow-band images of filters F656N ( $m({\rm H}\alpha )$) and F502N ( $m{\rm [OIII]}$) can be compared with those of the wide-band filters F675W (R) and F555W (V) respectively to derive a measure of the equivalent width of the H$\alpha $ and [OIII] lines. When the magnitudes are expressed in the HST-system, the magnitude differences $R-\mbox{$m({\rm H}\alpha)$ }$ and $V-\mbox{$m{\rm [OIII]}$ }$ are by definition equal to 0.0 if the spectrum of a source is a featureless, flat continuum (i.e. the spectrum of the source is a continuum $F_\lambda=\rm const.$ without a photospheric H$\alpha $ absorption, and there is no HII region around the star). The differences $R-\mbox{$m({\rm H}\alpha)$ }$ and $V-\mbox{$m{\rm [OIII]}$ }$ are either positive or negative if the source spectrum has an emission or an absorption line, respectively, falling in the narrow band filter, independently of the interstellar extinction. With the Vega-system magnitudes one has to fold in both the non-zero spectral slope and the discrete features present in $\alpha $ Lyrae's spectrum. Therefore, a featureless flat continuum would correspond to $R-\mbox{$m({\rm H}\alpha)$ }\simeq +0.08$ and $V-\mbox{$m{\rm [OIII]}$ }\simeq -0.26$ colors in the Vega-system.

Figure 4a shows the $m({\rm H}\alpha )$ versus R and Fig. 4b shows $m{\rm [OIII]}$ versus V for the subset of sources for which we could measure these magnitudes with an accuracy better than 0.2. The figure shows that many sources have H$\alpha $ emission ( $\mbox{$m({\rm H}\alpha)$ }
< R$) but none (!) of the sources has [OIII] emission (note that $m{\rm [OIII]}$ is slightly fainter than the V magnitude as appropriate for complete absence of an emission line). The lack of [OIII] emission indicates that the far-UV flux, at $\lambda < 350$ Å  i.e. at energies higher than the second ionization potential of oxygen, is quite low. For main sequence stars with $L>2.5 \times 10^5~ \mbox{$L_{\odot}$ }$ (i.e. with $M > 30~\mbox{$M_{\odot}$ }$ and $\mbox{$T_{\rm eff}$ }> 33~000$ K), surrounded by an HII region with approximately solar abundances, we would expect $ V -
\mbox{$m{\rm [OIII]}$ }> R - \mbox{$m({\rm H}\alpha)$ }$. We will show later, on the basis of the study of the energy distributions, that many of the objects are very young clusters with ages less than a 10 Myr. The lack of [OIII] emission shows that these clusters do not contain stars with $T_{\rm eff}$ above about 30 000 K, which corresponds to about 25 to 30 $M_{\odot }$ (e.g. Chiosi & Maeder 1986). We can exclude the possibility that the lack of [OIII] emission be due to just a high metallicity, which could reduce the electron temperature in an HII region and weaken optical forbidden lines considerably, without requiring a lower effective temperature, or, equivalently, a low upper mass cutoff. This is because in many HII regions in M 51 and in other metal-rich spiral galaxies not only are the [OIII] lines faint or absent but also the HeI lines are unusually faint relative to Balmer lines (Panagia 2000; Lenzuni & Panagia, in preparation). This result indicates that He is only partially ionized and, therefore, that the ionizing radiation field is indeed produced exclusively by stars with effective temperatures much lower than 33 000 K . So we conclude that the upper mass limit for clusters in the inner spiral arms of M 51 is about 25 to 30 $M_{\odot }$.


  \begin{figure}
\par\includegraphics[width=8.8cm,clip]{h3780f4a.ps}\par\includegraphics[width=8.8cm,clip]{h3780f4b.ps}\end{figure} Figure 4: The top figure shows $m({\rm H}\alpha )$ versus R and the lower figure shows $m{\rm [OIII]}$ versus V for objects were these magnitudes could be determined with an accuracy better than 0.2 mag. Notice that many objects have H$\alpha $ emission, but no object has detectable [OIII] emission.
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4 Cluster evolution models

To determine the age, initial mass and E(B-V) of the clusters, we compare the observed energy distributions with energy distributions derived from theoretical cluster evolutionary synthesis models. We used two sets of models: the Starburst99 models for ages up to 1 Gyr, and the Frascati models for ages of 10 Myr to 5 Gyr. In this section the models are described.

4.1 Starburst99 cluster evolution models

To determine the age, initial mass and E(B-V) of the clusters, we compare the observed energy distributions with energy distributions derived from theoretical cluster evolutionary synthesis models. We used two sets of models: the Starburst99 models for ages up to 1 Gyr, and the Frascati models for ages of 10 Myr to 5 Gyr. In this section the models are described.

   
4.2 Starburst99 cluster evolution models

We compared the observed spectral energy distributions (SED) of our objects with the cluster evolutionary synthesis models of Leitherer et al. (1999), i.e. the Starburst99 models for instantaneous star formation. In these models, the stellar atmosphere models of Lejeune et al. (1997) are included. For stars with a strong mass loss the Schmutz et al. (1992) extended model atmospheres are used. The stellar evolution models of the Geneva group are included in these models. For our analysis we used the models of the Spectral Energy Distributions (SEDs).

In the cluster models the stars are assumed to be formed with a classical Salpeter IMF-slope of ${\rm d} \log (N) /{\rm d}\log (M) =-2.35$. The lower cut-off mass is $M_{\rm low} = 1~M_{\odot}$. We adopt two values for the upper cut-off mass: the standard value of $M_{\rm up} =
100~M_{\odot}$, and the value of $\mbox{$M_{\rm up}$ }= 30~ \mbox{$M_{\odot}$ }$. This last value is adopted because it is suggested by the lack of [OIII] emission (see Sect. 3.1). The total initial mass of all models is 106 $M_{\odot }$. Leitherer et al. (1999) present models for 5 different metallicities, from Z= 0.001 to $Z=0.040 = 2 \times Z_{\odot}$. Observations of HII-regions have shown that the metallicity of the inner region of M 51 is approximately $2 ~ Z_\odot$ or slightly higher (e.g. Diaz et al. 1991; Hill et al. 1997). Therefore we adopt the models with Z=0.020 and 0.040. The almost solar metallicity agrees with the study of Lamers et al. (2002), who found that the extinction properties and the gas to dust-ratio in the bulge of M 51 is very similar to that in the Milky Way. So we use four sets of models, denoted by the pair $(Z,\mbox{$M_{\rm up}$ })$ of (0.02, 100), (0.02, 30), (0.04, 100) and (0.04, 30). For these combinations we calculated the SEDs of the cluster models, taking into account the nebular continuum emission.

To obtain the absolute magnitudes from the theoretical spectral energy distributions in the five broad-band filters and the two narrow-band filters we convolved the predicted spectra of the Starburst99 models with the WFPC2 filter profiles. The spectrum of Vega was also convolved with the filter functions in order to find the zero-points of the magnitudes in the VEGAMAG system. For each combination of Z and $\mbox{$M_{\rm up}$ }$ we calculated the SED of 195 models in the range of 0.1 Myr to 1 Gyr, with time steps increasing from 0.5 Myr for the youngest models to 10 Myr for the oldest models.

The adopted lower mass limit of 1 $M_{\odot }$ for the cluster stars has consequences for the derived masses of the clusters. If the IMF with a slope of -2.35 has a lower mass limit of 0.2 $M_{\odot }$, as for the Orion Nebula Cluster (Hillenbrand 1997), the derived masses of the clusters would be a factor 2.09 higher for an upper limit of 30 $M_{\odot }$. If the lower limit is 0.6 $M_{\odot }$, the mass of the clusters will be a factor 1.28 higher than those of the Starburst99 models for $M_{\rm up}=30$ $M_{\odot }$. We will take this effect into account in the determination of the cluster masses.

Some of the theoretical energy distributions in the WFPC2 wide-band filters used in this study are shown in Fig. 5, for clusters with an initial mass of 106 $M_{\odot }$ at the distance of M 51. During the first 5 Myrs the UV flux remains high because most of the O-type stars have main sequence ages longer than 5 Myr. Between 5 and 10 Myr the O-type stars disappear. This results in a general decrease at all magnitudes, except in the I band where the red supergiants start to dominate. At later ages the flux decreases at all wavelengths as stars end their lives. After 900 Myrs only stars of types late-B and later have survived.


  \begin{figure}
\par\includegraphics[width=8.8cm,clip]{h3780f5.ps} \end{figure} Figure 5: Examples of some characteristics of the theoretical energy distributions, in magnitude versus wavelength (Å) of the UBVRI filters (from left to right), for STARBURST99 clusters with an initial mass of 106 $M_{\odot }$ at the distance of M 51. The age of the cluster in Myrs is indicated. The evolutionary variation is discussed in Sect. 4.1.
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Figure 5 shows that at any wavelength in the observed range the flux decreases with time. This fading of the clusters indicates that the detection limit of the clusters will gradually shift to those of higher mass as the clusters age. This is because the flux of a cluster (for a given stellar initial mass function) at any age and wavelength is proportional to the initial number of stars. The more massive the initial cluster, the brighter the cluster and the longer the flux will remain above the detection limit as the cluster fades due to stellar evolution. For any given detection limit, we can calculate the lower mass limit of the observable cluster as a function of age.

Figure 6 shows the relation between the initial mass of a cluster and its age when it fades below the detection limit, derived from the Starburst99 models. The R-magnitude (R) of a cluster of initial mass Mi without extinction at the adopted distance of 8.4 Mpc of M 51 (dm=29.62) is related to the absolute R-magnitude (MR) predicted for the Starburst99 models of 106 $M_{\odot }$ by

 \begin{displaymath}R(t)=M_R(t) + 29.62 - 2.5 \times \log \left(M/10^6\right)\cdot
\end{displaymath} (1)

So, for a given detection limit $R_{\rm lim}$ the critical mass $M_{\rm lim}$ of a cluster that can be detected at age t is given by

 \begin{displaymath}\log M_{\rm lim}(t)~=~6+0.4 \times(M_R(t)+29.62-R_{\rm lim}).
\end{displaymath} (2)

We have adopted the R magnitudes to calculate the observed lower limits of the distributions for two reasons: (a) all clusters were detected in the R band and (b) the effect of extinction is small in the R band. The resulting relation between $M_{\rm lim}$ and age is shown in Fig. 6 for detection limits of $R_{\rm lim}$= 22.0 and 23.0 mag. We will use these limits later, in Sect. 5, to explain the distribution of clusters in the mass versus age diagram.


  \begin{figure}
\par\includegraphics[width=8.8cm,clip]{h3780f6.ps}\end{figure} Figure 6: The relation between the critical initial mass $M_{\rm lim}$ and age, derived for two values of the R-band magnitude limit; 22.0 and 23.0 mag. It is calculated from the Starburst99 cluster models, for a distance of 8.4 Mpc and no extinction. Only clusters with an initial mass higher than $M_{\rm lim}$ can be detected as faint as $R_{\rm lim}$ at time t. Alternatively, clusters with a mass $M_{\rm lim}$ can only be detected down to a magnitude $R_{\rm lim}$ when they are younger than the age t, indicated by these relations.
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Figure 7 shows the variations of the colours of the Starburst99 models for solar metallicity and with an upper mass limit of 30 $M_{\odot }$. The figure shows that the colours do not change monotonically, but that there are peaks and dips, especially in the age range of $6.5 < \log(t) < 7.3$. These are related to the phases of the appearance of red supergiants that also produced the dips in the limiting magnitude curves of Fig. 6.

   
4.3 The Frascati models

Since the Starburst99 models only cover the age range up to 1 Gyr, we also used synthetic cluster models for older ages from the Frascati group. These "Frascati-models'' were calculated by Romaniello (1998) from the evolutionary tracks of Brocato & Castellani (1993) and Cassisi et al. (1994) using the HST-WFPC2 magnitudes derived from the stellar atmosphere models by Kurucz (1993). These models are for instantaneous formation of a cluster of solar metallicity stars in the mass range of 0.6 to 25 $M_{\odot }$, with a total initial mass of 50 000 $M_{\odot }$, distributed according to Salpeter's IMF. These models cover an age range of 10 to 5000 Myr. There are 48 models with timesteps increasing from 10 Myr for the youngest ones to 500 Myr for the oldest ones. We have increased the magnitudes of the Frascati models by -3.526 mag in order to scale these models to a total mass of 106 $M_{\odot }$ in the mass range of 1.0 to 25 $M_{\odot }$; i.e. -3.25 mag correction for the conversion from $5\times 10^4$ to $1\times 10^6$ $M_{\odot }$, and 0.279 mag correction for the conversion from a lower stellar mass limit of 0.6 $M_{\odot }$ to 1.0 $M_{\odot }$. In this way the masses can be compared directly with those of the Starburst99 models.

The Starburst99 models are expected to be more accurate for the younger clusters, because they are based on the evolutionary tracks of the Geneva-group which include massive stars. The Frascati models are expected to be more accurate for the old clusters, because they include stars with masses down to 0.6 $M_{\odot }$.

  \begin{figure}
\par\includegraphics[width=8.8cm,clip]{h3780f7.ps}\end{figure} Figure 7: The variations of colours with age of the Starburst99 models of Z=0.02 and an upper mass limit of 30 $M_{\odot }$. Notice the periods of rapid variability near the peaks and dips around $t \simeq 6$ and 16 Myrs, $\log (t) \simeq 6.8$ and 7.2.
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4.4 The extinction curve

To determine the values of E(B-V) of the clusters we assume the mean galactic reddening law. Lamers et al. (2002) and Scuderi et al. (2002) have shown that the extinction law of respectively the bulge and the core of M 51 agree very well with the galactic law. The values of Ri=Ai/E(B-V) for the HST-WFPC2 filters have been calculated by Romaniello (1998). They are respectively 4.97, 4.13, 3.11, 2.41 and 1.91 for the U, B, V, R and I bands.

In the fitting of the energy distributions we did not take into account the disruption of clusters. We assumed that the stars contribute to the total energy distribution of the clusters until the cluster is completely dissolved and is no longer detectable as a point source. This is a reasonable assumption because we measured the magnitudes in a circle of 12 pc radius (see Sect. 2).


  \begin{figure}
\par\includegraphics[width=10cm,clip]{h3780f8.ps} \end{figure} Figure 8: Example of some fits. The filled dots represent the observed energy distributions of objects measured in at least four bands, with their error bars in magnitude versus wavelength (in $\mu $m). In several cases the error bars are smaller than the size of the dots. Crosses indicate magnitude lower limits. The parameters of the fits are indicated in an array $(E(B-V),~\log(t),~\log(\mbox{$M_{\rm cl}$ }))$. The second array gives the uncertainties in these parameters. The line is the best fit obtained with the maximum likelihood method. Top figures: fits with $\mbox{$\chi^2_{\nu}$ }< 1$; bottom figures: fits with $\mbox{$\chi^2_{\nu}$ }\simeq 3$. Notice that the uncertainty of the fit parameters depends not only on $\chi _{\nu }^2$ but also strongly on the quality of the data. For instance, the errors in the magnitudes of the last two clusters are very small, so that the fit parameters are accurate, despite the high value of $\chi _{\nu }^2$.
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5 Fitting the observed energy distributions to observed cluster models

   
5.1 The fitting procedure

We have fitted the energy distributions of the clusters with good photometry in four or more filters, viz. UBVRI, BVRI, UVRI and UBVR (see Table 1), with the energy distributions of the cluster evolutionary synthesis models, discussed above, using a three dimensional maximum likelihood method. The three fitting parameters are: the age of the cluster (t), the reddening (E(B-V)) and the initial mass of the cluster (M). For the clusters detected in only three filters we reduce the parameter space and make a two dimensional maximum likelihood fit. For objects not detected in a band, we adopted the magnitude lower limits (described in Sect. 3) to check which fits were acceptable[*].

   
5.2 Three dimensional maximum likelihood method

This method was applied to sources that are detected in at least four bands. We fitted the observed energy distributions with those predicted for the Starburst99 cluster models and the Frascati models (see Sect. 4.2). For each model-age we have two fitting parameters M and E(B-V). The cluster models are for an initial cluster mass of 106 $M_{\odot }$. For other masses the flux simply scales $M/10^6~\mbox{$M_{\odot}$ }$. We have adopted an uncertainty in the model fluxes of 5 percent (0.05 mag) in all bands.

To reduce the range in masses in the parameter space, we make an initial guess of the cluster mass based on the observed magnitudes, since the distance to M 51 is known. By calculating the average difference in magnitude - weighted by the errors - between the theoretical energy distribution for 106 $M_{\odot }$ and the observed one, we have a good first approximation of the mass of the cluster:

 
$\displaystyle M_{\rm guess}(E(B-V),\tau) \simeq \frac{\sum_{\lambda}
1/\sigma_{...
...-
m_{\lambda}^{\rm mod}(E(B-V),\tau)\right\}}{\sum_{\lambda}1/\sigma_{\lambda}}$     (3)

with E(B-V) between 0.0 and 2.0 in steps of 0.02, where $\sigma$ is the uncertainty in the magnitude. This is a reasonable range, compared to the average colour excess for the bulge of 0.2 found by Lamers et al. (2002). With this initial guess we then make a three dimensional likelihood analysis, using a mass range from 1/1.5 to 1.5 times the initial mass estimate in steps of 0.004 dex. The extinction was varied between 0.0 and 2.0 in steps of 0.01 and the age was varied between 0.1 Myr and 1 Gyr for the Starburst99 models and between 10 Myr to 5 Gyr for the Frascati models.

For every fit we obtain a value for the reduced $\chi^2$, i.e. $\chi^2_{\nu}$ = $\chi^2$/$\nu$, where $\nu$ is the number of free parameters i.e. the number of the observed data points minus the number of parameters in the theoretical model. For a good fit, $\chi^2_{\nu}$ should be about unity. We checked that the fits were consistent with the faint magnitude limits of the filters in which the object was not detected. If not, the fit was rejected. The fit with the minimum value of $\chi^2_{\nu}$ was adopted as the best fit and the corresponding values of E(B-V), age and Mi were adopted. This method was applied for fits with the four sets of the Starburst99 models and with the Frascati models. Figure 8 shows some examples of the results of the fitting process.

To estimate the uncertainty in the determined parameters we use confidence limits. If $\mbox{$\chi^2_{\nu}$ }< \mbox{$\chi^2_{\nu}$ }(\min)+1$ then the resulting parameters, i.e. $\log (t)$, $\log (M_i)$ and E(B-V), are within the 68.3% probability range. So the accepted ranges in age, mass and extinction are derived from the fits which have $\mbox{$\chi^2_{\nu}$ }(\min) < \mbox{$\chi^2_{\nu}$ }< \mbox{$\chi^2_{\nu}$ }(\min)+1$. With this method we derived the ages, initial masses[*] and extinction with their uncertainties of 602 clusters.

Figure 9 shows a histogram of number of clusters as function of E(B-V). We will use this distribution for the two dimensional maximum likelihood fit of clusters detected in three bands only. The redding is small: 90% of the clusters have a reddening lower than 0.40; 67% of the clusters have a reddening lower than 0.18 and 23% have no detectable reddening.

