# Constraints on the curvature of nuclear symmetry energy from recent
astronomical data within the KIDS framework

Hana Gil<EMAIL_ADDRESS>Center of Extreme Nuclear Matter, Korea
University, Seoul 02841, Korea  Panagiota Papakonstantinou<EMAIL_ADDRESS>Rare Isotope Science Project, Institute for Basic Science, Daejeon 34047,
Korea  Chang Ho Hyun<EMAIL_ADDRESS>Department of Physics Education, Daegu
University, Gyeongsan 38453, Korea

###### Abstract

We investigate the density dependence of the nuclear symmetry energy $S(\rho)$
in the KIDS (Korea-IBS-Daegu-SKKU) framework for the nuclear equation of state
(EoS) and energy-density functional (EDF). The aim is to constrain the value
of the curvature parameter ($K_{\rm sym}$) based on recent astronomical data.
First, assuming a standard saturation point, we calculate bulk nuclear
properties within KIDS-EDF for different values of the compression modulus of
symmetric nuclear matter ($K_{0}$) and of the leading-order symmetry energy
parameters, i.e., the symmetry energy ($J$) and slope ($L$) at saturation
density, each within a broadly accepted range, as well as $K_{\rm sym}$. All
of the above EoS parameters are varied independently of each other. The
skewness parameter ($Q_{\rm sym}$) is presently kept fixed at 650 MeV. For all
EoS parameter sets which describe the selected nuclear data within better than
$0.3\%$, we calculate the neutron-star equation of state and mass-radius
relation and analyze the results in terms of Pearson correlation coefficients
$r$. We find that the value of $K_{\rm sym}$ is strongly correlated with the
radius of both a canonical and a massive star ($|r|>0.9$). If we impose that
all known astronomical constraints on the neutron star radii must be
satisfied, we deduce $-150<K_{\rm sym}<0$. As a result, the symmetry energy as
a function of the density is consistently found to have an inflection point at
$\rho_{0}<\rho<2\rho_{0}$. We take the opportunity to report that the neutron
skin thickness of 208Pb shows no correlation at all with the neutron star
radii ($|r|<0.1$), in contrast with studies which focus on the role of $L$
only.

##  I Introduction

The physics of dense nuclear matter has entered a golden age thanks to
previously unattainable data from diverse objects and phenomena in the
Universe. They include millisecond pulsars Demorest et al. (2010); Cromartie
et al. (2020), X-ray bursts from low-mass X-ray binaries (LMXBs) Steiner et
al. (2010); d’Etivaux et al. (2019), compact binaries Antoniadis et al.
(2013), gravitational waves (GWs) from neutron star merges Raithel and Özel
(2019); Abbott et al. (2018, 2017, 2020), and soft X-rays from pulsars Riley
et al. (2019); Miller et al. (2021a). Most notable regarding the physics of
neutron stars may be the possibility to determine the mass and radius of a
single object, thus obtaining strong constraints to the mass and radius of
neutron stars, and eventually the nuclear equation of state (EoS).

One key issue for dense nuclear matter is to constrain the EoS and in
particular the nuclear symmetry energy $S(\rho)$ at baryonic densities $\rho$
higher than the saturation density $\rho_{0}$ of symmetric nuclear matter
Baldo and Burgio (2016); Oertel et al. (2017); Holt and Lim (2018); Li et al.
(2021). By convention, the density dependence is encoded in the values of its
derivatives at saturation density. The following expressions for the energy
per particle $\mathcal{E}(\rho,\delta)$ at density $\rho$ and isospin
asymmetry $\delta$ summarize the necessary definitions:

$\displaystyle{\cal E}(\rho,\delta)$ $\displaystyle=$ $\displaystyle
E(\rho)+S(\rho)\delta^{2}+O(\delta^{4}),$ (1) $\displaystyle E(\rho)$
$\displaystyle=$ $\displaystyle
E_{0}+\frac{1}{2}K_{0}x^{2}+\frac{1}{6}Q_{0}x^{3}+\cdots,$ (2) $\displaystyle
S(\rho)$ $\displaystyle=$ $\displaystyle J+Lx+\frac{1}{2}K_{\rm
sym}x^{2}+\frac{1}{6}Q_{\rm sym}x^{3}+\cdots.$ (3)

Denoting the neutron and proton densities as $\rho_{n}$ and $\rho_{p}$,
respectively, we have $\rho=\rho_{n}+\rho_{p}$,
$\delta=(\rho_{n}-\rho_{p})/\rho$, and $x=(\rho-\rho_{0})/3\rho_{0}$. In
symmetric nuclear matter ($\delta=0$) at densities where $|x|<1$, the density
dependence of the EoS is controlled dominantly by $K_{0}$, while in neutron-
rich matter ($\delta\approx 1$) the EoS below and above $\rho_{0}$ is largely
driven by $L$ and $K_{\rm sym}$.

The saturation point as represented by the values of $E_{0}$ and $\rho_{0}$ is
considered rather well known: Different theoretical assumptions lead to a
maximal disagreement of the order of $1-2$ MeV for $E_{0}\approx-16$ MeV
Atkinson et al. (2020) and $0.01-0.02$ fm for $\rho_{0}\approx 0.16$ fm-3
Dutra et al. (2012), i.e., roughly 12$\%$ at most. The uncertainty in
$J\approx 30$ MeV is of the order of a few MeV. Determining the EoS in the
density region relevant for nuclei and neutron stars is then equivalent to
determining the values of $K_{0}$, $L$ and $K_{\rm sym}$. ($Q_{\rm sym}$ is
also a relevant parameter but with a more marginal role Papakonstantinou et
al. (2018); Gil et al. (2019a).) The above three parameters are poorly
constrained. $K_{0}$ is nonetheless best known among them: The empirically
determined range is $200-260$ MeV Dutra et al. (2012); Garg and Colò (2018). A
recent calculation based on microscopic theory predicts $K_{0}=282$ MeV
Brandes et al. (2021), which is one of the largest values in the recent
literature. The current status of $L$ is summarized comprehensively in Ref. Li
et al. (2021), where 24 new analyses of neutron stars give $57.7\pm 19$ MeV at
68% confidence level. The above range is consistent with the range $L=58.7\pm
28.1$ MeV provided by a previous survey Oertel et al. (2017) and with the
earlier empirical range $L=40-76$ MeV Dutra et al. (2012).

Compared with the above, $K_{\rm sym}$ is very poorly determined, with model
estimates ranging from $-400$ MeV to positive values Li et al. (2021). Let us
summarize how current constraints on $K_{\rm sym}$ have been obtained. A
standard way is to identify correlations between $K_{\rm sym}$ and better-
known model parameters, namely $J$ and $L$, by surveying up to hundreds of
models. A $K_{\rm sym}$ value is then deduced from the values of the other
parameters. Recent works along this line propose $K_{\rm sym}$ values $-112\pm
71$ Mondal et al. (2017), and $-100\pm 100$ MeV Margueron et al. (2018).
Another way to obtain correlations among EoS parameters is to use effective
field theories that provide a platform to calculate the correlations and
uncertainties with realistic nuclear forces. A recent work obtains $K_{\rm
sym}=-150$ to $-70$ MeV Lim and Holt (2019), which is a result of correlation
between $K_{\rm sym}$ and $3J-L$ with appropriate ranges of $J$ and $L$.

One may also identify correlations between model predictions for observables
that can be measured and the EoS parameter of interest. One example is the
relation of the energy of the giant monopole resonance with the nuclear
incompressibility $K_{0}$ Garg and Colò (2018). As regards $K_{\rm sym}$,
recent works apply a Bayesian analysis to the tidal deformability of neutron
stars. The results vary broadly and depend on the technical details and
assumptions. For example Ref. Malik et al. (2018) obtains $K_{\rm sym}=-113$
to $-52$ MeV if $L=40-62$ MeV, and Ref. Raithel and Özel (2019) gives $K_{\rm
sym}=-374$ to $45$ MeV. The 16 new analyses of neutron star observables in Li
et al. (2021) suggest a range $K_{\rm sym}=-107\pm 88$ MeV at 68% confidence
level. This range excludes positive values, but the uncertainty is far larger
than for $K_{0}$ and $L$.