   
5.3 Two dimensional maximum likelihood method

For the clusters observed in only three bands, it is not possible to make a three dimensional maximum likelihood fit. To reduce the parameter space we adopted the probability distribution of E(B-V) in the range of E(B-V) between 0.0 and 0.4, as shown in Fig. 9. For every value of E(B-V) between 0.0 and 0.40 (in steps of 0.02) and for every age of the model cluster, we first determine the mass of the cluster by means of Eq. (3). The results of the three dimensional fits have shown this is a good approximation. This results in a maximum likelihood age of the cluster for every value of E(B-V).

The $\chi^2_{\nu}$ which comes out from the two dimensional maximum likelihood method is used to distinguish between the accepted and rejected fits. For the parameter $\nu$ we used a value of 3-1=2, because we only fit the age of the cluster. The mass of the cluster comes from the scaling of the magnitudes to the best-fit model. A fit is accepted if it agrees with the lower magnitude limits in the filters where it was not measured. To determine the age of the cluster, we average the ages, weighted by the probability that each particular value of E(B-V) occurs, derived by normalizing the distribution in Fig. 9 in the range of 0.0 < E(B-V)<0.40. The error in the age is determined by calculating the value of the standard deviation $\sigma$ of the age, again weighted with the probability that the value of E(B-V) occurs. The value of E(B-V) is determined by using the one which belongs to the model with the age closest to the average age. The initial mass of the cluster is then calculated by Eq. (3) for the adopted value of E(B-V). With this method we derived the age, initial mass and the extinction of 275 clusters, using both the Starburst99 models and the Frascati models.

   
5.4 Starburst99 or Frascati models?

We have compared the energy distributions of the objects with five sets of models: four sets of Starburst99 models, with $Z=Z_{\odot}$ or $2 ~ Z_\odot$ and $\mbox{$M_{\rm up}$ }=30$ or 100 $M_{\odot }$, and the Frascati models with $Z=Z_{\odot}$ and $\mbox{$M_{\rm up}$ }=25$ $M_{\odot }$. Based on the lack of [OIII] emission we adopt the models with $\mbox{$M_{\rm up}$ }=25$ or 30 $M_{\odot }$. The models with $\mbox{$M_{\rm up}$ }=100$ $M_{\odot }$ are only used later to check the influence of this adopted upper limit on our results.

  \begin{figure}
\par\includegraphics[width=8.8cm,clip]{h3780f9.ps} \end{figure} Figure 9: Histogram of the values of E(B-V) from the fits with observations in BVRI and UBVRI. The extinction is small: 90% of the clusters have $\mbox{$E(B-V)$ }<0.40$.
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We have compared the ages derived from fitting the observed SEDs with the Starburst99 models and the Frascati models, for objects measured in at least four filters and with fits of $\mbox{$\chi^2_{\nu}$ }< 3.0$. We found that in the age range of 10 to 800 Myr there is a reasonable correlation between the results of the SB99 models and the Frascati models, with the Frascati models giving ages systematically about 0.4 dex smaller than the SB99 models. In this age range we adopt the SB99 models, because they are based on more reliable evolutionary tracks, better stellar atmosphere models and because the nebular continuum is included. We find that in this mass range the fits with the SB99 models have smaller $\mbox{$\chi_{\nu}^2$ }$ than the fits with the Frascati-models. For objects with ages above about 700 Myrs ( $\log (t)
> 8.85$) the Frascati-models give the most reliable fits with smaller $\mbox{$\chi_{\nu}^2$ }$ than the SB99 models. This is probably because the lower mass limit of the SB99 models is 1 $M_{\odot }$, and the Frascati models go down to 0.6 $M_{\odot }$. Moreover the SB99 models do not go beyond 1 Gyr. Based on this comparison we adopt the SB99 fits for ages less than 700 Myrs and the results of the Frascati models for older ages.

   
5.5 Uncertainties in the derived parameters

The determination of the cluster parameters, age, mass and extinction, by means of the two or thee dimensional maximum likelihood fitting method, i.e. the 3(2)DEF-method, results not only in the values of $\log(\mbox{$M_{\rm cl}$ })$, $\log (t)$ and E(B-V) but also in their maximum and minimum acceptable values. The best-fit values are not necessarily in the middle of the minimum and the maximum values. If we define the uncertainties in the parameters, $\Delta E(B-V)$, $\Delta
\log(\mbox{$M_{\rm cl}$ })$ and $\Delta \log(t)$ as half the difference between the maximum and mimimum values, we find that 30 percent of the clusters have $\Delta E(B-V)<0.08$, 50 percent have $\Delta E(B-V)<0.11$ and 70 percent have $\Delta E(B-V)<0.15$. For the uncertainties in the mass determination we find $\Delta \log(\mbox{$M_{\rm cl}$ })<0.20$, <0.33 and <0.55 for 30, 50 and 70 percent of the clusters respectively. For the uncertainties in the age determination we find $\Delta \log(t)<0.23$, <0.39 and <0.69 for 30, 50 and 70 percent of the clusters respectively. Taking the values for 50 percent of the clusters as representative, we conclude that the uncertainties are $\Delta E(B-V)\simeq 0.11$, $\Delta \log(\mbox{$M_{\rm cl}$ }) \simeq 0.33$ and $\Delta \log(t) \simeq 0.39$.

   
5.6 Contamination of the cluster sample by stars?

To estimate the number of stars that may contaminate our cluster sample we use the stellar population in the solar neighbourhood. From the tabulated stellar densities as a function of spectral type (Allen 1976) we derived the number of stars brighter than a certain value of MV per pc3. Using the mass density of $0.13~ \mbox{$M_{\odot}$ }$pc-3, we derived the number of stars per unit stellar mass. The results are listed in Table 2. The total stellar mass of the observed region of M 51 (see Fig. 2) is estimated to be about 1/20 of the total mass of $5\times 10^{10}$ $M_{\odot }$ in the disk of that galaxy (Athanassoula et al. 1987), i.e. about $2.5\times 10^{9}$ $M_{\odot }$. This implies that we can expect the following numbers of stars brighter than MV<-6.5 per spectral type in the observed region: 4 (O), 13 (B), 6 (A), 6 (F), 6 (G), <1 (K) and <1 (M). So we can expect of the order of 40 bright stars with MV<-6.5 in the observed region of M 51. However, these are all massive young supergiants of which the vast majority will be in clusters! So the number of bright stars outside clusters, that may contaminate our sample of clusters will be considerable smaller, and we expect it to be smaller than about 20 out of the total sample of 877. Moreover, we have shown above, from the lack of O[III] emission, that the clusters in M 51 have a shortage of massive stars with M>30 $M_{\odot }$. We can expect this effect also to occur for the massive field stars. This would reduce the number of expected contaminating stars even further. Tests have shown that a considerable fraction of possibly remaining stellar sources will be eliminated by the requirement that their energy distribution should fit that of cluster models within a given accuracy. Based on all these considerations, we conclude that contamination of our cluster sample with very massive stars of MV<-6.5 outside clusters is expected to be negligible.

 

 
Table 2: Numbers of stars above a certain absolute magnitude limit in the solar neighbourhood.

Limit
O B A F G K M Total

MV < -5.5
-8.3 -7.6 -8.0 -7.4 -7.4 -8.5 -8.5 -6.9
MV < -6.5 -8.8 -8.3 -8.6 -8.6 -8.6 <-9.5 <-9.5 -7.9
MV < -7.5 -9.8 -9.3 -9.6 -9.6 -9.6 <-10.5 <-10.5 -8.9

(1) The data are in log (Number/per $M_{\odot }$).
(2) The number of stars with MV<-7.5 was estimated to be about 10 times smaller than for MV<-6.5 because of the small number
of very massive stars formed, and their short evolution time.

   
6 The mass versus age distribution

We discuss the results from the fitting of the observed energy distributions to those of cluster models with solar metallicity and with and upper mass limit of 30 $M_{\odot }$. We have checked that the fits with twice solar metallicity and with an upper limit of 100 $M_{\odot }$ give about the same results.

Figure 10 shows the mass versus age distribution of sources with Mv<-7.5 (to eliminate possible stellar sources) and with energy distributions that could be fitted to that of a cluster models with an accuracy of $\mbox{$\chi^2_{\nu}$ }\le 3.0$. (The distributions for clusters with $\mbox{$\chi^2_{\nu}$ }\le 1$ or 10, not shown here, show the same distribution, but with 294 and 508 clusters respectively.) We see that the lower limit of the mass increases with increasing age, from about 1000 $M_{\odot }$ at $t\simeq 5$ Myrs to about $5\times 10^4$ $M_{\odot }$ at 1 Gyr. This is due to the expected effect of fading of the clusters as they age (see Sect. 4.1). The full line in the figure is the fading line in the R magnitude for clusters which have a limiting magnitude of $R_{\rm lim}=22.0$ at the distance of M 51 for a reddening of E(B-V) = 0. The line in Fig. 10 thus gives the mass of the clusters, that reaches this magnitude detection limit, as a function of age.


  \begin{figure}
\par\includegraphics[width=8.8cm,clip]{h3780f10.ps}\end{figure} Figure 10: The mass versus age relation of the 392 clusters with MV < -7.5, whose energy distribution could be fitted with an accuracy of $\mbox{$\chi^2_{\nu}$ }< 3.0$. The cross shows the characteristic uncertainties (Sect. 5.5). The full line is the predicted fading line due to the evolution of clusters with E(B-V) = 0 and with a limiting magnitude of $R_{\rm lim}=22.0$ at the distance of M 51. This line roughly agrees with the observed lower limit. The distribution is discussed in the text.
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These initial mass versus age distribution of the clusters in Fig. 10 show the following characteristics:
- (i) The lower mass limit increases with age due to the fading of the clusters. The observed lower limit agrees with the predicted ones for the R band. There are even hints of the presence of the predicted dips in the lower limit near $\log(t)=6.8$ and 7.2. This strengthens our confidence in the adopted models.
- (ii) There are clear concentrations in the distribution at $\log(t)=6.70$ and 7.45 and possibly also around $\log(t) \simeq 7.2$. These are due to the properties of the cluster models and the adopted method. In Fig. 7 we have shown that the colours of the models do not change monotonically with time, but that there are phases when the colours change rapidly with time. These phases occur in the range of $6.5 < \log(t) < 7.3$. Large changes in the colours of the models occur just before and after the peaks where the slopes of the curves in Fig. 7 are large. It is more difficult to fit the observed energy distributions with high accuracy to models in the age range when the spectral changes are large, than in the age range when the changes are small. So there is a tendency of the model fits to concentrate in agebins just outside the age-regions of large spectral changes. This explains the concentrations and the voids in the derived age distributions of the clusters between about $6.5 < \log(t) < 7.5$.
- (iii) The density of the points drops at $\log(t) > 7.5$. Since the age scale is logarithmic, we might have expected an increasing density of points towards the higher ages, which is not observed. This is due to the disruption or dispersion of the clusters (see first paragraphs of Sect. 7).

We conclude that the mass versus age distribution agrees with the expected evolutionary fading of the clusters and that the decrease in numbers of clusters with age shows the affect of disruption/dispersion of clusters with time. The concentrations of the clusters at ages around $\log(t)=6.8$, 7.2 and 7.45 are due to statistical effects and do not represent periods of enhanced cluster formation.

   
7 The cluster initial mass function

The data in Fig. 10 and the detailed study of this distribution by Boutloukos & Lamers (2002) show that the clusters in the inner spiral arms of M 51 disrupt on a time scale of about tens of Myrs. In fact, these authors derived the dependence of the disruption time on the initial mass of the clusters in the inner spiral arms of M 51 as

 \begin{displaymath}\log t_{\rm disr} = \log t_4 ~+~\gamma \times \log (M_{\rm cl}/10^4~\mbox{$M_{\odot}$ })
\end{displaymath} (4)

with $\log t_4 = 7.64 \pm 0.22$ and $\gamma=0.62 \pm 0.06$ for the mass range of $3 \le \log (\mbox{$M_{\rm cl}$ }/ \mbox{$M_{\odot}$ }) \le 5.2 $, where $M_{\rm cl}$ is the initial mass of the cluster. We see that clusters with an initial mass larger than 104 $M_{\odot }$ survive $4\times10^7$ years. Clusters with an initial mass of only 103 $M_{\odot }$ disrupt on a time scale of $1\times10^7$ yrs. This implies that the cluster initial mass function cannot be derived from the total sample of clusters, because the disruption will produce a strong bias towards the more massive clusters. However for the youngest clusters with ages less than about 10 Myr disruption is not yet an important effect and, therefore, these clusters can be used to derive the initial cluster mass function.


  \begin{figure}
\includegraphics[width=8.8cm,clip]{h3780f11.ps}\end{figure} Figure 11: Histograms of the mass of clusters (in $\log M_{\rm cl}$) with an age of 10 Myrs or younger. The light shaded area shows the distribution of all 354 clusters. The dark shaded area shows the histogram of clusters with an accurate mass determination of $\Delta \log M_{\rm cl} < 0.25$. The steep part at $\log(M) < 3.0$ is due to the detection limit. The decrease at $\log(M) >3.0 $ reflects the slope of the cluster IMF. (All masses have to be increased by a factor 2.1 if the lower limit of the stellar mass is 0.2 $M_{\odot }$ rather than the value of 1 $M_{\odot }$ that was adopted in the Starburst99 models.)
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Figure 11 shows the resulting mass distribution of clusters with an age less or equal to 10 Myr for two samples of clusters. The first sample contains all 354 clusters younger than 10 Myr. The second sample contains 168 clusters in the same age range but with a mass determination of $\Delta \log(\mbox{$M_{\rm cl}$ }) \le 0.25$. Both samples show the same characteristics: a steep increase in number between $2.5 < \log \mbox{$M_{\rm cl}$ }<3.0$ and a slow decrease to higher masses. The steep increase is due to the detection limit or the disruption of the low mass clusters. The slow decrease reflects the cluster initial mass function (CIMF). The decrease indicates that the clusters are formed with an CIMF that has a negative slope of ${\rm d}\log (N)/{\rm d}\log (M)$, as expected.

If the CIMF can be written as a power law of the type

 \begin{displaymath}N(M)~{\rm d}M~ \sim ~ M^{\alpha}~{\rm d}M~~~~~{\rm for}~~\mbox{$M_{\rm min}$ }<M<\mbox{$M_{\rm max}$ }
\end{displaymath} (5)

then the normalized cumulative distribution will be
 
    $\displaystyle \Sigma (M)=A - B\times M^{-\alpha+1}~~~~~{\rm with}$  
    $\displaystyle A=B \times \mbox{$M_{\rm min}$ }^{-\alpha+1}$  
    $\displaystyle B=\left(M_{\rm min}^{-\alpha+1}~-~M_{\rm max}^{-\alpha+1}\right)^{-1}\cdot$ (6)

Figure 12 shows the observed and predicted normalized cumulative distribution of the 149 clusters with an age less than 10 Myr and with a mass $\mbox{$M_{\rm cl}$ }>2.5\times 10^3~\mbox{$M_{\odot}$ }$ that are used for the determination of the CIMF. We eliminated the clusters with $ \mbox{$M_{\rm cl}$ }<2.5\times 10^3~\mbox{$M_{\odot}$ }$ from the sample because Fig. 11 shows that the sample may not be complete for smaller masses. The cumulative distributions of the 84 clusters of $M>2.5\times 10^3~\mbox{$M_{\odot}$ }$, younger than 10 Myr, which are fitted to the models with an accuracy of $\mbox{$\chi^2_{\nu}$ }\le 3.0$, or of the 66 clusters with $\Delta \log(\mbox{$M_{\rm cl}$ }) \le 0.25$, not shown here, (where $\Delta
\log(\mbox{$M_{\rm cl}$ })$ is the uncertainty in the mass determination), have the same shape as the distribution in Fig. 12. For these three samples we have determined the values of $\alpha $ and $M_{\rm min}$ by means of a linear regression under the reasonable assumption that $\mbox{$M_{\rm min}$ }\ll\mbox{$M_{\rm max}$ }$, which implies that $A \simeq 1$. The resulting values of $\alpha $ and $M_{\rm min}$ are listed in Table 3. The table shows that $\alpha \simeq 2.1$ for all three samples.


 

 
Table 3: The CIMF for clusters with t<10 Myr and $ \mbox{$M_{\rm cl}$ }<2.5\times 10^3~\mbox{$M_{\odot}$ }$.

Sample
Nr $\log \mbox{$M_{\rm min}$ }$ $\alpha $

All
149 3.49 2.12 $\pm$ 0.26
$\Delta \log \mbox{$M_{\rm cl}$ }< 0.25$ 66 3.48 2.04 $\pm$ 0.41
$\mbox{$\chi^2_{\nu}$ }< 3.0$ 82 3.46 2.16 $\pm$ 0.40



  \begin{figure}
\par\includegraphics[width=8.8cm,clip]{h3780f12.ps}\end{figure} Figure 12: The cumulative mass distribution of 149 clusters with an age less than 10 Myrs and an inital mass of $\log (M) > 3.40$. The full line is the best power-law fits for an IMF with the value of $\alpha $ and $M_{\rm min}$ from Table 3. The dashed line is the fit with $\alpha =2.00$.
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The predicted cumulative distribution with the derived values of $\alpha=2.12$ and $M_{\rm min}$ is shown in Fig. 12 (full line). The figure shows a slight underabundance of clusters in the range of $4.0 < \log (\mbox{$M_{\rm cl}$ }) < 4.3$ and a slight overabundance in the range of $\log (\mbox{$M_{\rm cl}$ })>4.3$. In fact, for the mass range of $3.5 < \log (\mbox{$M_{\rm cl}$ }) <
4.3$ a fit with $\alpha =2.00$, shown by dashed lines, fits the distribution excellently. We conclude that the CIMF of clusters younger than 10 Myr has a slope of $\alpha \simeq 2.1 \pm 0.3$ in the mass range of $3.0 < \log (\mbox{$M_{\rm cl}$ }) < 5.0$ and a slope of $2.00 \pm 0.05$ in the range of $3.0 < \log(\mbox{$M_{\rm cl}$ }) < 4.3~\mbox{$M_{\odot}$ }$.

The derived exponent of the cluster IMF is very similar to the value of $\alpha = 2.0$ of young clusters in the Antennae galaxies, as found by Zhang & Fall (1999). It shows that the IMF of clusters formed in the process of galaxy-galaxy interaction is very similar to the one of clusters formed in the spiral arms of a galaxy, long after the interaction. This mass distribution is also similar to that of giant molecular clouds (e.g. McKee 1999; Myers 1999). This may support the suggestion that the mass distribution of the clusters is determined by the mass distribution of the clouds from which they originate.

   
8 The cluster formation history

One of the goals of this paper is to study the influence of the interaction between M 51 and its companion on the cluster formation in the region of the inner spiral arms. To this purpose we compare the observed age distribution of the clusters with predictions for a constant cluster formation rate. This comparison is hampered by two effects: (a) the disruption of clusters and (b) the fading of clusters below the detection limit. The disruption time of the clusters in the inner spiral arms of M 51 is given by Eq. (4). We see that only clusters with an initial mass larger than about 104 $M_{\odot }$ will survive more than 40 Myrs.