In a few cases $K_{\rm sym}$ is determined more directly from experiment. In
Ref. Cozma (2018), elliptic flow data are used to obtain allowed ranges of $L$
and $K_{\rm sym}$. The result is $K_{\rm sym}=96\pm 315({\rm exp})\pm 170({\rm
th})\pm 166({\rm sys})$. While elliptic flow data are obtained from
experiments on Earth, astronomical data have also been used: In Ref. d’Etivaux
et al. (2019), the thermal emission from LMXB is analyzed, and the authors
obtain $K_{\rm sym}=-155$ to $-3$ MeV. The uncertaintly in $K_{\rm sym}$ is
significantly lower than in the elliptic-flow work, but at the same time the
value of $L$ was estimated to be $37.2^{+9.2}_{-8.9}$ MeV, which is on the
lower side of the generally accepted range.

Our poor knowledge of $K_{\rm sym}$ represents our poor knowledge of the EoS
in the broad density domain necessary for the description of nuclei and
neutron stars. Let us point out also that most theoretical models providing
input for the above analyses do not provide independent values for $K_{\rm
sym}$, but rather values strongly correlated with the dominant parameters $J$
and $L$ owing to a deficiency in independent model parameters. For a
discussion pertaining to Skyrme models see, e.g., Gil et al. (2021). As
exceptions besides ab initio calculations we may mention the meta-model
Margueron et al. (2018), which however has minimal applicability at low
densities and finite nuclei Chatterjee et al. (2017), and the KIDS (Korea-IBS-
Daegu-SKKU) framework Papakonstantinou et al. (2018); Gil et al. (2019a, 2021)
for the nuclear EoS and energy density functional (EDF), which provides a
unified approach to both nuclear-structure and astronomical types of data and
is used in this work.

The KIDS EoS of homogeneous matter, specifically the energy per particle, has
the analytical form

$\mathcal{E}(\rho,\delta)=\mathcal{T}(\rho,\delta)+\sum_{i=0}^{n}c_{i}(\delta)\rho^{1+i/3},$
(4)

where $\mathcal{T}$ is the kinetic energy per particle of a free Fermi gas and
$c_{i}(\delta)$ can be assumed quadratic to $\delta$. The expansion in terms
of the cubic root of the density is informed by effective field theories and
ab initio calculations and can accommodate any set of EoS parameters as
defined in Eqs. (2), (3) Papakonstantinou et al. (2018); Papakonstantinou and
Gil (2018). The EoS with the desired parameters is readily transposed to a
nuclear EDF for finite nuclei with the additional freedom of choosing the
values for the effective mass if desired Gil et al. (2017, 2019b, 2019a). In
Ref. Gil et al. (2021), we explored the density dependence of the symmetry
energy in the KIDS framework by considering bulk properties of magic and open-
shell nuclei and neutron-star properties. In particular, we explored the
parameter space for $(J,L,K_{\rm sym})$ for a fixed EoS for symmetric matter,
$E_{0}=-16$ MeV, $\rho_{0}=0.16$ fm-3, $K_{0}=240$ MeV. The less relevant
parameter $Q_{\rm sym}$ was fixed to $650$ MeV. We also examined $K_{\tau}$,
which is the droplet-model counterpart of $K_{\rm sym}$ and more appropriate
for nuclei, by using the correspondence

$K_{\tau}=K_{\rm sym}-\left(6+\frac{Q_{0}}{K_{0}}\right)L.$ (5)

Departures from existing model-dependent correlations between $K_{\rm sym}$
and $J,L$ Mondal et al. (2017) were observed. Among other results, we
concluded that $K_{\rm sym}$ is negative and no lower than $-200$ MeV and
suggested inconclusively $-400$ to $-300$ MeV as a range of likely values for
$K_{\tau}$. In Ref. Gil and Hyun (2021), the compression modulus $K_{0}$ of
symmetric nuclear matter was explored in a similar manner and the results were
found consistent with the current literature.