Figure 13 shows the histogram of the formation rates of the detected clusters, in number per Myr, for 140 clusters with $\mbox{$M_{\rm cl}$ }> 10^4$ $M_{\odot }$ and with an energy distribution that is fitted with an accuracy of $\mbox{$\chi^2_{\nu}$ }\le 3.0$. The sample of 111 clusters with $\mbox{$M_{\rm cl}$ }> 10^4$ $M_{\odot }$ and with an age uncertainty of $\Delta
\log(t) < 0.25$, and the full sample of 285 clusters with $\mbox{$M_{\rm cl}$ }> 10^4$ $M_{\odot }$, not shown here, have a distribution very similar to the one shown in Fig. 12.


  \begin{figure}
\par\includegraphics[width=8.8cm,clip]{h3780f13.ps}\end{figure} Figure 13: The formation rates of the observed clusters with an initial mass of $M_{\rm i} > 10^4$ $M_{\odot }$  in number per Myr, for clusters with an accuracy of the fit of the energy distribution of $\mbox{$\chi^2_{\nu}$ }\le 3.0$. The $ 1 \sigma $ uncertainty due to the Poisson statistics in each bin ( $\sigma = 1/\sqrt (N)$) is indicated. The diagram shows that the formation rate of the observed clusters decreases with age. This is due to the disruption of the older clusters.
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All three samples show about the same characteristics.
(a) There is a general trend of a decrease in the cluster formation rate towards increasing age.
(b) There is a steep drop around $\log(t)\simeq 7.5$. This drop is the result of the concentration of clusters at ages $\log(t)=7.45$ that was apparent in the mass versus age diagrams of Fig. 10, and was explained in Sect. 6.
(c) There is no clear evidence for a peak in the cluster formation rate near $\log(t)\simeq 8.6$, which is the time of the interaction of M 51 with its companion, and which is the age of the huge starburst in the nucleus of M 51. There is a hint of a small peak around $\log(t) \simeq 8.1$. However this peak is only $2 \sigma$ high. Its reality has to be verified with a larger sample of clusters.
(d) The peak in the last bin of 5 Gyr contains all the clusters ages older than 3 Gyr, because the cluster models that we used for fitting the energy distributions do not go beyond 5 Gyr.
We have checked that these characteristics are not the result of the binning process: the same features appear for different choices of the binning parameters.

The general decrease in the formation rate of the observed clusters is partly due to the evolutionary fading of the clusters and partly due to the disruption of clusters. In Sect. 6 and in Fig. 10 we have shown that clusters with an initial mass of 104 $M_{\odot }$ fade below the detection limit when they are older than $\log(t)=8.2$. This can explain the decrease in the formation rate of clusters older than about 150 Myrs. However, clusters with $\mbox{$M_{\rm cl}$ }>10^4~\mbox{$M_{\odot}$ }$ and younger than about 100 Myr should still all be detectable. The fact that we see a decrease in the apparent cluster formation rate must thus be due to the disruption of clusters (unless for some unknown reason the cluster formation rate has been steadily increasing from 100 Myrs up to now, which we consider unlikely).

It is interesting that the CFR in the inner spiral arms of M 51, at a distance of about 1 to 3 kpc from the nucleus, does not show any evidence for a peak at the age of the strongest interaction of M 51 with its companion galaxy. The closest approach occurred about 250-400 Myrs ago according to the dynamical models of Barnes (1998) or 400-500 and 50-100 Myrs ago according to Salo & Laurikainen (2000). The only significant peak occurred at $\log(t) \simeq 7.4$. However we attributed this peak to the large changes in the energy distributions of the models in the age range of $6.5 < \log(t) < 7.5$, and not to a real increase in the CFR.

   
9 Summary and conclusions

We have studied images of the inner spiral arms of the interacting galaxy M 51 obtained with the HST-WFPC2 camera in broad-band UBVRI and in the narrow band H$\alpha $ and [OIII] filters. The study can be summarized as follows:

1.
We found a total of 877 point-like objects, which are probably clusters. Many of the clusters are strong H$\alpha $ emitters, but none of the clusters, not even the youngest ones, have an excess of radiation in the [OIII] line at 5007 Å (F502N-filter). This suggests that the upper mass limit of the stars in the clusters is about 25 to 30 $M_{\odot }$.

2.
We have compared their energy distributions with those of Starburst99 cluster models (Leitherer et al. 1999) for instantaneous star formation with a stellar IMF of exponent 2.35, solar metallicity, a lower and upper stellar mass limit of 1 $M_{\odot }$ and 30 $M_{\odot }$ respectively. The energy distributions were also compared with those of the Frascati models (Romaniello 1998). For clusters younger than 700 Myr the results from the fitting with the Starburst99 models were adopted because these models are more accurate for young clusters and the fits of the energy distributions are better than those of the Frascati models. For older clusters the results from the fits with the Frascati models were adopted.

3.
For clusters that were observed in four or five bands a three dimensional maximum likelihood method was used to derive the properties of the clusters from the comparison between the observed and predicted energy distributions. The free parameters are the age t and E(B-V), which together determined the shape of the energy distribution, and the initial cluster mass $M_{\rm cl}$ which determines the absolute magnitude. For clusters that were not observed in all bands, the empirically derived lower magnitudes limits were taken into account.

4.
For clusters that were observed in only three bands the age and mass were derived in a two-dimensional maximum likelihood fitting of the energy distributions, with t and $M_{\rm cl}$ as free parameters. The observed probability distribution of E(B-V) was used as a weighting factor in the fitting procedure.
5.
The histogram of E(B-V) is strongly peaked at very small $E(B-V) \simeq 0$. All cluster have a reddening smaller than E(B-V)<1.0 and 67% of the clusters have E(B-V)<0.18.

6.
We have analysed the observed clusters also with cluster models of higher metallicity, $Z=2\times Z_{\odot}$. These higher metallicity models fit the observations considerably worse than the solar metallicity models. For instance, for solar metallicity models the energy distribution of 294 clusters can be fitted with an accuracy of $\mbox{$\chi^2_{\nu}$ }\le 1.0$ and 392 with $\mbox{$\chi^2_{\nu}$ }\le 3.0$. For models with twice the solar metallicity these numbers are respectively 138 and 217. So the energy distributions of the clusters support the adopted solar metallicity.

7.
The clusters have masses in the range of $2.5 < \log (\mbox{$M_{\rm cl}$ }) <
5.7$ and ages of $\log(t) >5.0$. These masses are the initial masses of the clusters, i.e. the current mass corrected for stellar evolution effects, but not corrected for evaporation or disruption. All derived masses have to be multiplied by a factor 1.3 if the lower mass of the stars is 0.6 $M_{\odot }$, instead of the adopted 1 $M_{\odot }$, and by a factor 2.1 if the lower mass is 0.2 $M_{\odot }$, as found for the Orion Nebula cluster.

8.
The distribution of the clusters in a mass-versus-age diagram shows the predicted lower limit due to the evolutionary fading of the clusters, including the dips at $\log (t) \simeq 6.8$ and 7.1. Three apparent concentrations at $\log(t)=6.7$, 7.2 and 7.45 are not real but due to the properties of the cluster models used.

9.
About 60% of the clusters are younger than 40 Myr. The number of older clusters is much less than expected for a constant cluster formation rate. This is partly due to the evolutionary fading of low mass clusters below the detection limit, and partly due to the disruption of the clusters.

10.
The cluster initial mass function (CIMF) was derived from the cumulative mass distribution of clusters younger than 10 Myr, for which disruption has not occured. The CIMF has a slope of $\alpha = 2.1 \pm 0.3$ in the range of $3.0 < \log (\mbox{$M_{\rm cl}$ }) < 5.0$ and $\alpha= 2.00 \pm 0.05$ in the range of $3.0 < \log (\mbox{$M_{\rm cl}$ }) < 4.5$ $M_{\odot }$, for $N(\mbox{$M_{\rm cl}$ }) \sim \mbox{$M_{\rm cl}$ }^{-\alpha}$. This slope is the same to that found in the interacting Antennae galaxies (Zhang & Fall 1999). Zhang and Fall deived a power law slope of the CIMF of $\alpha=1.95 \pm 0.03$ and $2.00 \pm 0.04$ for two cluster samples of the Antennae galaxies. The good agreement between these slopes and the one found by us suggests that $\alpha $ is about the same for cluster formation triggered by strong galaxy-galaxy interactions, such as presently going on in the Antennae, as for cluster formation that is not dominated by the interactions.

11.
The age distribution of clusters with $\mbox{$M_{\rm cl}$ }> 10^4$ $M_{\odot }$, is used to derive the history of the cluster formation rate (CFR). There is a general trend of a decrease of the formation rate of the observed clusters with age. It is unlikely that the real CFR has been increasing continuously from about 1 Gyr to the present time. The decrease of the CFR with age of clusters younger than about 100 Myr cannot be due to evolutionary fading, but it is due to the disruption of clusters. For clusters older than 200 Myr the decrease of the derived CFR could, at least partly, be due to evolutionary fading.

12.
There is no evidence for a peak in the CFR at about 400 Myr, which is the time of the interaction of M 51 with its companion and the age of the huge starburst in the nucleus.

In a forthcoming paper we describe the cluster formation as a function of location in a large part of M 51, using the same methods as used here (Bastian et al. 2002). The disruption of clusters in M 51, derived from the results of the study presented here, are described by Boutloukos & Lamers (2002).

Acknowledgements
H.J.G.L.M.L. and N.B. are grateful to the Space Telescope Scence Institute for hospitality and financial support during several stays. We thank Claus Leitherer for help and advice in the calculation of the cluster models. Support for the SINS program GO-9114 was provided by NASA through a grant from the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc. under NASA contract NAS 5-26555. N.B. ackowledges a grant from the Netherlands Organization for Scientific Research. We thank the unknown referee for constructive comments that resulted in an improvement of this paper.

References

 

Online Material



  Table 4: Coordinates and HST-WFPC2 broad-band photometry of 881 clusters in the inner regions of the M51.

Explanation of columns:
(1) : an index number of all point sources
(2) : an old index number
(3) : the x-coordinate of the HST-WF2 chip
(4) : the y coordinate of the HST-WF2 chip
pixel (x=1,y=1) is RA(2000) 13h 29 m 55.90 s,    DEC(2000) = +47 degr 11 min 27.2 sec
pixel (x=800, y=800) is RA(2000) 13h 29 m 57.94 s,    DEC(2000) = +47 degr 13 min 16.6 sec
(5) through (16): magnitudes in the VEGAMAG system (Holtzman et al. 1995 PASP 107, 156)
magn 0.00 means: not observed (ouside the observed field)
magn 99.99 means: source too faint, only lower magn limit
lower magn. limits: F336W=20.0, F439W=22.0, F555W=22.0, F675W=21.5, F814W=21.0 (see paper)
(5) and (6) : magn and uncertainty in F255W filter
(7) and (8) : magn and uncertainty in F336W filter
(9) and (10): magn and uncertainty in F439W filter
(11) and (12): magn and uncertainty in F555W filter
(13) and (14): magn and uncertainty in F675W filter
(15) and (16): magn and uncertainty in F814W filter
(17): 6-digit code that summarizes the observations
first digit refers to F255W filter, last digit to F814W filter
0 = not observed (outside observed HST-field),
1 = observed magnitude
9 = lower magnitude limit only
 

i
i(old) x y mag $\Delta$mag mag $\Delta$mag mag $\Delta$mag mag $\Delta$mag mag $\Delta$mag mag $\Delta$mag icode
        F255W F255W F336W F336W F439W F439W F555W F555W F675W F675W F814W F814W  
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17)

1
1001 69.777 36.890 0.00 9.99 0.00 9.99 20.88 0.06 20.77 0.10 20.54 0.12 20.19 0.13 001111
2 1002 97.360 36.866 0.00 9.99 0.00 9.99 21.56 0.12 21.29 0.18 20.89 0.19 20.56 0.21 001111
3 1003 205.844 38.133 0.00 9.99 99.99 -9.99 18.70 0.02 18.72 0.04 18.53 0.04 18.53 0.04 091111
4 1004 303.164 38.382 0.00 9.99 99.99 -9.99 21.49 0.07 20.92 0.09 20.30 0.10 19.88 0.10 091111
5 1005 545.934 38.252 0.00 9.99 0.00 9.99 21.48 0.09 21.21 0.13 22.58 0.15 22.55 0.20 001111
6 1006 572.451 38.762 0.00 9.99 0.00 9.99 21.51 0.07 21.50 0.05 20.38 0.09 20.40 0.03 001111
7 1007 203.947 39.183 0.00 9.99 99.99 -9.99 18.70 0.02 18.72 0.04 18.60 0.04 18.53 0.04 091111
8 1008 525.198 39.474 0.00 9.99 0.00 9.99 21.27 0.08 21.90 0.06 21.80 0.08 20.29 0.14 001111
9 1009 566.688 38.493 0.00 9.99 0.00 9.99 21.66 0.08 22.20 0.06 22.08 0.08 20.58 0.16 001111
10 1010 52.926 39.867 0.00 9.99 0.00 9.99 20.95 0.02 20.60 0.03 20.21 0.02 19.84 0.01 001111
11 1011 76.592 39.070 0.00 9.99 0.00 9.99 20.74 0.06 20.68 0.10 20.43 0.11 20.82 0.06 001111
12 1012 429.070 39.393 0.00 9.99 99.99 -9.99 20.61 0.04 21.60 0.06 21.10 0.06 20.82 0.06 091111
13 1013 574.315 40.026 0.00 9.99 0.00 9.99 21.52 0.07 21.57 0.05 20.38 0.09 20.39 0.03 001111
14 1014 124.414 40.596 0.00 9.99 0.00 9.99 21.65 0.10 21.21 0.13 20.79 0.15 20.45 0.17 001111
15 1015 108.407 42.775 0.00 9.99 0.00 9.99 21.83 0.18 21.23 0.17 20.80 0.17 20.41 0.17 001111
16 1016 61.610 42.668 0.00 9.99 0.00 9.99 21.13 0.07 20.88 0.10 20.66 0.12 20.29 0.13 001111
17 1017 94.948 42.821 0.00 9.99 0.00 9.99 21.39 0.11 21.12 0.14 20.88 0.17 20.56 0.18 001111
18 1018 130.911 44.346 0.00 9.99 0.00 9.99 21.54 0.07 21.11 0.10 20.67 0.12 20.28 0.12 001111
19 1019 161.545 46.265 0.00 9.99 0.00 9.99 21.55 0.08 21.35 0.11 21.02 0.14 20.82 0.17 001111
20 1020 761.764 46.129 0.00 9.99 0.00 9.99 22.26 0.09 22.04 0.14 21.90 0.19 21.62 0.23 001111
21 1021 127.567 46.993 0.00 9.99 0.00 9.99 21.03 0.05 20.88 0.08 20.71 0.10 20.53 0.13 001111
22 1022 174.604 47.935 0.00 9.99 0.00 9.99 21.36 0.09 21.33 0.08 20.96 0.08 21.07 0.10 001111
23 1023 198.918 47.934 0.00 9.99 99.99 -9.99 20.26 0.04 20.21 0.04 19.98 0.03 19.77 0.04 091111
24 1024 285.837 48.290 0.00 9.99 99.99 -9.99 21.95 0.07 21.81 0.10 21.73 0.14 21.34 0.14 091111
25 1025 396.059 47.656 0.00 9.99 99.99 -9.99 21.88 0.15 21.69 0.11 21.31 0.10 20.78 0.09 091111
26 1026 410.019 49.293 0.00 9.99 99.99 -9.99 22.16 0.10 22.28 0.15 22.28 0.23 22.12 0.28 091111
27 1027 750.016 48.923 0.00 9.99 0.00 9.99 23.09 0.10 22.17 0.05 21.83 0.05 21.67 0.06 001111
28 1028 282.445 49.499 0.00 9.99 99.99 -9.99 21.99 0.07 21.75 0.09 21.67 0.12 21.33 0.12 091111
29 1029 321.740 49.780 0.00 9.99 99.99 -9.99 22.43 0.15 21.43 0.08 21.22 0.11 20.99 0.13 091111
30 1030 407.301 49.749 0.00 9.99 99.99 -9.99 22.22 0.11 22.28 0.15 22.28 0.23 22.12 0.28 091111
31 1031 466.216 50.264 0.00 9.99 99.99 -9.99 22.65 0.08 22.47 0.08 22.17 0.12 22.24 0.19 091111
32 1032 396.267 52.842 0.00 9.99 99.99 -9.99 22.54 0.16 21.76 0.10 21.74 0.11 21.42 0.12 091111
33 1033 114.423 53.970 0.00 9.99 0.00 9.99 20.39 0.03 20.36 0.04 20.07 0.04 19.85 0.04 001111
34 1034 121.414 55.540 0.00 9.99 0.00 9.99 20.12 0.03 20.04 0.04 19.82 0.03 19.41 0.02 001111
35 1035 268.249 55.877 0.00 9.99 99.99 -9.99 23.26 0.17 22.59 0.11 21.93 0.09 21.54 0.10 091111
36 1036 331.802 57.324 0.00 9.99 99.99 -9.99 20.74 0.03 20.39 0.04 19.89 0.04 19.96 0.04 091111
37 1037 535.170 56.934 0.00 9.99 0.00 9.99 21.97 0.07 22.04 0.09 21.87 0.09 21.49 0.10 001111
38 1038 116.142 56.934 0.00 9.99 0.00 9.99 20.27 0.03 20.36 0.04 20.07 0.04 19.85 0.04 001111
39 1039 167.955 57.502 0.00 9.99 0.00 9.99 20.44 0.05 20.51 0.06 20.56 0.08 20.33 0.08 001111
40 1040 170.836 58.538 0.00 9.99 0.00 9.99 20.44 0.05 20.52 0.06 20.56 0.08 20.33 0.08 001111
41 1041 525.110 58.058 0.00 9.99 0.00 9.99 21.93 0.06 21.70 0.05 21.48 0.05 21.35 0.06 001111
42 1042 166.230 59.921 0.00 9.99 0.00 9.99 20.44 0.05 20.51 0.06 20.50 0.09 20.33 0.08 001111
43 1043 112.343 60.052 0.00 9.99 0.00 9.99 21.70 0.08 21.72 0.08 21.44 0.08 21.00 0.08 001111
44 1044 305.707 60.538 0.00 9.99 99.99 -9.99 22.24 0.13 21.78 0.10 21.54 0.11 21.37 0.12 091111
45 1045 120.777 61.204 0.00 9.99 0.00 9.99 21.31 0.05 21.31 0.05 21.22 0.06 20.79 0.05 001111
46 1046 236.218 61.127 0.00 9.99 20.58 0.07 21.51 0.08 21.02 0.07 20.76 0.06 20.25 0.04 011111
47 1047 101.849 61.690 0.00 9.99 0.00 9.99 20.64 0.03 20.49 0.04 20.24 0.03 19.85 0.03 001111
48 1048 147.727 61.854 0.00 9.99 0.00 9.99 23.92 0.28 23.17 0.15 22.72 0.19 22.65 0.23 001111
49 1049 239.238 62.420 0.00 9.99 99.99 -9.99 21.32 0.06 21.02 0.07 20.46 0.05 20.25 0.04 091111
50 1050 333.120 61.344 0.00 9.99 99.99 -9.99 20.46 0.03 20.00 0.04 19.51 0.03 19.39 0.03 091111
51 1051 115.436 63.298 0.00 9.99 0.00 9.99 22.21 0.12 22.14 0.11 22.23 0.17 21.56 0.12 001111
52 1052 366.011 63.936 0.00 9.99 0.00 9.99 0.00 9.99 0.00 9.99 0.00 9.99 0.00 9.99 000000
53 1053 180.443 64.247 0.00 9.99 99.99 -9.99 21.19 0.06 21.33 0.07 21.29 0.09 21.10 0.10 091111
54 1054 186.320 65.387 0.00 9.99 99.99 -9.99 21.28 0.07 21.47 0.09 21.43 0.09 21.20 0.09 091111
55 1055 189.263 64.997 0.00 9.99 99.99 -9.99 21.30 0.07 21.47 0.09 21.43 0.09 21.20 0.09 091111
56 1056 295.339 65.924 0.00 9.99 99.99 -9.99 22.09 0.09 21.93 0.09 21.67 0.10 21.55 0.12 091111
57 1057 339.525 66.312 0.00 9.99 99.99 -9.99 20.46 0.03 21.16 0.07 21.28 0.12 20.65 0.09 091111
58 1058 704.435 65.891 0.00 9.99 0.00 9.99 20.96 0.02 19.69 0.03 18.78 0.02 18.27 0.01 001111
59 1059 120.354 66.506 0.00 9.99 0.00 9.99 21.88 0.10 21.91 0.10 21.62 0.09 21.33 0.10 001111
60 1060 205.697 67.172 0.00 9.99 99.99 -9.99 21.68 0.10 21.87 0.12 21.99 0.15 22.14 0.21 091111
61 1061 669.088 67.450 0.00 9.99 0.00 9.99 20.62 0.03 20.63 0.04 20.06 0.03 20.31 0.03 001111
62 1062 176.183 68.228 0.00 9.99 99.99 -9.99 21.54 0.14 21.65 0.18 20.87 0.09 21.02 0.11 091111
63 1063 525.031 69.065 0.00 9.99 0.00 9.99 20.53 0.03 20.47 0.04 20.24 0.04 19.76 0.03 001111
64 1064 346.036 70.244 0.00 9.99 99.99 -9.99 21.62 0.06 21.17 0.06 20.65 0.05 20.53 0.06 091111
65 1065 671.381 70.373 0.00 9.99 0.00 9.99 20.16 0.02 20.17 0.03 20.06 0.03 19.97 0.03 001111
66 1066 785.974 69.852 0.00 9.99 0.00 9.99 22.17 0.05 22.07 0.05 21.95 0.07 21.46 0.05 001111
67 1067 189.981 71.181 0.00 9.99 99.99 -9.99 21.49 0.09 21.62 0.10 21.47 0.09 21.34 0.11 091111
68 1068 346.184 71.762 0.00 9.99 99.99 -9.99 21.62 0.06 21.17 0.06 20.65 0.05 20.53 0.06 091111
69 1069 364.211 72.775 0.00 9.99 99.99 -9.99 22.45 0.13 22.28 0.13 21.46 0.09 22.18 0.23 091111
70 1070 668.342 73.060 0.00 9.99 0.00 9.99 20.16 0.02 20.17 0.03 20.06 0.03 19.97 0.03 001111
71 1071 242.968 73.628 0.00 9.99 99.99 -9.99 21.41 0.07 21.64 0.11 21.71 0.12 21.34 0.10 091111
72 1072 671.147 74.145 0.00 9.99 0.00 9.99 20.75 0.03 20.80 0.04 20.06 0.03 20.35 0.03 001111
73 1073 192.589 74.232 0.00 9.99 99.99 -9.99 21.43 0.09 21.42 0.09 20.94 0.06 21.08 0.09 091111
74 1074 186.513 75.468 0.00 9.99 99.99 -9.99 21.11 0.08 20.98 0.09 20.81 0.09 20.69 0.12 091111
75 1075 348.268 78.906 0.00 9.99 20.76 0.07 21.61 0.07 21.49 0.08 21.39 0.12 21.42 0.19 011111
76 1076 268.008 79.150 0.00 9.99 99.99 -9.99 21.96 0.06 21.47 0.05 21.11 0.05 20.68 0.04 091111
77 1077 386.075 80.239 0.00 9.99 99.99 -9.99 21.84 0.09 21.84 0.11 21.54 0.10 20.68 0.06 091111
78 1078 738.295 78.718 0.00 9.99 0.00 9.99 22.69 0.09 22.43 0.08 22.15 0.09 22.15 0.12 001111
79 1079 123.082 79.714 0.00 9.99 0.00 9.99 21.94 0.10 21.63 0.07 21.22 0.06 20.63 0.05 001111
80 1080 181.086 80.025 0.00 9.99 99.99 -9.99 21.07 0.11 21.04 0.13 20.94 0.14 20.61 0.13 091111
81 1081 346.778 78.771 0.00 9.99 20.76 0.07 21.61 0.07 21.49 0.08 21.39 0.12 21.42 0.19 011111
82 1082 366.021 80.299 0.00 9.99 99.99 -9.99 21.47 0.06 21.23 0.07 21.03 0.08 20.87 0.08 091111
83 1083 192.484 81.165 0.00 9.99 99.99 -9.99 21.35 0.10 21.49 0.12 21.64 0.15 21.34 0.15 091111
84 1084 384.795 80.218 0.00 9.99 99.99 -9.99 21.83 0.09 21.84 0.11 21.54 0.10 20.68 0.06 091111
85 1085 773.664 80.598 0.00 9.99 0.00 9.99 20.79 0.03 20.92 0.04 20.97 0.03 21.15 0.05 001111
86 1086 211.979 82.174 0.00 9.99 99.99 -9.99 20.99 0.05 21.03 0.06 21.15 0.07 20.67 0.06 091111
87 1087 778.906 81.590 0.00 9.99 0.00 9.99 21.71 0.04 21.76 0.05 20.97 0.03 22.12 0.10 001111
88 1088 353.643 82.627 0.00 9.99 99.99 -9.99 22.73 0.20 22.45 0.24 22.47 0.39 21.68 0.24 091111
89 1089 391.806 83.000 0.00 9.99 19.13 0.03 20.39 0.03 20.40 0.04 20.59 0.05 20.48 0.05 011111
90 1090 408.671 82.891 0.00 9.99 18.06 0.02 19.32 0.02 19.36 0.03 19.36 0.03 19.42 0.03 011111
91 1091 82.919 83.349 0.00 9.99 0.00 9.99 22.72 0.18 22.69 0.15 22.55 0.18 22.27 0.20 001111
92 1092 423.812 83.545 0.00 9.99 18.07 0.02 19.15 0.02 19.14 0.03 19.01 0.02 19.00 0.02 011111
93 1093 467.789 83.448 0.00 9.99 20.33 0.06 21.60 0.06 21.37 0.06 21.55 0.09 21.68 0.14 011111
94 1094 476.741 83.902 0.00 9.99 99.99 -9.99 22.85 0.17 22.57 0.16 22.66 0.26 22.12 0.19 091111
95 1095 405.152 84.295 0.00 9.99 99.99 -9.99 19.74 0.03 19.79 0.04 19.71 0.03 19.63 0.03 091111
96 1096 159.250 86.178 0.00 9.99 99.99 -9.99 19.94 0.02 19.05 0.03 18.27 0.02 18.06 0.01 091111
97 1097 212.126 85.818 0.00 9.99 99.99 -9.99 20.55 0.04 20.46 0.04 20.34 0.04 19.89 0.03 091111
98 1098 450.541 85.989 0.00 9.99 18.93 0.03 20.28 0.03 20.42 0.04 20.29 0.04 20.12 0.04 011111
99 1099 409.000 86.757 0.00 9.99 18.88 0.03 20.24 0.04 20.39 0.06 20.16 0.04 20.43 0.07 011111
100 1100 483.035 86.958 0.00 9.99 21.31 0.15 22.24 0.10 22.16 0.10 21.89 0.11 21.33 0.08 011111
101 1101 588.541 86.989 0.00 9.99 0.00 9.99 22.31 0.06 21.89 0.05 21.59 0.05 21.93 0.08 001111
102 1102 597.034 86.759 0.00 9.99 0.00 9.99 21.96 0.05 21.86 0.05 21.61 0.06 21.77 0.09 001111
103 1103 198.197 88.783 0.00 9.99 99.99 -9.99 17.02 0.02 17.46 0.03 17.22 0.02 16.98 0.01 091111
104 1104 458.209 88.552 0.00 9.99 17.94 0.02 19.24 0.02 19.20 0.03 19.04 0.02 18.95 0.01 011111
105 1105 209.861 88.742 0.00 9.99 99.99 -9.99 20.55 0.04 20.46 0.04 20.34 0.04 20.28 0.05 091111
106 1106 388.385 90.800 0.00 9.99 99.99 -9.99 21.84 0.14 21.88 0.16 22.01 0.18 21.84 0.20 091111
107 1107 399.189 88.331 0.00 9.99 17.93 0.02 19.31 0.02 19.45 0.03 19.50 0.03 19.47 0.02 011111
108 1108 729.687 88.669 0.00 9.99 0.00 9.99 22.01 0.05 21.69 0.05 21.87 0.06 21.55 0.06 001111
109 1109 223.098 89.655 0.00 9.99 99.99 -9.99 21.99 0.09 22.01 0.09 21.63 0.07 21.23 0.09 091111
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428 1428 558.318 386.355 0.00 9.99 99.99 -9.99 22.05 0.07 22.10 0.08 21.99 0.10 21.48 0.08 091111
429 1429 787.239 387.785 0.00 9.99 0.00 9.99 21.88 0.05 21.74 0.05 21.47 0.05 21.34 0.05 001111
430 1430 572.304 389.421 0.00 9.99 19.10 0.03 20.11 0.03 20.01 0.04 19.78 0.02 19.79 0.02 011111
431 1431 600.856 388.513 0.00 9.99 99.99 -9.99 23.57 0.13 22.49 0.05 22.00 0.05 21.65 0.05 091111
432 1432 740.053 388.987 0.00 9.99 99.99 -9.99 23.17 0.13 22.89 0.09 22.69 0.10 22.21 0.09 091111
433 1433 574.714 389.043 0.00 9.99 19.10 0.03 20.12 0.03 20.01 0.04 19.78 0.02 19.79 0.02 011111
434 1434 77.688 391.805 0.00 9.99 99.99 -9.99 22.33 0.06 22.30 0.05 22.21 0.07 22.00 0.08 091111
435 1435 554.757 392.964 0.00 9.99 99.99 -9.99 22.88 0.13 22.80 0.13 22.10 0.08 21.18 0.05 091111
436 1436 726.172 392.632 0.00 9.99 99.99 -9.99 23.09 0.10 23.11 0.09 22.77 0.09 22.06 0.08 091111
437 1437 541.099 393.613 0.00 9.99 99.99 -9.99 23.70 0.17 22.81 0.08 22.22 0.07 21.86 0.07 091111
438 1438 207.021 395.349 0.00 9.99 99.99 -9.99 23.07 0.09 22.82 0.06 22.81 0.08 22.55 0.09 091111
439 1439 693.810 395.236 0.00 9.99 99.99 -9.99 22.82 0.07 21.98 0.04 21.46 0.04 21.14 0.04 091111
440 1440 577.768 396.660 0.00 9.99 99.99 -9.99 21.32 0.06 21.21 0.06 20.99 0.06 20.87 0.05 091111
441 1441 564.649 399.310 0.00 9.99 18.86 0.03 20.15 0.03 20.21 0.04 20.18 0.03 20.07 0.03 011111
442 1442 338.775 400.490 0.00 9.99 99.99 -9.99 23.08 0.09 23.09 0.09 22.74 0.09 22.33 0.09 091111
443 1443 569.160 400.406 0.00 9.99 99.99 -9.99 21.84 0.09 22.08 0.10 21.65 0.07 22.24 0.16 091111
444 1444 582.837 401.940 0.00 9.99 19.75 0.05 21.02 0.05 21.89 0.09 21.32 0.06 21.21 0.07 011111
445 1445 580.811 402.288 0.00 9.99 19.75 0.05 21.02 0.05 21.89 0.09 21.32 0.06 21.21 0.07 011111
446 1446 584.695 402.582 0.00 9.99 19.75 0.05 21.02 0.05 21.89 0.09 21.32 0.06 21.21 0.07 011111
447 1447 771.187 403.004 0.00 9.99 0.00 9.99 22.06 0.05 21.97 0.05 21.57 0.04 21.63 0.04 001111
448 1448 608.346 403.752 0.00 9.99 99.99 -9.99 22.52 0.06 22.55 0.06 22.68 0.08 22.54 0.10 091111
449 1449 575.207 405.051 0.00 9.99 19.93 0.05 21.18 0.04 21.33 0.05 21.39 0.06 21.43 0.07 011111
450 1450 68.627 406.425 0.00 9.99 99.99 -9.99 22.92 0.12 22.36 0.07 22.05 0.06 21.62 0.06 091111
451 1451 566.511 405.532 0.00 9.99 99.99 -9.99 20.74 0.03 20.81 0.04 20.59 0.04 20.70 0.05 091111
452 1452 429.004 407.007 0.00 9.99 99.99 -9.99 23.04 0.08 22.83 0.07 22.67 0.08 22.32 0.09 091111
453 1453 74.312 408.103 0.00 9.99 99.99 -9.99 21.70 0.04 21.75 0.04 21.75 0.05 21.49 0.05 091111
454 1454 750.368 407.886 0.00 9.99 18.89 0.02 20.10 0.02 20.20 0.03 20.14 0.02 19.90 0.02 011111
455 1455 575.155 410.131 0.00 9.99 20.09 0.08 21.35 0.08 21.23 0.07 21.32 0.09 21.19 0.09 011111
456 1456 529.407 412.153 0.00 9.99 99.99 -9.99 23.74 0.19 23.45 0.14 23.51 0.22 23.45 0.25 091111
457 1457 343.549 416.367 0.00 9.99 99.99 -9.99 23.05 0.10 22.71 0.08 22.40 0.08 22.04 0.07 091111
458 1458 583.810 417.413 0.00 9.99 21.26 0.12 22.32 0.09 22.20 0.07 22.08 0.10 22.27 0.15 011111
459 1459 573.905 420.682 0.00 9.99 99.99 -9.99 21.12 0.03 21.16 0.04 21.04 0.04 21.21 0.06 091111
460 1460 708.407 421.076 0.00 9.99 99.99 -9.99 23.09 0.08 23.23 0.08 23.23 0.12 23.20 0.18 091111
461 1461 574.669 421.910 0.00 9.99 19.94 0.04 21.15 0.04 21.15 0.04 21.04 0.04 21.21 0.06 011111