In this work, we examine the acceptable values of $K_{\rm sym}$ by taking
advantage of recent astronomical data from LMXB Steiner et al. (2010),
GW170817 Abbott et al. (2018), GW190425 Abbott et al. (2020) and NICER Miller
et al. (2021a). We explore both $K_{0}$ and $K_{\rm sym}$ at the same time, as
well as $J$ and $L$. Note that in Gil et al. (2021), $K_{0}$ is fixed to 240
MeV, while in Ref. Gil and Hyun (2021) the focus was on the uncertainties in
$J$ and $L$. Considering broadly accepted ranges for the four parameters
$K_{0},J,L,K_{\rm sym}$ (equivalently, $K_{\tau}$ instead of $K_{\rm sym}$)
independently of each other, the total number of EoSs examined initially is
about 4000. Next, we select a fraction of them (roughly$10\%$) which describe
bulk data of selected nuclei most precisely, use them to calculate neutron-
star properties, and analyze the results. We evaluate correlation coefficients
for the model parameters and predictions, revealing a strong correlation
between $K_{\rm sym}$ and neutron star radii. By imposing all astronomical
constraints at the same time, we deduce $-150<K_{\rm sym}<0$ MeV. We take the
opportunity to comment also on the neutron skin thickness of 208Pb measured
recently by the PREX collaboration Adhikari et al. (2021).

The paper is organized as follows. In Sec. II we perform the first filtering
of parameter sets using bulk nuclear data. In Sec. III, we analyze our
calculations for neutron-star properties and compare them with the above-
mentioned astronomical constraints. The 358 sets used at this stage and
selected results are available as supplementary material. We provide a summary
and perspectives in Sec. IV.

##  II EoS Parameters and correlation analysis

The standard KIDS EoS has three free parameters for the EoS of symmetric
nuclear matter ($c_{i>2}(0)=0$) and four for neutron matter, or equivalently
the symmetry energy ($c_{i>3}(1)=0$) Papakonstantinou et al. (2018); Gil et
al. (2019a). This means that seven leading EoS parameters,
$(\rho_{0},E_{0},K_{0})$ and $(J,L,K_{\rm sym},Q_{\rm sym})$, can be
controlled independently. Higher-order parameters such as $Q_{0}$ do not
vanish, but will fully depend on those seven. Although arbitrary extentsions
to any number of free parameters are straightforward, the use of seven low-
order KIDS parameters has been found optimal and suffices for our purposes. As
already mentioned, compared to $K_{0},J,L,K_{\rm sym}$, the saturation point
$(E_{0},\rho_{0})$ is quite accurately known and will be kept fixed at $(-16$
MeV, $0.16$ fm${}^{-3})$. As in Gil et al. (2021), the less relevant parameter
$Q_{\rm sym}$ will be kept fixed to the value of $650$ MeV.

We begin by spanning the ranges $K_{0}=[230,260]$ MeV, $J=[30,34]$ MeV,
$L=[40,70]$ MeV, $K_{\tau}=[-420,-240]$ MeV in increments of $\Delta J=0.5$
MeV, $\Delta K_{0}=\Delta L=5$ MeV and $\Delta K_{\tau}=20$ MeV. In total,
this gives us $7\times 9\times 7\times 10=4410$ EoS sets. At this stage, we
use $K_{\tau}$ instead of $K_{\rm sym}$, because we are examining finite
nuclei. The relation between the two is straightforward, Eq. (5). For the
present choices, the value of $K_{\rm sym}$ ranges from $-300$ to $96$ MeV.
The $Q_{0}$ value fully depends on $K_{0}$ and for the present choices ranges
from $-373$ to $-313$ MeV.

For each EoS, a KIDS-EDF is obtained, which has the form of an extended Skyrme
functional Gil et al. (2017, 2019b, 2019a, 2021). Besides the EoS parameters,
the necessary additional EDF parameters, namely $W_{0}$ (strength of spin-
orbit force) and gradient terms represented by the Skyrme-like parameters
$t_{1},t_{2}$, are optimized by a fit to a few basic data Gil et al. (2019a,
2017). We note that the KIDS-EDF used at present has the simpler form given in
Ref. Gil et al. (2017), i.e., the exchange momentum-dependent terms
$y_{1,2}=t_{1,2}x_{1,2}$ are set to zero. The choice has no influence at all
on our results for homogeneous matter, while any influence on bulk nuclear
properties is too marginal to affect our current results Gil et al. (2019b,
2021).

We then examine how accurately each EoS describes bulk nuclear properties by
applying the corresponding EDF. As a measure of performance, we employ the
average deviation per datum (ADPD) defined by

$\displaystyle{\rm ADPD}(N)\equiv\frac{1}{N}\sum^{N}_{i=1}\left|\frac{O^{\rm
exp}_{i}-O^{\rm cal}_{i}}{O^{\rm exp}_{i}}\right|,$ (6)

where $O^{\rm exp}_{i}$ and $O^{\rm cal}_{i}$ denote the value of an
observable from experiment and theory, respectively. Since the focus is on the
EoS and not on nuclear structure, we will use only bulk properties of closed-
shell nuclei. Specifically, we use $N=13$ data: binding energy National
Nuclear Data Center, Brookhaven National Laboratory  and charge radius Angeli
and Marinova (2013) of 16O, 40Ca, 48Ca, 90Zr, 132Sn, 208Pb, and binding energy
of 218U National Nuclear Data Center, Brookhaven National Laboratory . The
results are summarized in Fig. 1.

Figure 1: Values of the criterion ADPD(13) with the examined sets of
$(K_{0},J,L,K_{\tau})$. For each value of $K_{0}$, results with different
$K_{\tau}$ are shown displaced for visibility.

Roughly one tenth of all the EoSs give a value of ADPD less than $0.3\%$ and
will be examined further. The values of their parameters are available as
supplementary material. The cutoff of $0.3\%$ that we impose here is a rather
stringent one. Values for the same ADPD(13) as provided by representative
Skyrme functionals are given in Table 1.

| SLy4 | HFB9 | SkM* | UNEDF0
---|---|---|---|---
ADPD(13) | 0.86 | 0.87 | 0.84 | 0.98
ADPD(7) | 0.30 | 0.36 | 0.38 | 0.59
Table 1: ADPD(13), see Eq. (6), in units of percentage, calculated with
representative Skyrme force models.

Since those functionals are typically fitted to very different data, for
comparison we also tabulate the values they give for 7 data only, namely the
masses of 16O, 40Ca, 48Ca, 90Zr, 132Sn, 208Pb, and 218U.

With each of the roughly 380 EoS sets selected, we calculate the neutron star
EoS, solve the TOV equations, and obtain the mass-radius relations of the
neutron star in a standard way Gil et al. (2019a, 2021). We are interested in
particular in the radius $R_{1.4}$ and tidal deformability $\Lambda$ of a
canonical neutron star with a mass roughly equal to $1.4$ solar masses and in
the radius $R_{2.0}$ of a two-solar mass neutron star. All sets predict the
existence of such massive neutron stars.

Next, we evaluate the Pearson correlation coefficient $r_{XY}$ between EoS
parameters or predicted observables $X,Y$

$r_{XY}=\frac{\overline{XY}-\bar{X}\bar{Y}}{\sigma_{X}\sigma_{Y}};\sigma_{X}=\sqrt{\overline{X^{2}}-{\bar{X}}^{2}}$
(7)

and list the results in the lower triangle of Table 2. The values will be
updated to those of the upper triangle after we consider the astronomical
observations in Sec. III. We include the quantity $3J-L$, whose correlation
with $K_{\rm sym}$ has been discussed before, see Ref. Gil et al. (2021) and
references therein. Along with EoS parameters, we include the predictions for
$R_{1.4}$, $R_{2.0}$, and the neutron skin thickness of 208Pb.