462 1462 93.641 424.773 0.00 9.99 99.99 -9.99 22.79 0.08 22.41 0.05 21.93 0.05 21.47 0.04 091111
463 1463 583.625 425.486 0.00 9.99 99.99 -9.99 22.08 0.06 21.84 0.05 21.06 0.04 21.07 0.05 091111
464 1464 583.665 426.524 0.00 9.99 99.99 -9.99 22.09 0.06 21.84 0.05 21.06 0.04 21.07 0.05 091111
465 1465 131.027 428.645 0.00 9.99 99.99 -9.99 22.60 0.06 22.40 0.05 21.92 0.05 21.83 0.05 091111
466 1466 575.922 430.165 0.00 9.99 99.99 -9.99 22.66 0.09 22.47 0.07 22.19 0.06 21.93 0.08 091111
467 1467 591.644 431.560 0.00 9.99 99.99 -9.99 22.11 0.06 22.04 0.05 21.80 0.05 21.88 0.07 091111
468 1468 602.371 435.672 0.00 9.99 99.99 -9.99 22.31 0.06 22.29 0.05 22.23 0.06 21.97 0.07 091111
469 1469 164.477 447.565 0.00 9.99 99.99 -9.99 22.40 0.06 22.28 0.05 21.82 0.04 21.74 0.05 091111
470 1470 600.978 447.663 0.00 9.99 99.99 -9.99 22.42 0.07 22.01 0.05 21.73 0.05 21.59 0.06 091111
471 1471 583.941 451.530 0.00 9.99 99.99 -9.99 22.91 0.08 22.79 0.07 22.56 0.07 22.16 0.08 091111
472 1472 607.492 453.791 0.00 9.99 19.88 0.03 20.83 0.03 20.77 0.03 20.58 0.03 20.15 0.02 011111
473 1473 613.518 453.901 0.00 9.99 18.57 0.02 19.63 0.02 19.60 0.03 19.42 0.02 18.97 0.01 011111
474 1474 568.311 457.146 0.00 9.99 99.99 -9.99 23.11 0.10 22.88 0.07 22.54 0.08 21.35 0.04 091111
475 1475 677.263 459.161 0.00 9.99 99.99 -9.99 21.80 0.04 21.87 0.04 21.47 0.03 21.73 0.05 091111
476 1476 80.880 462.483 0.00 9.99 99.99 -9.99 22.19 0.05 22.31 0.06 21.75 0.05 22.52 0.12 091111
477 1477 573.105 466.017 0.00 9.99 99.99 -9.99 22.61 0.06 22.69 0.06 22.68 0.08 22.43 0.10 091111
478 1478 561.298 470.198 0.00 9.99 99.99 -9.99 22.50 0.07 22.58 0.07 22.64 0.09 22.76 0.12 091111
479 1479 54.251 471.523 0.00 9.99 99.99 -9.99 22.19 0.09 21.48 0.10 20.59 0.06 20.64 0.09 091111
480 1480 762.296 472.885 0.00 9.99 99.99 -9.99 22.60 0.06 21.74 0.04 21.23 0.03 20.99 0.03 091111
481 1481 619.964 477.800 0.00 9.99 99.99 -9.99 23.13 0.09 22.95 0.08 22.69 0.09 22.33 0.09 091111
482 1482 110.818 479.012 0.00 9.99 99.99 -9.99 21.69 0.03 21.74 0.04 21.67 0.04 21.34 0.04 091111
483 1483 677.965 481.104 0.00 9.99 99.99 -9.99 22.47 0.06 22.52 0.06 22.71 0.08 22.88 0.14 091111
484 1484 614.170 481.829 0.00 9.99 99.99 -9.99 22.61 0.06 22.02 0.04 21.49 0.04 21.02 0.03 091111
485 1485 676.112 481.294 0.00 9.99 99.99 -9.99 22.47 0.06 22.52 0.06 22.71 0.08 22.88 0.14 091111
486 1486 656.304 487.128 0.00 9.99 99.99 -9.99 22.96 0.08 23.05 0.07 23.01 0.09 22.99 0.14 091111
487 1487 577.481 489.622 0.00 9.99 99.99 -9.99 22.03 0.04 21.71 0.04 21.36 0.03 21.13 0.03 091111
488 1488 640.808 489.188 0.00 9.99 99.99 -9.99 22.08 0.04 22.25 0.05 22.54 0.06 22.39 0.08 091111
489 1489 621.604 490.109 0.00 9.99 99.99 -9.99 22.58 0.07 22.13 0.05 21.45 0.04 21.05 0.03 091111
490 1490 569.109 490.439 0.00 9.99 99.99 -9.99 23.08 0.12 22.57 0.07 22.28 0.07 22.01 0.07 091111
491 1491 673.196 490.984 0.00 9.99 99.99 -9.99 22.10 0.05 22.67 0.06 22.22 0.06 22.37 0.08 091111
492 1492 584.576 501.115 0.00 9.99 99.99 -9.99 22.30 0.06 22.22 0.05 22.15 0.06 21.51 0.05 091111
493 1493 208.900 503.134 0.00 9.99 99.99 -9.99 21.81 0.04 21.77 0.04 20.81 0.03 21.77 0.05 091111
494 1494 265.427 506.604 0.00 9.99 99.99 -9.99 21.96 0.04 21.88 0.04 21.72 0.04 21.53 0.04 091111
495 1495 94.427 508.649 0.00 9.99 99.99 -9.99 23.12 0.10 22.98 0.08 22.65 0.08 22.21 0.09 091111
496 1496 279.016 513.754 0.00 9.99 99.99 -9.99 21.58 0.04 21.52 0.04 21.40 0.04 20.95 0.03 091111
497 1497 106.812 515.020 0.00 9.99 99.99 -9.99 21.76 0.04 21.60 0.04 21.42 0.03 21.09 0.04 091111
498 1498 284.425 517.005 0.00 9.99 99.99 -9.99 21.96 0.04 21.66 0.04 21.32 0.03 21.05 0.03 091111
499 1499 280.813 521.272 0.00 9.99 99.99 -9.99 21.98 0.05 21.94 0.04 21.95 0.05 21.37 0.04 091111
500 1500 778.926 523.741 0.00 9.99 99.99 -9.99 22.47 0.05 22.37 0.05 22.16 0.04 21.87 0.05 091111
501 1501 355.119 533.099 0.00 9.99 99.99 -9.99 24.07 0.20 22.92 0.06 22.26 0.05 21.89 0.05 091111
502 1502 270.240 534.588 0.00 9.99 99.99 -9.99 23.11 0.09 22.98 0.07 22.83 0.08 22.70 0.10 091111
503 1503 333.068 545.974 0.00 9.99 99.99 -9.99 22.30 0.05 22.30 0.05 22.22 0.05 22.20 0.07 091111
504 1504 756.161 548.588 0.00 9.99 99.99 -9.99 22.65 0.06 22.66 0.06 22.61 0.07 22.50 0.10 091111
505 1505 619.495 549.322 0.00 9.99 99.99 -9.99 23.42 0.10 23.28 0.07 22.78 0.07 22.87 0.11 091111
506 1506 190.048 555.667 0.00 9.99 99.99 -9.99 22.71 0.07 22.55 0.06 22.42 0.06 22.29 0.08 091111
507 1507 356.846 557.002 0.00 9.99 99.99 -9.99 23.07 0.09 23.03 0.07 22.77 0.07 22.68 0.10 091111
508 1508 281.730 560.533 0.00 9.99 99.99 -9.99 22.96 0.09 23.02 0.08 23.05 0.11 22.69 0.11 091111
509 1509 794.213 567.502 0.00 9.99 0.00 9.99 22.24 0.05 21.96 0.04 21.60 0.04 21.15 0.04 001111
510 1510 241.093 568.960 0.00 9.99 99.99 -9.99 21.68 0.03 21.51 0.04 21.23 0.03 20.75 0.02 091111
511 1511 483.708 568.902 0.00 9.99 99.99 -9.99 23.07 0.08 22.90 0.06 22.55 0.06 22.25 0.06 091111
512 1512 693.710 574.871 0.00 9.99 99.99 -9.99 22.87 0.08 22.57 0.05 22.40 0.05 22.22 0.08 091111
513 1513 794.071 578.376 0.00 9.99 0.00 9.99 23.29 0.14 23.29 0.11 23.47 0.20 23.94 0.51 001111
514 1514 784.719 591.197 0.00 9.99 0.00 9.99 21.91 0.04 21.85 0.04 21.65 0.04 21.40 0.03 001111
515 1515 286.385 594.533 0.00 9.99 20.52 0.05 21.45 0.03 21.31 0.04 21.06 0.03 21.00 0.03 011111
516 1516 378.652 596.342 0.00 9.99 99.99 -9.99 22.73 0.07 22.71 0.06 22.41 0.06 22.06 0.06 091111
517 1517 692.201 596.785 0.00 9.99 99.99 -9.99 22.67 0.07 22.00 0.04 21.65 0.03 21.41 0.04 091111
518 1518 742.849 598.391 0.00 9.99 0.00 9.99 22.72 0.06 22.53 0.05 22.25 0.05 21.87 0.05 001111
519 1519 349.408 599.087 0.00 9.99 99.99 -9.99 22.17 0.05 22.07 0.04 21.73 0.04 21.24 0.03 091111
520 1520 677.031 602.605 0.00 9.99 99.99 -9.99 22.53 0.06 22.55 0.05 22.42 0.06 22.47 0.08 091111
521 1521 356.900 602.607 0.00 9.99 99.99 -9.99 23.81 0.16 23.69 0.12 23.31 0.12 23.07 0.13 091111
522 1522 371.832 628.318 0.00 9.99 99.99 -9.99 22.14 0.05 22.00 0.04 21.87 0.04 21.70 0.05 091111
523 1523 116.305 629.372 0.00 9.99 99.99 -9.99 23.48 0.15 23.36 0.13 22.67 0.09 22.41 0.11 091111
524 1524 413.275 630.313 0.00 9.99 99.99 -9.99 22.59 0.06 21.74 0.04 21.00 0.03 21.01 0.03 091111
525 1525 429.057 629.706 0.00 9.99 99.99 -9.99 22.32 0.05 22.38 0.05 22.24 0.05 21.91 0.05 091111
526 1526 381.028 641.851 0.00 9.99 99.99 -9.99 22.30 0.05 22.26 0.05 22.06 0.05 21.89 0.06 091111
527 1527 254.082 646.700 0.00 9.99 99.99 -9.99 22.89 0.08 22.69 0.06 22.77 0.07 22.53 0.09 091111
528 1528 299.524 647.450 0.00 9.99 99.99 -9.99 22.20 0.05 22.02 0.05 21.83 0.04 21.66 0.05 091111
529 1529 330.648 656.099 0.00 9.99 99.99 -9.99 22.56 0.06 22.49 0.05 22.36 0.06 22.38 0.08 091111
530 1530 84.115 657.317 0.00 9.99 99.99 -9.99 21.19 0.03 21.09 0.04 20.80 0.03 20.62 0.03 091111
531 1531 113.040 656.399 0.00 9.99 99.99 -9.99 22.58 0.07 22.35 0.05 22.05 0.06 21.76 0.07 091111
532 1532 294.015 657.809 0.00 9.99 99.99 -9.99 22.33 0.05 22.24 0.05 22.15 0.05 22.12 0.08 091111
533 1533 400.417 658.118 0.00 9.99 99.99 -9.99 22.66 0.07 22.58 0.06 22.43 0.06 22.00 0.07 091111
534 1534 328.081 665.089 0.00 9.99 99.99 -9.99 23.34 0.11 23.46 0.11 23.56 0.18 23.09 0.16 091111
535 1535 399.068 679.284 0.00 9.99 99.99 -9.99 21.98 0.04 21.85 0.04 21.61 0.04 21.30 0.04 091111
536 1536 117.021 696.737 0.00 9.99 99.99 -9.99 21.63 0.04 21.44 0.04 21.13 0.03 20.74 0.03 091111
537 1537 111.042 708.182 0.00 9.99 99.99 -9.99 22.93 0.11 22.57 0.10 22.32 0.09 21.80 0.08 091111
538 1538 134.911 717.622 0.00 9.99 99.99 -9.99 22.78 0.09 22.73 0.08 22.66 0.10 22.31 0.11 091111
539 1539 224.082 717.442 0.00 9.99 99.99 -9.99 22.36 0.05 22.05 0.05 21.89 0.04 21.61 0.05 091111
540 1540 308.373 721.547 0.00 9.99 99.99 -9.99 21.41 0.03 21.17 0.04 20.87 0.03 20.64 0.03 091111
541 1541 652.167 720.258 0.00 9.99 0.00 9.99 23.61 0.13 22.79 0.05 22.26 0.05 22.03 0.05 001111
542 1542 103.527 735.360 0.00 9.99 99.99 -9.99 23.55 0.14 23.16 0.12 22.31 0.08 23.23 0.25 091111
543 1543 432.117 735.118 0.00 9.99 99.99 -9.99 22.90 0.08 22.93 0.08 22.77 0.09 22.64 0.12 091111
544 1544 607.231 738.921 0.00 9.99 0.00 9.99 21.26 0.03 21.22 0.04 21.07 0.03 20.70 0.03 001111
545 1545 601.138 741.525 0.00 9.99 0.00 9.99 19.80 0.02 19.74 0.03 19.53 0.02 19.20 0.01 001111
546 1546 486.824 744.689 0.00 9.99 99.99 -9.99 22.62 0.06 22.51 0.05 22.30 0.06 21.85 0.06 091111
547 1547 79.173 758.036 0.00 9.99 0.00 9.99 23.41 0.18 22.99 0.13 22.60 0.14 22.43 0.15 001111
548 1548 183.112 768.732 0.00 9.99 99.99 -9.99 23.31 0.17 22.86 0.12 22.57 0.13 22.37 0.14 091111
549 1549 188.603 769.760 0.00 9.99 99.99 -9.99 22.86 0.10 22.66 0.10 22.45 0.11 22.48 0.13 091111
550 1550 92.636 771.057 0.00 9.99 0.00 9.99 23.15 0.14 22.88 0.11 22.04 0.07 22.17 0.10 001111
551 1551 450.931 775.354 0.00 9.99 99.99 -9.99 22.27 0.06 22.14 0.06 21.86 0.05 21.51 0.05 091111
552 1552 193.780 777.790 0.00 9.99 99.99 -9.99 21.82 0.04 21.10 0.04 20.60 0.03 20.36 0.02 091111
553 1553 190.247 779.389 0.00 9.99 99.99 -9.99 21.78 0.04 21.45 0.04 21.20 0.04 21.04 0.04 091111
554 1554 205.240 780.272 0.00 9.99 99.99 -9.99 23.46 0.16 22.17 0.05 21.63 0.05 21.27 0.04 091111
555 1555 540.705 796.984 0.00 9.99 0.00 9.99 23.28 0.18 22.90 0.21 23.40 0.23 22.78 0.17 001111
556 2001 191.725 39.718 0.00 9.99 0.00 9.99 20.91 0.12 19.61 0.05 20.29 0.18 99.99 -9.99 001119
557 2003 207.260 44.400 0.00 9.99 99.99 -9.99 18.71 0.02 18.78 0.04 18.59 0.04 99.99 -9.99 091119
558 2005 195.225 49.074 0.00 9.99 18.79 0.03 20.87 0.04 20.30 0.04 20.01 0.03 99.99 -9.99 011119
559 2007 213.963 50.610 0.00 9.99 99.99 -9.99 22.25 0.09 22.33 0.11 21.82 0.13 99.99 -9.99 091119
560 2008 198.511 52.734 0.00 9.99 99.99 -9.99 20.36 0.03 20.30 0.04 20.01 0.03 99.99 -9.99 091119
561 2013 787.242 59.741 0.00 9.99 0.00 9.99 22.97 0.10 22.85 0.08 22.61 0.10 99.99 -9.99 001119
562 2015 236.292 61.166 0.00 9.99 20.58 0.07 21.53 0.08 21.01 0.05 20.80 0.06 99.99 -9.99 011119
563 2016 293.684 62.570 0.00 9.99 99.99 -9.99 22.30 0.10 22.11 0.10 22.13 0.14 99.99 -9.99 091119
564 2017 188.961 64.985 0.00 9.99 99.99 -9.99 21.58 0.10 21.83 0.13 21.57 0.11 99.99 -9.99 091119
565 2019 540.953 68.418 0.00 9.99 0.00 9.99 22.45 0.10 21.75 0.06 21.94 0.11 99.99 -9.99 001119
566 2023 347.951 79.284 0.00 9.99 20.76 0.07 21.85 0.08 21.79 0.12 21.46 0.16 99.99 -9.99 011119
567 2024 385.095 79.916 0.00 9.99 99.99 -9.99 21.99 0.09 22.06 0.10 21.65 0.08 99.99 -9.99 091119
568 2026 778.882 81.427 0.00 9.99 0.00 9.99 20.80 0.03 20.98 0.04 20.98 0.03 99.99 -9.99 001119
569 2027 394.191 84.468 0.00 9.99 19.13 0.03 20.36 0.03 20.61 0.04 20.56 0.03 99.99 -9.99 011119
570 2029 483.056 86.934 0.00 9.99 21.31 0.15 22.42 0.12 22.26 0.09 21.93 0.11 99.99 -9.99 011119
571 2030 193.553 88.581 0.00 9.99 15.88 0.02 17.03 0.02 17.52 0.03 17.21 0.02 99.99 -9.99 011119
572 2035 189.493 94.219 0.00 9.99 15.88 0.02 17.03 0.02 17.52 0.03 17.21 0.02 99.99 -9.99 011119
573 2036 104.463 94.127 0.00 9.99 0.00 9.99 22.48 0.12 22.53 0.12 22.27 0.11 99.99 -9.99 001119
574 2037 139.203 95.932 0.00 9.99 99.99 -9.99 22.39 0.11 22.46 0.12 21.70 0.08 99.99 -9.99 091119
575 2038 391.481 94.591 0.00 9.99 20.34 0.10 21.42 0.08 21.37 0.09 21.48 0.11 99.99 -9.99 011119
576 2040 292.400 96.467 0.00 9.99 99.99 -9.99 23.12 0.11 22.77 0.11 22.48 0.14 99.99 -9.99 091119
577 2042 494.850 97.992 0.00 9.99 17.48 0.02 18.92 0.02 19.08 0.03 18.69 0.02 99.99 -9.99 011119
578 2043 130.798 98.891 0.00 9.99 99.99 -9.99 21.88 0.08 22.16 0.10 22.02 0.11 99.99 -9.99 091119
579 2046 453.130 100.285 0.00 9.99 21.33 0.16 22.66 0.15 22.87 0.17 22.65 0.20 99.99 -9.99 011119
580 2047 414.876 102.298 0.00 9.99 18.07 0.02 19.33 0.03 20.23 0.07 20.26 0.05 99.99 -9.99 011119
581 2048 448.130 103.276 0.00 9.99 20.01 0.05 21.22 0.05 21.31 0.05 21.37 0.06 99.99 -9.99 011119
582 2049 406.016 103.548 0.00 9.99 18.07 0.02 19.33 0.03 19.35 0.04 19.21 0.03 99.99 -9.99 011119
583 2052 286.040 108.788 0.00 9.99 99.99 -9.99 23.08 0.14 23.22 0.15 22.93 0.17 99.99 -9.99 091119
584 2053 143.525 110.868 0.00 9.99 99.99 -9.99 22.55 0.12 22.53 0.10 22.49 0.17 99.99 -9.99 091119
585 2054 426.402 110.319 0.00 9.99 19.98 0.07 21.46 0.08 21.61 0.08 21.69 0.13 99.99 -9.99 011119
586 2055 349.419 113.489 0.00 9.99 99.99 -9.99 21.97 0.06 21.51 0.05 21.09 0.05 99.99 -9.99 091119
587 2058 404.706 115.327 0.00 9.99 20.13 0.08 21.57 0.10 21.66 0.11 21.52 0.14 99.99 -9.99 011119
588 2059 424.022 114.720 0.00 9.99 16.50 0.02 17.51 0.02 17.63 0.03 17.33 0.02 99.99 -9.99 011119
589 2062 388.805 123.669 0.00 9.99 99.99 -9.99 22.36 0.13 22.18 0.11 21.99 0.16 99.99 -9.99 091119
590 2063 158.887 126.317 0.00 9.99 99.99 -9.99 22.24 0.11 22.21 0.11 22.08 0.15 99.99 -9.99 091119
591 2064 305.644 126.717 0.00 9.99 99.99 -9.99 23.17 0.15 23.31 0.17 22.58 0.15 99.99 -9.99 091119
592 2066 474.234 125.668 0.00 9.99 20.05 0.06 21.28 0.05 21.23 0.06 20.81 0.06 99.99 -9.99 011119
593 2068 468.594 125.989 0.00 9.99 99.99 -9.99 21.85 0.11 21.25 0.06 21.47 0.10 99.99 -9.99 091119
594 2069 151.309 127.938 0.00 9.99 20.52 0.06 21.52 0.05 21.34 0.05 20.93 0.05 99.99 -9.99 011119
595 2073 161.170 131.454 0.00 9.99 99.99 -9.99 21.83 0.08 22.04 0.13 21.60 0.10 99.99 -9.99 091119
596 2075 376.920 134.378 0.00 9.99 99.99 -9.99 22.41 0.09 22.37 0.10 22.24 0.13 99.99 -9.99 091119
597 2077 165.460 133.908 0.00 9.99 99.99 -9.99 22.10 0.08 22.11 0.09 21.97 0.14 99.99 -9.99 091119
598 2078 310.281 134.889 0.00 9.99 99.99 -9.99 22.21 0.06 22.04 0.05 21.58 0.07 99.99 -9.99 091119
599 2079 379.342 139.608 0.00 9.99 99.99 -9.99 22.35 0.06 22.26 0.07 21.71 0.06 99.99 -9.99 091119
600 2080 581.277 146.574 0.00 9.99 0.00 9.99 22.58 0.11 22.62 0.13 21.41 0.06 99.99 -9.99 001119
601 2081 563.052 148.677 0.00 9.99 99.99 -9.99 22.22 0.09 22.25 0.11 22.24 0.17 99.99 -9.99 091119
602 2082 148.023 149.684 0.00 9.99 99.99 -9.99 23.15 0.15 23.35 0.17 23.19 0.19 99.99 -9.99 091119
603 2083 169.135 149.575 0.00 9.99 99.99 -9.99 21.85 0.06 21.94 0.08 21.19 0.09 99.99 -9.99 091119
604 2084 764.724 154.427 0.00 9.99 0.00 9.99 21.32 0.05 21.17 0.05 20.44 0.05 99.99 -9.99 001119
605 2087 241.037 178.739 0.00 9.99 19.17 0.04 20.50 0.06 20.03 0.04 20.40 0.07 99.99 -9.99 011119
606 2088 638.398 182.929 0.00 9.99 0.00 9.99 23.48 0.15 23.28 0.11 23.38 0.17 99.99 -9.99 001119
607 2091 558.473 203.885 0.00 9.99 99.99 -9.99 22.61 0.07 22.77 0.09 22.80 0.17 99.99 -9.99 091119
608 2092 125.056 213.875 0.00 9.99 99.99 -9.99 23.39 0.19 23.28 0.15 23.21 0.19 99.99 -9.99 091119
609 2093 664.617 213.141 0.00 9.99 0.00 9.99 22.57 0.08 21.29 0.04 20.84 0.03 99.99 -9.99 001119
610 2094 139.945 217.994 0.00 9.99 99.99 -9.99 22.63 0.09 22.72 0.08 22.48 0.09 99.99 -9.99 091119
611 2095 293.363 218.359 0.00 9.99 99.99 -9.99 23.15 0.14 22.83 0.11 22.52 0.11 99.99 -9.99 091119
612 2096 696.593 218.428 0.00 9.99 0.00 9.99 23.01 0.09 22.34 0.05 21.82 0.04 99.99 -9.99 001119
613 2097 168.077 222.960 0.00 9.99 99.99 -9.99 22.32 0.08 22.39 0.09 22.25 0.09 99.99 -9.99 091119
614 2099 275.565 229.883 0.00 9.99 99.99 -9.99 22.24 0.05 22.05 0.05 21.88 0.07 99.99 -9.99 091119
615 2100 219.325 232.792 0.00 9.99 99.99 -9.99 22.81 0.09 22.83 0.09 22.81 0.12 99.99 -9.99 091119
616 2101 690.322 235.533 0.00 9.99 0.00 9.99 23.39 0.13 23.27 0.12 23.20 0.16 99.99 -9.99 001119
617 2102 412.326 243.561 0.00 9.99 99.99 -9.99 22.54 0.08 22.22 0.07 21.68 0.07 99.99 -9.99 091119
618 2104 141.199 254.152 0.00 9.99 99.99 -9.99 23.42 0.19 23.15 0.12 23.02 0.17 99.99 -9.99 091119
619 2105 295.125 253.615 0.00 9.99 99.99 -9.99 23.15 0.14 23.16 0.13 22.84 0.15 99.99 -9.99 091119
620 2106 585.300 254.149 0.00 9.99 99.99 -9.99 23.09 0.16 23.19 0.18 22.80 0.18 99.99 -9.99 091119
621 2109 701.345 261.524 0.00 9.99 0.00 9.99 21.64 0.04 21.49 0.05 21.02 0.05 99.99 -9.99 001119
622 2113 642.761 295.684 0.00 9.99 99.99 -9.99 21.70 0.06 21.89 0.07 21.39 0.09 99.99 -9.99 091119
623 2114 781.920 298.601 0.00 9.99 0.00 9.99 21.23 0.03 20.90 0.03 19.53 0.02 99.99 -9.99 001119
624 2115 374.024 302.674 0.00 9.99 99.99 -9.99 22.56 0.11 22.62 0.13 22.39 0.16 99.99 -9.99 091119
625 2117 344.436 306.309 0.00 9.99 99.99 -9.99 22.69 0.09 22.78 0.11 21.61 0.06 99.99 -9.99 091119
626 2119 372.441 308.898 0.00 9.99 99.99 -9.99 22.22 0.07 22.14 0.08 21.85 0.09 99.99 -9.99 091119
627 2120 531.124 315.122 0.00 9.99 99.99 -9.99 22.77 0.12 22.89 0.16 22.80 0.19 99.99 -9.99 091119
628 2121 110.674 316.445 0.00 9.99 99.99 -9.99 23.07 0.10 23.23 0.09 23.23 0.14 99.99 -9.99 091119
629 2123 653.436 316.168 0.00 9.99 99.99 -9.99 21.89 0.06 21.58 0.05 21.23 0.05 99.99 -9.99 091119
630 2124 671.436 319.543 0.00 9.99 99.99 -9.99 22.36 0.06 22.36 0.07 21.96 0.06 99.99 -9.99 091119
631 2125 69.990 324.321 0.00 9.99 99.99 -9.99 22.98 0.11 23.07 0.12 22.61 0.09 99.99 -9.99 091119
632 2126 103.311 326.203 0.00 9.99 99.99 -9.99 23.48 0.12 23.67 0.11 23.44 0.14 99.99 -9.99 091119
633 2128 522.515 329.313 0.00 9.99 99.99 -9.99 20.39 0.03 20.31 0.04 20.01 0.03 99.99 -9.99 091119
634 2129 627.281 331.272 0.00 9.99 99.99 -9.99 22.10 0.06 21.51 0.04 22.05 0.07 99.99 -9.99 091119
635 2134 429.915 368.082 0.00 9.99 99.99 -9.99 22.47 0.08 22.57 0.10 22.23 0.12 99.99 -9.99 091119
636 2136 422.994 370.288 0.00 9.99 99.99 -9.99 22.34 0.07 22.31 0.08 22.03 0.09 99.99 -9.99 091119
637 2137 428.915 373.280 0.00 9.99 99.99 -9.99 23.04 0.14 22.92 0.13 22.70 0.17 99.99 -9.99 091119
638 2138 763.401 380.570 0.00 9.99 0.00 9.99 21.64 0.04 21.56 0.04 20.82 0.03 99.99 -9.99 001119
639 2139 558.459 386.504 0.00 9.99 99.99 -9.99 22.19 0.07 22.45 0.08 22.14 0.08 99.99 -9.99 091119
640 2140 77.927 387.649 0.00 9.99 99.99 -9.99 22.65 0.09 22.67 0.09 22.89 0.14 99.99 -9.99 091119
641 2141 735.327 389.035 0.00 9.99 99.99 -9.99 23.25 0.14 23.35 0.10 23.08 0.11 99.99 -9.99 091119
642 2142 405.318 391.936 0.00 9.99 99.99 -9.99 23.35 0.11 23.37 0.10 23.11 0.13 99.99 -9.99 091119
643 2143 64.533 397.287 0.00 9.99 99.99 -9.99 22.73 0.09 22.75 0.08 22.68 0.12 99.99 -9.99 091119
644 2144 76.297 395.499 0.00 9.99 99.99 -9.99 22.39 0.07 22.50 0.08 22.85 0.12 99.99 -9.99 091119
645 2146 64.388 396.236 0.00 9.99 99.99 -9.99 22.71 0.09 22.76 0.08 22.66 0.12 99.99 -9.99 091119
646 2147 699.038 397.055 0.00 9.99 99.99 -9.99 22.48 0.06 22.57 0.06 22.54 0.09 99.99 -9.99 091119
647 2149 574.550 421.590 0.00 9.99 19.94 0.04 21.20 0.04 21.31 0.05 21.19 0.05 99.99 -9.99 011119
648 2150 659.331 431.846 0.00 9.99 99.99 -9.99 23.08 0.08 22.93 0.06 22.79 0.08 99.99 -9.99 091119
649 2151 165.742 447.270 0.00 9.99 99.99 -9.99 22.36 0.05 22.31 0.05 21.76 0.04 99.99 -9.99 091119
650 2152 165.108 447.619 0.00 9.99 99.99 -9.99 22.38 0.05 22.31 0.05 21.76 0.04 99.99 -9.99 091119
651 2153 543.975 463.884 0.00 9.99 99.99 -9.99 23.36 0.11 23.19 0.08 22.83 0.09 99.99 -9.99 091119
652 2154 615.180 490.618 0.00 9.99 99.99 -9.99 22.84 0.08 22.85 0.09 22.28 0.08 99.99 -9.99 091119
653 2155 627.507 498.859 0.00 9.99 99.99 -9.99 23.22 0.12 23.08 0.09 23.29 0.16 99.99 -9.99 091119
654 2156 634.673 500.907 0.00 9.99 99.99 -9.99 23.24 0.11 23.26 0.08 22.98 0.11 99.99 -9.99 091119
655 2157 365.699 508.740 0.00 9.99 99.99 -9.99 22.86 0.08 23.15 0.08 22.73 0.07 99.99 -9.99 091119
656 2158 215.571 518.575 0.00 9.99 99.99 -9.99 21.94 0.04 22.04 0.04 21.94 0.05 99.99 -9.99 091119
657 2159 750.015 549.377 0.00 9.99 99.99 -9.99 23.72 0.17 23.41 0.12 22.91 0.10 99.99 -9.99 091119
658 2160 693.675 574.964 0.00 9.99 99.99 -9.99 22.95 0.09 22.66 0.06 22.44 0.06 99.99 -9.99 091119
659 2161 397.200 589.510 0.00 9.99 99.99 -9.99 23.00 0.08 22.94 0.06 23.45 0.13 99.99 -9.99 091119
660 2163 265.637 599.170 0.00 9.99 99.99 -9.99 23.10 0.09 23.08 0.07 22.91 0.09 99.99 -9.99 091119
661 2164 383.590 638.152 0.00 9.99 99.99 -9.99 22.98 0.10 23.52 0.14 23.61 0.16 99.99 -9.99 091119
662 2165 399.244 680.139 0.00 9.99 21.11 0.07 21.97 0.04 21.94 0.04 21.60 0.04 99.99 -9.99 011119
663 2166 476.093 709.264 0.00 9.99 99.99 -9.99 23.54 0.13 23.49 0.09 23.47 0.13 99.99 -9.99 091119
664 2168 177.466 739.666 0.00 9.99 99.99 -9.99 23.14 0.14 23.07 0.11 22.95 0.15 99.99 -9.99 091119
665 2169 141.720 746.099 0.00 9.99 99.99 -9.99 22.84 0.09 23.08 0.08 22.84 0.09 99.99 -9.99 091119
666 2170 182.887 746.890 0.00 9.99 99.99 -9.99 22.48 0.06 22.21 0.05 22.51 0.08 99.99 -9.99 091119
667 2171 422.010 755.157 0.00 9.99 99.99 -9.99 23.44 0.17 23.46 0.14 23.20 0.14 99.99 -9.99 091119
668 2172 465.286 755.062 0.00 9.99 99.99 -9.99 22.27 0.05 22.33 0.05 22.17 0.06 99.99 -9.99 091119
669 3057 786.075 69.995 0.00 9.99 0.00 9.99 99.99 -9.99 22.31 0.05 21.92 0.05 21.50 0.05 009111
670 3063 186.756 75.080 0.00 9.99 99.99 -9.99 99.99 -9.99 21.10 0.06 20.79 0.05 20.72 0.07 099111
671 3064 342.793 76.268 0.00 9.99 99.99 -9.99 99.99 -9.99 21.12 0.07 21.10 0.11 20.84 0.11 099111
672 3071 147.880 80.387 0.00 9.99 99.99 -9.99 99.99 -9.99 21.97 0.08 21.38 0.07 21.49 0.10 099111
673 3073 773.783 80.484 0.00 9.99 0.00 9.99 99.99 -9.99 20.98 0.04 20.98 0.03 21.13 0.04 009111
674 3074 423.992 83.424 0.00 9.99 18.07 0.02 99.99 -9.99 19.20 0.03 19.01 0.02 19.01 0.02 019111
675 3075 394.610 84.231 0.00 9.99 99.99 -9.99 99.99 -9.99 20.61 0.04 20.56 0.03 20.53 0.05 099111
676 3076 159.617 86.250 0.00 9.99 99.99 -9.99 99.99 -9.99 19.11 0.03 18.25 0.02 18.07 0.01 099111
677 3077 450.666 85.986 0.00 9.99 18.93 0.03 99.99 -9.99 20.47 0.04 20.28 0.04 20.06 0.03 019111
678 3078 588.801 86.906 0.00 9.99 0.00 9.99 99.99 -9.99 21.93 0.06 21.53 0.06 21.83 0.12 009111
679 3079 458.568 88.719 0.00 9.99 17.94 0.02 99.99 -9.99 19.26 0.03 19.04 0.02 18.97 0.01 019111
680 3082 583.138 93.717 0.00 9.99 0.00 9.99 99.99 -9.99 19.99 0.03 19.66 0.02 19.22 0.01 009111
681 3083 118.589 95.417 0.00 9.99 0.00 9.99 99.99 -9.99 21.90 0.09 21.46 0.08 21.05 0.08 009111
682 3085 239.431 97.636 0.00 9.99 99.99 -9.99 99.99 -9.99 22.05 0.13 21.57 0.10 20.98 0.08 099111
683 3086 351.064 97.557 0.00 9.99 18.76 0.02 99.99 -9.99 18.90 0.03 18.38 0.02 18.19 0.01 019111
684 3088 411.197 100.692 0.00 9.99 19.05 0.05 99.99 -9.99 20.39 0.07 20.25 0.05 19.95 0.04 019111
685 3092 405.891 104.326 0.00 9.99 18.07 0.02 99.99 -9.99 19.35 0.04 19.21 0.03 19.07 0.03 019111
686 3098 411.168 105.771 0.00 9.99 18.07 0.02 99.99 -9.99 19.35 0.04 19.21 0.03 19.07 0.03 019111
687 3099 198.325 106.783 0.00 9.99 99.99 -9.99 99.99 -9.99 21.73 0.15 20.95 0.11 20.96 0.12 099111
688 3102 426.865 108.712 0.00 9.99 19.98 0.07 99.99 -9.99 21.65 0.08 21.72 0.13 21.96 0.17 019111
689 3103 473.227 109.490 0.00 9.99 19.86 0.04 99.99 -9.99 20.92 0.05 20.80 0.04 20.64 0.05 019111
690 3105 426.056 109.546 0.00 9.99 19.98 0.07 99.99 -9.99 21.61 0.08 21.69 0.13 21.95 0.17 019111
691 3111 437.354 119.007 0.00 9.99 20.61 0.10 99.99 -9.99 21.75 0.08 21.84 0.09 21.97 0.16 019111
692 3114 437.032 119.426 0.00 9.99 20.61 0.10 99.99 -9.99 21.75 0.08 21.84 0.09 21.97 0.16 019111
693 3116 662.671 119.739 0.00 9.99 0.00 9.99 99.99 -9.99 22.70 0.09 22.21 0.08 21.97 0.09 009111
694 3117 416.674 120.525 0.00 9.99 16.50 0.02 99.99 -9.99 20.47 0.05 17.33 0.02 19.90 0.04 019111
695 3118 466.371 121.412 0.00 9.99 99.99 -9.99 99.99 -9.99 21.19 0.06 21.29 0.07 21.04 0.07 099111
696 3120 517.112 123.075 0.00 9.99 99.99 -9.99 99.99 -9.99 22.93 0.14 22.50 0.13 21.89 0.12 099111
697 3121 440.818 124.797 0.00 9.99 20.79 0.14 99.99 -9.99 22.09 0.10 21.73 0.10 21.67 0.14 019111
698 3122 465.491 124.071 0.00 9.99 99.99 -9.99 99.99 -9.99 21.25 0.06 21.29 0.07 21.04 0.07 099111
699 3124 407.128 125.122 0.00 9.99 99.99 -9.99 99.99 -9.99 21.69 0.09 21.41 0.08 21.10 0.09 099111
700 3131 193.724 133.594 0.00 9.99 99.99 -9.99 99.99 -9.99 22.36 0.05 21.88 0.08 21.57 0.07 099111
701 3133 662.772 132.407 0.00 9.99 0.00 9.99 99.99 -9.99 22.68 0.09 22.48 0.11 22.39 0.14 009111
702 3134 162.160 132.573 0.00 9.99 99.99 -9.99 99.99 -9.99 21.97 0.11 21.60 0.10 21.00 0.06 099111
703 3136 499.093 133.520 0.00 9.99 99.99 -9.99 99.99 -9.99 22.81 0.08 22.74 0.11 22.64 0.16 099111
704 3137 430.548 135.423 0.00 9.99 19.62 0.04 99.99 -9.99 21.26 0.07 20.99 0.06 21.38 0.11 019111
705 3138 306.500 135.586 0.00 9.99 99.99 -9.99 99.99 -9.99 22.59 0.12 22.24 0.16 21.94 0.13 099111
706 3141 318.137 137.793 0.00 9.99 19.94 0.03 99.99 -9.99 21.23 0.04 20.88 0.04 21.18 0.06 019111
707 3144 443.346 140.092 0.00 9.99 99.99 -9.99 99.99 -9.99 21.20 0.07 20.47 0.04 20.36 0.04 099111
708 3146 144.016 142.781 0.00 9.99 99.99 -9.99 99.99 -9.99 22.02 0.07 21.76 0.07 21.19 0.05 099111
709 3147 442.854 141.020 0.00 9.99 99.99 -9.99 99.99 -9.99 21.20 0.07 20.47 0.04 20.50 0.04 099111
710 3149 764.284 141.686 0.00 9.99 0.00 9.99 99.99 -9.99 22.61 0.09 21.72 0.07 21.56 0.07 009111
711 3151 472.053 143.729 0.00 9.99 99.99 -9.99 99.99 -9.99 22.11 0.08 21.68 0.09 21.55 0.09 099111
712 3152 182.359 145.464 0.00 9.99 99.99 -9.99 99.99 -9.99 21.17 0.05 21.08 0.05 20.85 0.05 099111
713 3153 463.769 144.695 0.00 9.99 99.99 -9.99 99.99 -9.99 22.93 0.17 22.50 0.17 22.02 0.15 099111
714 3159 563.719 148.727 0.00 9.99 99.99 -9.99 99.99 -9.99 22.25 0.11 22.24 0.17 21.84 0.16 099111
715 3160 253.495 150.355 0.00 9.99 99.99 -9.99 99.99 -9.99 22.58 0.07 21.60 0.06 21.21 0.06 099111
716 3162 625.847 151.020 0.00 9.99 0.00 9.99 99.99 -9.99 21.57 0.04 20.43 0.03 19.50 0.02 009111
717 3164 564.867 150.841 0.00 9.99 99.99 -9.99 99.99 -9.99 22.24 0.11 22.24 0.17 21.80 0.14 099111
718 3167 76.884 153.926 0.00 9.99 99.99 -9.99 99.99 -9.99 21.55 0.04 21.14 0.04 20.71 0.03 099111
719 3168 600.230 155.234 0.00 9.99 0.00 9.99 99.99 -9.99 22.86 0.15 22.35 0.14 21.77 0.13 009111
720 3170 267.730 155.296 0.00 9.99 99.99 -9.99 99.99 -9.99 22.68 0.07 22.09 0.08 21.79 0.09 099111
721 3171 361.304 157.029 0.00 9.99 99.99 -9.99 99.99 -9.99 22.73 0.07 21.96 0.06 21.61 0.06 099111
722 3172 587.162 156.919 0.00 9.99 0.00 9.99 99.99 -9.99 18.48 0.03 17.98 0.02 17.42 0.01 009111
723 3173 712.477 158.412 0.00 9.99 0.00 9.99 99.99 -9.99 22.38 0.06 21.83 0.05 21.80 0.07 009111
724 3174 763.076 157.516 0.00 9.99 0.00 9.99 99.99 -9.99 21.17 0.05 20.46 0.05 20.60 0.05 009111
725 3176 478.373 161.316 0.00 9.99 99.99 -9.99 99.99 -9.99 21.55 0.05 21.73 0.08 21.09 0.07 099111
726 3177 185.996 160.586 0.00 9.99 99.99 -9.99 99.99 -9.99 21.88 0.08 21.30 0.06 21.08 0.08 099111
727 3178 444.636 161.591 0.00 9.99 99.99 -9.99 99.99 -9.99 22.25 0.07 21.81 0.07 21.48 0.06 099111
728 3182 598.917 162.759 0.00 9.99 0.00 9.99 99.99 -9.99 22.55 0.11 21.83 0.11 21.25 0.10 009111
729 3185 600.409 167.101 0.00 9.99 0.00 9.99 99.99 -9.99 22.61 0.06 21.77 0.07 21.42 0.06 009111
730 3188 761.007 167.444 0.00 9.99 0.00 9.99 99.99 -9.99 19.16 0.03 18.64 0.02 18.59 0.01 009111
731 3191 223.006 169.180 0.00 9.99 16.46 0.02 99.99 -9.99 17.92 0.03 17.70 0.02 17.68 0.01 019111
732 3192 469.369 171.041 0.00 9.99 99.99 -9.99 99.99 -9.99 22.14 0.09 22.13 0.12 22.03 0.19 099111
733 3193 478.644 171.151 0.00 9.99 18.87 0.02 99.99 -9.99 19.70 0.03 19.29 0.02 19.09 0.01 019111
734 3194 125.701 174.253 0.00 9.99 99.99 -9.99 99.99 -9.99 22.14 0.05 21.59 0.05 21.39 0.05 099111
735 3196 733.236 175.105 0.00 9.99 0.00 9.99 99.99 -9.99 22.90 0.09 22.30 0.09 21.90 0.09 009111
736 3198 471.303 179.697 0.00 9.99 99.99 -9.99 99.99 -9.99 22.86 0.11 22.57 0.14 22.21 0.15 099111
737 3201 237.947 182.077 0.00 9.99 18.81 0.03 99.99 -9.99 20.03 0.04 19.75 0.03 19.51 0.02 019111
738 3202 757.904 184.616 0.00 9.99 0.00 9.99 99.99 -9.99 21.97 0.05 21.24 0.05 21.05 0.04 009111
739 3203 326.695 186.159 0.00 9.99 99.99 -9.99 99.99 -9.99 21.43 0.05 20.90 0.04 20.72 0.04 099111
740 3204 693.765 185.835 0.00 9.99 0.00 9.99 99.99 -9.99 22.70 0.06 22.62 0.08 22.03 0.09 009111
741 3206 93.841 187.162 0.00 9.99 99.99 -9.99 99.99 -9.99 20.56 0.04 20.28 0.02 19.96 0.02 099111
742 3211 536.134 196.881 0.00 9.99 99.99 -9.99 99.99 -9.99 21.47 0.04 20.96 0.03 20.62 0.03 099111