| $K_{0}$ | $J$ | $L$ |  $3J-L$ | $K_{\rm{sym}}$ | $K_{\tau}$ | $\Delta R_{\rm np}$ | $R_{1.4}$ | $R_{2.0}$
---|---|---|---|---|---|---|---|---|---
$K_{0}$ | 1 | $-0.51$ | $-0.24$ | $\mathit{0.10}$ | $0.35$ | $0.50$ | $-0.58$ | $0.24$ | $0.46$
$J$ | $-0.39$ | 1 | $0.56$ | $-0.35$ | $\mathit{-0.06}$ | $-0.52$ | $0.62$ | $0.22$ | $\mathit{0.01}$
$L$ | $0.24$ | 0.45 | 1 | $\mathbf{-0.96}$ | $0.50$ | $-0.27$ | $0.65$ | $0.79$ | $0.65$
$3J-L$ | $-0.34$ | $-0.27$ | $\mathbf{-0.98}$ | 1 | $-0.60$ | $0.14$ | $-0.54$ | $-0.84$ | $-0.75$
$K_{\rm{sym}}$ | $0.56$ | $\mathit{0.09}$ | $\,\,0.83$ | $-0.88$ | 1 | $0.69$ | $-0.29$ | $\mathbf{0.90}$ | $\mathbf{0.91}$
$K_{\tau}$ | $0.62$ | $-0.30$ | $0.34$ | $-0.44$ | $0.80$ | 1 | $-0.85$ | $0.33$ | $0.43$
$\Delta R_{\rm np}$ | $-0.53$ | $0.56$ | $0.35$ | $-0.26$ | $-0.20$ | $-0.70$ | 1 | $\mathit{0.09}$ | $\mathit{-0.05}$
$R_{1.4}$ | $0.52$ | $0.21$ | $\mathbf{0.91}$ | $\mathbf{-0.93}$ | $\mathbf{0.96}$ | $0.66$ | $\mathit{-0.02}$ | 1 | $\mathbf{0.97}$
$R_{2.0}$ | 0.63 | $\mathit{0.09}$ | $0.85$ | $\mathbf{-0.90}$ | $\mathbf{0.96}$ | $0.69$ | $-0.11$ | $\mathbf{0.99}$ | 1
Table 2: Correlation between the shown quantities according to Eq. (7). Lower
triangle: Considering sets satisfying ADPD(13)$<0.3\%$. Upper triangle:
Considering sets which, in addition, satisfy selected astronomical
constraints, see Sec. III.

Note that adding $Q_{0}$ to the table would offer no new information: Its
correlation with all parameters would be the same as for $K_{0}$ and exactly 1
between $Q_{0}$ and $K_{0}$. That’s because, with $\rho_{0}$ and $E_{0}$ fixed
and having kept only three free parameters in the KIDS EoS of symmetric
matter, $Q_{0}$ is fully and linearly determined by $K_{0}$. In addition, the
correlation of $Q_{\rm sym}$ with the other parameters is not defined, because
we have kept its value fixed.

Numbers indicating strong (anti)correlation, $|r_{XY}|\geq 0.9$, are set in
boldface, while those indicating absence of correlations, $|r_{XY}|\leq 0.1$,
are set in underlined italics. Generally, the (anti)correlations between EoS
parameters are weak at this stage, i.e., no linear correlations are apparent.
Especially $K_{\rm sym}$ and $J$ appear uncorrelated. Neutron star radii are
strongly correlated with $K_{\rm sym}$ and to some extent $L$ and $3J-L$.
Notably, there are no correlations between the neutron skin thickness and the
properties of neutron stars, in contrast with studies which focus on the role
of $L$ only Reed et al. (2021).

All the tabulated numbers should be interpreted with some care. The parameters
and results which have been used as data sets do not necessarily follow
gaussian or symmetric distributions, owing, for example, to the range cutoffs
we have imposed in the EoS parameters, see also Fig. 1. Also, different values
would be obtained if different data and acceptance criteria were used.
Nevertheless, the highest and lowest values of $|r_{XY}|$ marked in the table
should carry some meaning. Also meaningful will be to inspect how the
correlation patterns change or persist when we impose the neutron star
constraints in the following.