743 3212 616.556 196.556 0.00 9.99 0.00 9.99 99.99 -9.99 22.97 0.08 22.19 0.06 21.82 0.07 009111
744 3213 242.471 199.162 0.00 9.99 19.80 0.04 99.99 -9.99 20.90 0.05 20.80 0.05 20.49 0.06 019111
745 3215 265.802 199.730 0.00 9.99 99.99 -9.99 99.99 -9.99 22.30 0.13 22.39 0.17 22.20 0.17 099111
746 3216 183.926 201.785 0.00 9.99 20.60 0.05 99.99 -9.99 22.08 0.07 22.61 0.17 21.81 0.13 019111
747 3218 404.075 202.950 0.00 9.99 99.99 -9.99 99.99 -9.99 22.31 0.05 21.61 0.04 21.63 0.05 099111
748 3219 744.730 203.583 0.00 9.99 0.00 9.99 99.99 -9.99 22.09 0.05 21.65 0.06 21.41 0.05 009111
749 3222 756.556 203.072 0.00 9.99 0.00 9.99 99.99 -9.99 22.57 0.07 22.55 0.13 22.31 0.13 009111
750 3223 401.872 204.899 0.00 9.99 99.99 -9.99 99.99 -9.99 22.50 0.05 21.61 0.04 21.63 0.05 099111
751 3226 700.812 207.074 0.00 9.99 0.00 9.99 99.99 -9.99 22.89 0.08 21.98 0.06 21.45 0.05 009111
752 3227 245.891 208.370 0.00 9.99 18.61 0.02 99.99 -9.99 19.78 0.03 19.53 0.02 19.08 0.02 019111
753 3228 177.438 208.920 0.00 9.99 99.99 -9.99 99.99 -9.99 22.53 0.10 22.11 0.08 21.83 0.09 099111
754 3230 724.677 209.583 0.00 9.99 0.00 9.99 99.99 -9.99 22.30 0.07 21.94 0.07 21.62 0.06 009111
755 3232 249.493 210.361 0.00 9.99 18.61 0.02 99.99 -9.99 19.78 0.03 19.53 0.02 19.08 0.02 019111
756 3233 546.863 213.163 0.00 9.99 99.99 -9.99 99.99 -9.99 22.70 0.08 21.42 0.04 22.11 0.11 099111
757 3234 183.718 212.644 0.00 9.99 99.99 -9.99 99.99 -9.99 22.24 0.07 22.10 0.09 21.93 0.11 099111
758 3237 242.951 214.657 0.00 9.99 99.99 -9.99 99.99 -9.99 22.06 0.11 21.70 0.09 21.68 0.13 099111
759 3239 659.935 214.262 0.00 9.99 0.00 9.99 99.99 -9.99 21.29 0.04 20.84 0.03 20.70 0.03 009111
760 3241 384.122 216.068 0.00 9.99 99.99 -9.99 99.99 -9.99 22.56 0.08 22.10 0.10 21.96 0.11 099111
761 3242 491.924 215.358 0.00 9.99 99.99 -9.99 99.99 -9.99 21.52 0.05 21.20 0.05 20.99 0.05 099111
762 3244 293.593 217.401 0.00 9.99 99.99 -9.99 99.99 -9.99 22.87 0.11 22.52 0.11 22.33 0.13 099111
763 3245 695.860 218.065 0.00 9.99 0.00 9.99 99.99 -9.99 22.34 0.05 21.82 0.04 21.61 0.05 009111
764 3246 770.931 218.883 0.00 9.99 0.00 9.99 99.99 -9.99 22.85 0.10 22.63 0.14 22.36 0.14 009111
765 3251 550.552 225.627 0.00 9.99 99.99 -9.99 99.99 -9.99 22.80 0.10 21.80 0.07 22.40 0.15 099111
766 3254 487.843 226.080 0.00 9.99 99.99 -9.99 99.99 -9.99 22.37 0.07 21.72 0.05 21.47 0.06 099111
767 3256 562.795 229.845 0.00 9.99 99.99 -9.99 99.99 -9.99 22.11 0.06 21.31 0.04 21.04 0.05 099111
768 3260 189.251 232.807 0.00 9.99 99.99 -9.99 99.99 -9.99 22.59 0.07 22.04 0.08 21.45 0.06 099111
769 3264 369.385 237.791 0.00 9.99 99.99 -9.99 99.99 -9.99 22.19 0.06 21.80 0.06 21.77 0.09 099111
770 3265 148.631 238.327 0.00 9.99 99.99 -9.99 99.99 -9.99 22.77 0.14 22.10 0.10 21.33 0.06 099111
771 3273 411.627 243.288 0.00 9.99 99.99 -9.99 99.99 -9.99 22.21 0.07 21.68 0.07 21.62 0.08 099111
772 3275 523.201 245.754 0.00 9.99 99.99 -9.99 99.99 -9.99 22.37 0.06 21.90 0.08 21.62 0.08 099111
773 3278 384.815 248.267 0.00 9.99 99.99 -9.99 99.99 -9.99 22.68 0.11 22.23 0.10 22.01 0.11 099111
774 3283 702.988 256.921 0.00 9.99 0.00 9.99 99.99 -9.99 20.91 0.04 20.17 0.02 19.72 0.02 009111
775 3289 572.429 262.411 0.00 9.99 99.99 -9.99 99.99 -9.99 21.51 0.04 20.93 0.04 20.93 0.04 099111
776 3291 121.744 265.527 0.00 9.99 99.99 -9.99 99.99 -9.99 20.88 0.03 20.64 0.03 20.91 0.03 099111
777 3292 274.665 263.570 0.00 9.99 99.99 -9.99 99.99 -9.99 21.60 0.05 21.29 0.05 20.90 0.04 099111
778 3295 257.840 265.301 0.00 9.99 99.99 -9.99 99.99 -9.99 22.48 0.06 22.24 0.08 21.98 0.09 099111
779 3296 85.481 266.093 0.00 9.99 99.99 -9.99 99.99 -9.99 22.47 0.05 22.31 0.06 22.15 0.07 099111
780 3297 396.279 266.193 0.00 9.99 99.99 -9.99 99.99 -9.99 22.73 0.08 22.03 0.06 21.98 0.09 099111
781 3298 416.842 266.281 0.00 9.99 99.99 -9.99 99.99 -9.99 22.98 0.08 22.63 0.09 22.55 0.15 099111
782 3302 668.334 268.700 0.00 9.99 0.00 9.99 99.99 -9.99 22.36 0.08 22.13 0.10 22.05 0.13 009111
783 3303 698.190 268.797 0.00 9.99 0.00 9.99 99.99 -9.99 22.73 0.07 22.19 0.07 22.86 0.19 009111
784 3305 349.508 274.424 0.00 9.99 99.99 -9.99 99.99 -9.99 22.29 0.09 22.08 0.09 21.71 0.08 099111
785 3306 483.675 275.599 0.00 9.99 99.99 -9.99 99.99 -9.99 22.23 0.07 21.61 0.05 21.49 0.06 099111
786 3307 623.115 278.435 0.00 9.99 99.99 -9.99 99.99 -9.99 22.02 0.07 21.49 0.07 20.94 0.05 099111
787 3308 625.659 279.119 0.00 9.99 99.99 -9.99 99.99 -9.99 22.03 0.07 21.48 0.06 20.93 0.05 099111
788 3310 615.923 283.795 0.00 9.99 99.99 -9.99 99.99 -9.99 22.57 0.09 21.87 0.08 21.46 0.07 099111
789 3311 654.863 284.668 0.00 9.99 99.99 -9.99 99.99 -9.99 22.18 0.06 21.02 0.06 21.15 0.09 099111
790 3314 647.496 286.718 0.00 9.99 99.99 -9.99 99.99 -9.99 22.04 0.11 21.57 0.14 21.46 0.19 099111
791 3316 251.600 289.114 0.00 9.99 99.99 -9.99 99.99 -9.99 22.89 0.09 21.87 0.06 21.61 0.07 099111
792 3318 654.968 288.543 0.00 9.99 99.99 -9.99 99.99 -9.99 22.27 0.06 20.96 0.04 21.13 0.08 099111
793 3319 788.855 290.080 0.00 9.99 0.00 9.99 99.99 -9.99 22.44 0.07 20.63 0.03 22.35 0.15 009111
794 3324 669.764 294.361 0.00 9.99 99.99 -9.99 99.99 -9.99 22.71 0.08 21.91 0.08 21.58 0.07 099111
795 3325 240.653 296.905 0.00 9.99 99.99 -9.99 99.99 -9.99 21.37 0.04 21.08 0.03 21.03 0.04 099111
796 3327 66.729 300.317 0.00 9.99 99.99 -9.99 99.99 -9.99 22.52 0.07 22.43 0.07 22.26 0.09 099111
797 3332 520.967 312.596 0.00 9.99 99.99 -9.99 99.99 -9.99 22.10 0.06 21.46 0.07 21.47 0.09 099111
798 3333 67.570 314.602 0.00 9.99 99.99 -9.99 99.99 -9.99 20.53 0.03 20.22 0.02 19.91 0.02 099111
799 3338 517.465 315.865 0.00 9.99 99.99 -9.99 99.99 -9.99 22.11 0.11 21.52 0.11 21.96 0.19 099111
800 3339 673.144 316.398 0.00 9.99 99.99 -9.99 99.99 -9.99 21.89 0.05 22.20 0.10 21.88 0.10 099111
801 3342 660.244 318.597 0.00 9.99 18.97 0.02 99.99 -9.99 19.80 0.03 19.54 0.02 19.29 0.02 019111
802 3346 526.747 322.633 0.00 9.99 20.09 0.05 99.99 -9.99 20.82 0.04 20.40 0.04 20.12 0.03 019111
803 3349 522.864 329.922 0.00 9.99 99.99 -9.99 99.99 -9.99 20.37 0.04 20.01 0.03 20.10 0.03 099111
804 3350 516.043 329.142 0.00 9.99 18.85 0.03 99.99 -9.99 19.98 0.04 19.86 0.03 19.85 0.03 019111
805 3352 521.050 331.682 0.00 9.99 99.99 -9.99 99.99 -9.99 20.32 0.04 20.01 0.03 20.13 0.03 099111
806 3356 83.825 342.383 0.00 9.99 99.99 -9.99 99.99 -9.99 21.68 0.04 21.27 0.04 20.81 0.03 099111
807 3358 526.122 346.925 0.00 9.99 99.99 -9.99 99.99 -9.99 21.55 0.08 21.27 0.08 21.10 0.08 099111
808 3361 511.814 350.526 0.00 9.99 17.52 0.02 99.99 -9.99 18.09 0.03 17.67 0.02 20.68 0.07 019111
809 3367 528.884 355.226 0.00 9.99 99.99 -9.99 99.99 -9.99 22.53 0.14 21.94 0.13 21.79 0.14 099111
810 3369 514.940 356.607 0.00 9.99 99.99 -9.99 99.99 -9.99 21.89 0.05 21.20 0.05 20.86 0.05 099111
811 3371 535.451 363.758 0.00 9.99 99.99 -9.99 99.99 -9.99 21.43 0.05 21.74 0.07 21.54 0.07 099111
812 3373 421.161 369.810 0.00 9.99 99.99 -9.99 99.99 -9.99 22.40 0.09 22.01 0.09 22.24 0.15 099111
813 3380 760.960 378.426 0.00 9.99 0.00 9.99 99.99 -9.99 21.27 0.04 20.82 0.03 20.41 0.02 009111
814 3382 77.735 381.935 0.00 9.99 99.99 -9.99 99.99 -9.99 21.30 0.04 20.81 0.03 20.28 0.02 099111
815 3384 557.089 383.877 0.00 9.99 99.99 -9.99 99.99 -9.99 22.35 0.08 22.20 0.09 21.58 0.07 099111
816 3386 558.841 386.148 0.00 9.99 99.99 -9.99 99.99 -9.99 22.43 0.08 22.14 0.08 21.58 0.07 099111
817 3391 555.272 392.308 0.00 9.99 21.54 0.13 99.99 -9.99 22.87 0.19 22.12 0.13 21.28 0.09 019111
818 3392 562.751 393.559 0.00 9.99 99.99 -9.99 99.99 -9.99 21.23 0.05 21.13 0.06 20.61 0.04 099111
819 3393 562.667 393.148 0.00 9.99 99.99 -9.99 99.99 -9.99 21.20 0.05 21.13 0.06 20.61 0.04 099111
820 3395 693.694 395.132 0.00 9.99 99.99 -9.99 99.99 -9.99 22.05 0.04 21.50 0.04 21.14 0.03 099111
821 3397 64.819 396.520 0.00 9.99 99.99 -9.99 99.99 -9.99 22.75 0.08 22.68 0.12 22.44 0.13 099111
822 3402 65.737 399.040 0.00 9.99 99.99 -9.99 99.99 -9.99 22.75 0.08 22.68 0.12 22.49 0.14 099111
823 3404 583.411 400.841 0.00 9.99 99.99 -9.99 99.99 -9.99 21.94 0.07 21.34 0.07 21.31 0.08 099111
824 3406 580.906 402.229 0.00 9.99 99.99 -9.99 99.99 -9.99 21.79 0.08 21.38 0.07 21.31 0.08 099111
825 3407 776.334 404.832 0.00 9.99 0.00 9.99 99.99 -9.99 22.52 0.06 22.35 0.07 22.00 0.07 009111
826 3411 107.215 408.869 0.00 9.99 99.99 -9.99 99.99 -9.99 22.94 0.08 22.74 0.09 22.92 0.16 099111
827 3415 343.478 416.871 0.00 9.99 99.99 -9.99 99.99 -9.99 22.81 0.07 22.31 0.07 22.01 0.06 099111
828 3417 177.953 417.540 0.00 9.99 99.99 -9.99 99.99 -9.99 22.91 0.07 22.72 0.08 22.52 0.10 099111
829 3419 578.659 422.064 0.00 9.99 19.94 0.04 99.99 -9.99 21.45 0.05 21.09 0.05 21.25 0.07 019111
830 3420 92.317 426.676 0.00 9.99 99.99 -9.99 99.99 -9.99 22.47 0.05 21.92 0.04 21.43 0.04 099111
831 3424 766.451 433.663 0.00 9.99 99.99 -9.99 99.99 -9.99 22.51 0.05 22.20 0.05 21.78 0.05 099111
832 3430 583.974 451.190 0.00 9.99 99.99 -9.99 99.99 -9.99 22.91 0.06 22.57 0.07 22.19 0.09 099111
833 3431 74.747 454.029 0.00 9.99 99.99 -9.99 99.99 -9.99 22.67 0.06 22.12 0.05 21.47 0.04 099111
834 3434 679.091 461.621 0.00 9.99 20.30 0.04 99.99 -9.99 21.89 0.04 21.43 0.03 22.08 0.06 019111
835 3438 54.720 471.494 0.00 9.99 99.99 -9.99 99.99 -9.99 21.55 0.10 20.88 0.03 20.69 0.10 099111
836 3440 762.278 473.001 0.00 9.99 99.99 -9.99 99.99 -9.99 21.80 0.04 21.24 0.03 20.99 0.03 099111
837 3446 577.110 489.525 0.00 9.99 99.99 -9.99 99.99 -9.99 21.77 0.04 21.33 0.03 21.10 0.03 099111
838 3447 621.659 490.239 0.00 9.99 99.99 -9.99 99.99 -9.99 22.24 0.05 21.47 0.04 21.08 0.04 099111
839 3451 527.801 499.113 0.00 9.99 99.99 -9.99 99.99 -9.99 22.90 0.05 22.45 0.05 22.29 0.07 099111
840 3453 584.541 501.005 0.00 9.99 99.99 -9.99 99.99 -9.99 22.38 0.06 22.23 0.07 21.65 0.06 099111
841 3456 660.710 504.099 0.00 9.99 99.99 -9.99 99.99 -9.99 22.81 0.05 22.32 0.06 22.94 0.12 099111
842 3457 265.742 506.331 0.00 9.99 99.99 -9.99 99.99 -9.99 21.98 0.04 21.74 0.04 21.58 0.04 099111
843 3459 684.418 506.969 0.00 9.99 99.99 -9.99 99.99 -9.99 22.80 0.05 22.08 0.05 22.05 0.06 099111
844 3460 94.534 508.788 0.00 9.99 99.99 -9.99 99.99 -9.99 22.96 0.06 22.58 0.07 22.24 0.09 099111
845 3464 284.742 516.575 0.00 9.99 99.99 -9.99 99.99 -9.99 21.74 0.04 21.38 0.04 21.09 0.04 099111
846 3465 697.507 517.887 0.00 9.99 99.99 -9.99 99.99 -9.99 22.94 0.07 22.59 0.07 22.71 0.10 099111
847 3467 280.469 521.160 0.00 9.99 99.99 -9.99 99.99 -9.99 21.98 0.05 21.91 0.06 21.41 0.05 099111
848 3468 283.989 524.166 0.00 9.99 99.99 -9.99 99.99 -9.99 22.14 0.05 22.21 0.08 21.70 0.07 099111
849 3471 107.178 528.285 0.00 9.99 99.99 -9.99 99.99 -9.99 22.98 0.09 22.66 0.09 22.39 0.12 099111
850 3474 160.962 530.828 0.00 9.99 99.99 -9.99 99.99 -9.99 22.92 0.06 22.54 0.06 22.24 0.07 099111
851 3478 355.771 532.929 0.00 9.99 99.99 -9.99 99.99 -9.99 22.97 0.06 22.17 0.05 21.83 0.05 099111
852 3479 270.686 534.886 0.00 9.99 99.99 -9.99 99.99 -9.99 23.00 0.06 22.83 0.07 22.60 0.09 099111
853 3483 756.344 548.441 0.00 9.99 99.99 -9.99 99.99 -9.99 22.74 0.06 22.65 0.07 22.50 0.09 099111
854 3488 189.590 565.543 0.00 9.99 99.99 -9.99 99.99 -9.99 22.85 0.07 22.16 0.05 21.65 0.05 099111
855 3489 483.678 568.473 0.00 9.99 99.99 -9.99 99.99 -9.99 22.98 0.06 22.51 0.06 22.29 0.06 099111
856 3492 693.770 574.488 0.00 9.99 99.99 -9.99 99.99 -9.99 22.67 0.06 22.44 0.06 22.21 0.06 099111
857 3498 554.105 584.408 0.00 9.99 99.99 -9.99 99.99 -9.99 22.37 0.05 21.55 0.03 21.01 0.03 099111
858 3499 78.325 588.904 0.00 9.99 99.99 -9.99 99.99 -9.99 22.58 0.06 22.09 0.05 21.95 0.07 099111
859 3501 378.933 596.287 0.00 9.99 99.99 -9.99 99.99 -9.99 22.76 0.06 22.37 0.06 22.01 0.06 099111
860 3504 677.184 602.218 0.00 9.99 99.99 -9.99 99.99 -9.99 22.62 0.05 22.45 0.06 22.60 0.10 099111
861 3506 167.631 609.193 0.00 9.99 99.99 -9.99 99.99 -9.99 22.95 0.07 22.79 0.08 22.48 0.10 099111
862 3510 413.802 630.151 0.00 9.99 99.99 -9.99 99.99 -9.99 21.77 0.04 20.97 0.03 21.03 0.03 099111
863 3512 254.244 647.120 0.00 9.99 99.99 -9.99 99.99 -9.99 22.73 0.06 22.73 0.08 22.64 0.11 099111
864 3513 776.356 647.286 0.00 9.99 0.00 9.99 99.99 -9.99 22.71 0.05 21.74 0.03 22.00 0.05 009111
865 3514 645.371 649.398 0.00 9.99 0.00 9.99 99.99 -9.99 22.75 0.05 22.43 0.06 22.15 0.07 009111
866 3518 113.300 656.633 0.00 9.99 99.99 -9.99 99.99 -9.99 22.40 0.06 22.06 0.06 21.66 0.05 099111
867 3519 330.494 655.928 0.00 9.99 99.99 -9.99 99.99 -9.99 22.57 0.05 22.37 0.06 22.49 0.09 099111
868 3521 115.587 657.942 0.00 9.99 99.99 -9.99 99.99 -9.99 22.40 0.06 22.05 0.06 21.64 0.05 099111
869 3527 117.695 696.573 0.00 9.99 99.99 -9.99 99.99 -9.99 21.48 0.04 21.10 0.03 20.72 0.03 099111
870 3528 571.378 698.581 0.00 9.99 99.99 -9.99 99.99 -9.99 22.84 0.06 22.77 0.08 22.49 0.09 099111
871 3531 66.218 702.070 0.00 9.99 99.99 -9.99 99.99 -9.99 22.67 0.08 21.75 0.05 21.57 0.06 099111
872 3532 72.336 705.016 0.00 9.99 99.99 -9.99 99.99 -9.99 22.85 0.08 21.67 0.04 22.73 0.16 099111
873 3536 490.174 710.649 0.00 9.99 99.99 -9.99 99.99 -9.99 22.36 0.05 21.71 0.04 21.26 0.03 099111
874 3537 135.139 717.314 0.00 9.99 99.99 -9.99 99.99 -9.99 22.87 0.09 22.78 0.11 22.43 0.11 099111
875 3538 652.532 720.315 0.00 9.99 0.00 9.99 99.99 -9.99 22.87 0.06 22.24 0.05 22.06 0.06 009111
876 3539 308.584 721.434 0.00 9.99 99.99 -9.99 99.99 -9.99 21.21 0.04 20.84 0.03 20.63 0.03 099111
877 3553 465.446 754.750 0.00 9.99 99.99 -9.99 99.99 -9.99 22.33 0.05 22.17 0.06 22.12 0.07 099111
878 3554 79.770 757.472 0.00 9.99 0.00 9.99 99.99 -9.99 22.80 0.09 22.56 0.12 22.33 0.14 009111
879 3563 92.888 770.598 0.00 9.99 0.00 9.99 99.99 -9.99 22.98 0.12 22.07 0.07 22.08 0.09 009111
880 3565 497.280 773.707 0.00 9.99 0.00 9.99 99.99 -9.99 22.94 0.08 21.90 0.05 21.49 0.05 009111
881 3570 197.398 793.743 0.00 9.99 99.99 -9.99 99.99 -9.99 22.97 0.09 22.31 0.10 21.99 0.10 099111

Photometry and coordinates by Nate Bastian, Oct 2001




  Table 5: Coordinates and HST-WFPC2 narrow-band $H\alpha$ and [OIII] photometry
of 114 sources in the inner regions of the M51.


Explanations of the columns:
(1) : id-nr of $H\alpha$ sources
(2) : corresponding number in the table of broadband photometry
(3) : x-coordinate of $H\alpha$ source on HST-WF2-chip
(4) : y-coordinate of $H\alpha$ source on HST-WF2-chip
pixel (x=1,y=1) is RA(2000) 13h 29 m 55.90 s,    DEC(2000) = +47 degr 11 min 27.2 sec
pixel (x=800, y=800) is RA(2000) 13h 29 m 57.94 s,    DEC(2000) = +47 degr 13 min 16.6 sec
(5) and (6) : magnitude and uncertainty of F656N filter ($H\alpha$)
(7) and (8) : magnitude and uncertainty of F502N filter ([OIII])
(9) and (10): magnitude and uncertainty of F814W broadband filter
(11) : ch = indication of position-overlap of $H\alpha$ source and F814W-source
ch=1 or 2: position overlap is okay ( $\Delta x<1.5$ and $\Delta y<1.5$ pixels)
ch=0: positioin overlap is suspect = ( $1.5<\Delta x<2.0$ or $1.5<\Delta y<2.0$ pixels)
(12) : co = indication of position-overlap of [OIII]-source and F814W source
co=2: position overlap is okay ( $\Delta x<1.5$ and $\Delta y<1.5$ pixels)
co=0: position overlap is suspect = ( $1.5<\Delta x<2.0$ or $1.5<\Delta y<2.0$ pixels)
 

i
i x y mag $\Delta$mag mag $\Delta$mag mag $\Delta$mag ch co
        F656N F656N F502N F502N F814W F814W    
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12)

1
3 205.734 39.004 17.42 0.06 0.00 -9.99 18.52 0.04 2 2
2 23 198.238 48.140 18.81 0.10 20.32 0.08 19.97 0.03 2 2
3 29 323.266 50.958 18.63 0.07 0.00 -9.99 21.21 0.11 0 0
4 36 332.184 58.848 17.46 0.04 0.00 -9.99 19.88 0.04 2 2
5 46 236.283 61.998 18.49 0.03 0.00 -9.99 20.75 0.06 2 2
6 64 346.368 70.546 18.37 0.06 0.00 -9.99 20.64 0.05 2 2
7 69 365.066 72.801 18.02 0.04 0.00 -9.99 21.45 0.09 2 2
8 73 191.900 74.562 20.90 0.34 0.00 -9.99 20.93 0.06 0 0
9 78 739.484 78.126 19.94 0.09 0.00 -9.99 22.14 0.09 2 2
10 82 366.854 80.942 19.94 0.26 0.00 -9.99 21.02 0.08 2 2
11 86 211.518 81.431 20.74 0.23 0.00 -9.99 21.14 0.07 2 2
12 89 391.984 84.434 20.47 0.28 20.98 0.14 20.58 0.05 2 2
13 90 409.678 83.898 17.48 0.03 0.00 -9.99 19.35 0.03 2 2
14 92 424.573 84.913 18.09 0.05 0.00 -9.99 19.00 0.02 2 2
15 95 405.611 85.742 19.37 0.32 19.63 0.05 19.70 0.03 2 2
16 97 211.500 85.842 20.64 0.22 0.00 -9.99 20.33 0.04 1 1
17 101 588.464 87.906 19.38 0.06 0.00 -9.99 21.58 0.05 2 2
18 104 458.625 89.786 18.25 0.04 0.00 -9.99 19.03 0.02 2 2
19 114 597.938 92.990 19.11 0.05 0.00 -9.99 21.20 0.05 2 2
20 115 193.332 92.727 16.76 0.01 17.36 0.01 17.21 0.02 2 2
21 123 347.589 96.067 17.96 0.04 0.00 -9.99 18.38 0.02 2 2
22 124 494.469 95.977 16.02 0.01 0.00 -9.99 18.69 0.02 2 2
23 125 265.415 96.590 20.12 0.09 21.33 0.17 20.32 0.03 2 2
24 126 216.358 97.176 18.23 0.03 18.65 0.02 18.23 0.02 2 2
25 128 406.709 98.486 18.96 0.07 0.00 -9.99 20.07 0.04 1 1
26 138 411.013 102.215 20.05 0.21 20.60 0.14 20.17 0.04 2 2
27 146 397.815 107.243 20.90 0.37 0.00 -9.99 21.57 0.18 2 2
28 147 411.708 106.580 19.17 0.09 19.74 0.06 19.15 0.02 2 2
29 150 244.717 109.584 19.94 0.08 20.83 0.10 19.65 0.03 2 2
30 152 473.422 110.659 19.74 0.14 0.00 -9.99 20.82 0.04 2 2
31 157 526.143 112.444 19.35 0.08 0.00 -9.99 20.56 0.04 2 2
32 160 414.819 115.533 17.02 0.01 0.00 -9.99 17.32 0.02 2 2
33 163 348.436 116.523 20.68 0.40 0.00 -9.99 20.97 0.05 2 2
34 164 522.710 117.270 18.76 0.05 0.00 -9.99 19.32 0.02 0 0
35 170 460.479 121.079 18.61 0.06 0.00 -9.99 20.03 0.03 2 2
36 174 477.496 123.460 17.32 0.03 0.00 -9.99 20.47 0.05 2 2
37 183 297.456 129.003 19.84 0.14 0.00 -9.99 20.83 0.04 2 2
38 193 318.314 138.756 18.42 0.03 0.00 -9.99 20.84 0.05 0 0
39 194 428.711 138.168 18.68 0.05 0.00 -9.99 21.21 0.09 2 2
40 195 437.139 138.800 19.79 0.20 0.00 -9.99 20.51 0.04 2 2
41 200 470.953 140.956 20.43 0.38 0.00 -9.99 21.72 0.09 2 2
42 206 433.796 145.512 20.59 0.37 0.00 -9.99 20.76 0.05 2 2
43 207 459.587 146.881 20.46 0.17 0.00 -9.99 21.22 0.06 0 0
44 217 555.034 153.558 19.50 0.05 0.00 -9.99 19.54 0.02 1 1
45 220 449.924 156.498 20.83 0.30 20.81 0.11 20.41 0.03 2 2
46 223 267.576 156.680 20.65 0.20 0.00 -9.99 22.14 0.08 2 2
47 227 218.344 157.311 18.26 0.04 0.00 -9.99 20.92 0.05 2 2
48 238 251.239 164.356 20.06 0.22 0.00 -9.99 21.92 0.09 2 2
49 244 226.605 165.671 17.55 0.06 17.99 0.01 17.69 0.02 2 2
50 251 479.256 172.567 19.50 0.05 20.16 0.06 19.29 0.02 2 2
51 253 407.696 173.420 19.66 0.09 0.00 -9.99 21.06 0.06 2 2
52 255 221.566 175.051 17.55 0.04 0.00 -9.99 21.15 0.10 2 2
53 256 239.506 175.965 18.76 0.10 0.00 -9.99 20.14 0.05 1 1
54 257 316.032 176.069 17.58 0.01 0.00 -9.99 20.25 0.02 2 2
55 259 538.957 178.281 20.02 0.07 0.00 -9.99 21.38 0.05 2 2
56 264 275.305 179.902 18.87 0.04 0.00 -9.99 21.06 0.04 2 2
57 265 237.222 181.948 18.32 0.06 20.10 0.07 19.73 0.04 2 2
58 267 191.514 183.677 19.66 0.14 0.00 -9.99 21.45 0.07 2 2
59 268 231.634 182.526 19.60 0.28 21.40 0.25 20.89 0.09 2 2
60 270 327.000 186.435 20.06 0.12 0.00 -9.99 20.87 0.04 2 2
61 274 251.996 186.189 20.62 0.35 0.00 -9.99 21.97 0.22 2 2
62 275 236.816 191.118 18.97 0.09 0.00 -9.99 21.60 0.13 0 0
63 281 238.834 195.885 20.01 0.15 20.93 0.13 20.48 0.06 2 2
64 282 257.190 196.812 19.60 0.09 0.00 -9.99 20.97 0.07 2 2
65 290 247.325 206.211 18.87 0.04 19.97 0.06 19.52 0.02 1 1
66 298 230.047 215.142 21.76 0.43 0.00 -9.99 21.33 0.06 2 2
67 300 493.298 216.898 20.32 0.13 0.00 -9.99 21.09 0.04 0 0
68 309 498.931 227.331 17.20 0.01 20.77 0.09 19.83 0.02 2 2
69 316 482.880 239.218 20.97 0.17 0.00 -9.99 21.52 0.04 2 2
70 320 522.998 245.496 21.21 0.26 0.00 -9.99 22.00 0.11 2 2
71 323 257.476 251.589 20.38 0.09 21.57 0.22 20.67 0.03 2 2
72 330 657.732 259.238 19.33 0.06 0.00 -9.99 19.32 0.02 0 0
73 332 578.737 261.714 19.50 0.07 0.00 -9.99 21.11 0.04 2 2
74 337 573.339 263.968 19.13 0.05 0.00 -9.99 20.93 0.03 0 0
75 352 578.367 281.535 19.64 0.08 0.00 -9.99 20.11 0.02 2 2
76 354 655.349 286.803 18.10 0.03 0.00 -9.99 21.12 0.05 0 0
77 358 696.580 296.227 21.08 0.19 0.00 -9.99 21.33 0.04 2 2
78 360 240.901 296.493 20.84 0.18 0.00 -9.99 21.09 0.03 2 2
79 361 393.765 297.706 18.63 0.02 0.00 -9.99 21.71 0.05 2 2
80 362 778.417 298.349 19.40 0.06 0.00 -9.99 19.53 0.02 2 2
81 363 635.102 299.969 19.44 0.09 0.00 -9.99 21.17 0.05 2 2
82 367 346.413 301.989 19.66 0.09 21.38 0.14 20.73 0.03 2 2
83 368 706.253 302.946 21.16 0.19 0.00 -9.99 21.46 0.04 2 2
84 372 607.908 312.120 20.86 0.19 0.00 -9.99 21.34 0.07 2 2
85 373 521.081 313.978 18.65 0.05 0.00 -9.99 21.30 0.05 2 2
86 378 367.258 314.923 20.64 0.16 0.00 -9.99 20.40 0.03 2 2
87 385 660.420 319.656 19.72 0.10 0.00 -9.99 19.57 0.02 2 2
88 388 519.272 321.917 19.73 0.21 0.00 -9.99 21.20 0.09 2 2
89 389 640.391 323.850 21.79 0.39 0.00 -9.99 21.23 0.05 2 2
90 393 508.769 330.281 18.90 0.10 19.81 0.05 19.16 0.02 2 2
91 394 517.462 328.769 18.86 0.12 0.00 -9.99 19.85 0.03 0 0
92 395 523.567 329.997 18.46 0.04 20.45 0.09 20.02 0.03 2 2
93 398 515.020 331.707 18.86 0.12 20.19 0.08 20.26 0.05 2 2
94 400 503.500 330.923 18.93 0.09 0.00 -9.99 19.87 0.03 2 2
95 405 740.318 341.535 20.22 0.08 0.00 -9.99 20.26 0.02 2 2
96 408 511.225 345.512 17.12 0.01 18.38 0.02 17.68 0.02 2 2
97 412 375.872 353.236 20.62 0.13 0.00 -9.99 20.42 0.02 2 2
98 416 519.026 359.529 20.65 0.19 0.00 -9.99 20.91 0.06 2 2
99 418 546.091 363.307 19.79 0.13 0.00 -9.99 22.13 0.09 2 2
100 419 398.875 365.987 21.34 0.26 0.00 -9.99 21.15 0.04 0 0
101 421 757.357 375.226 20.91 0.17 0.00 -9.99 20.58 0.03 2 2
102 422 762.276 378.157 20.66 0.13 0.00 -9.99 20.79 0.03 0 0
103 427 579.265 385.113 20.01 0.12 0.00 -9.99 20.43 0.03 2 2
104 429 787.790 389.245 20.46 0.11 0.00 -9.99 21.46 0.05 2 2
105 433 573.541 389.542 18.84 0.05 0.00 -9.99 19.77 0.02 0 0
106 441 566.322 400.157 18.89 0.04 0.00 -9.99 20.17 0.03 0 0
107 451 567.262 406.989 18.89 0.04 0.00 -9.99 20.58 0.04 2 2
108 454 750.864 407.931 20.21 0.09 0.00 -9.99 20.13 0.02 2 2
109 455 576.244 409.934 21.45 0.46 0.00 -9.99 21.31 0.09 2 2
110 464 584.322 426.102 18.27 0.04 0.00 -9.99 21.05 0.04 0 0
111 466 576.255 431.149 20.70 0.27 0.00 -9.99 22.18 0.06 2 2
112 467 592.140 432.517 20.08 0.11 0.00 -9.99 21.79 0.05 2 2
113 473 615.455 454.496 19.38 0.04 0.00 -9.99 19.42 0.02 0 0
114 515 287.260 594.394 19.17 0.04 0.00 -9.99 21.05 0.03 2 2

Photometry and coordinates by Nate Bastian and Henny Lamers, Oct 2001



Copyright ESO 2003