##  III Results for neutron stars

For the canonical neutron star, $M=1.4M_{\odot}$, the common range of all the
data for $R_{1.4}$ from LMXB, GW170817 and GW109425 is roughly $11.8-12.5$ km.
A recent work based on Bayesian analysis reports that the upper lmit of
$R_{1.4}$ will not exceed $\sim 12.5$ km M. Kim et al. (2021). Therefore, we
assume as acceptable a range of $R_{1.4}=11.8-12.5$ km. For $R_{2.0}$ we only
have the NICER measurement, taken for 2.08 solar masses, giving a much broader
interval.

Figure 2: (a)-(c): Predicted radii of neutron stars $R_{1.4}$ (for $1.4$ solar
masses) and $R_{2.0}$ (for $2.0$ solar masses) shown against $K_{\rm sym}$
(a),(c) and $3J-L$ (b) for all sets satisfying the basic constraint from
nuclear data, ADPD(13)$<0.3\%$. The dashed horizontal lines indicate combined
astronomical constraints for the minimum and maximum acceptable values. (d):
Symmetry energy corresponding to slected combinations of $(J,L,K_{0},K_{\rm
sym})$ values, indicated in units of MeV, roughly delimiting the allowed range
based on the $R_{1.4}$ constraint in (a). The shown constraint at $0.1$ fm-3
(Trippa et al.) is from Ref. Trippa et al. (2008) and the estimate for
$S(2\rho_{0})$ (Li et al.) is from Ref. Li et al. (2021).

The results we obtained for neutron star radii for the sets satisfying the
basic constraint from nuclear data, ADPD(13)$<0.3\%$, are shown as scatter
plots in Fig. 2 along with relevant astronomical constraints. Specifically, in
Fig. 2 (a) and (c) we show plots of $R_{1.4}$ and $R_{2.0}$, respectively,
against $K_{\rm sym}$ and in (b), a plot of $R_{1.4}$ against $3J-L$. Both
$K_{\rm sym}$ and $3J-L$ were found strongly (anti)correlated with the radii
(Table 2, lower triangle). In order to reveal other possible systematics, in
panels (a) and (c) we highlight the results for the highest and lowest values
of $L$ and in panel (b) we highlight values of $J$. All results are available
as supplementary material.

Imposing the strictest possible criterion of $11.8\leq R_{1.4}\leq 12.5$ km,
as mentioned above and indicated in Fig. 2(a), we obtain

$-150\leq K_{\rm sym}\leq 0~{}\mathrm{MeV}.$

Despite the varied range in $K_{0}$ and the different nuclear data considered
in this work, our results for $K_{\rm sym}$ remain perfectly consistent with
those in Ref. Gil et al. (2021), where we had deduced that $-200\leq K_{\rm
sym}\leq 0$ MeV. Let us note that we have also examined the dimensionless
tidal deformability $\Lambda_{1.4}$ of a canonical neutron star, which we
evaluated as $2.88\times 10^{-6}R_{1.4}^{7.5}$ (with $R_{1.4}$ in units of
[km]) annala  and found strongly correlated with $K_{\rm sym}$. For the EoS
sets which satisfy the imposed radius constraints, one finds
$315<\Lambda_{1.4}<486$, consistent with current estimates from the LIGO/Virgo
measurements.

A stratification with respect to $L$ is apparent in Fig. 2(a) with lower
radius values favoring generally lower values of $L$. Higher values of $J$ are
not favored. Overall, imposing again the strictest possible criterion of
$11.8\leq R_{1.4}\leq 12.5$ km, as indicated in Figs. 2(b), gives us
$30<3J-L<53$ MeV with $J=30-32$ MeV, implying roughly that

$L<3J-30\mbox{MeV}<66~{}\mbox{MeV}\quad,\quad
L>3J-53~{}\mbox{MeV}>37~{}\mbox{MeV}.$

One may impose more lenient criteria to the constraint on $R_{1.4}$, given the
uncertainty in all measurements. Then broader ranges would be obtained for the
EoS parameters. What is clear from our analysis is that an accurate and
precise measurement of a neutron star’s mass would be instrumental in
constraining the value of $K_{\rm sym}$ \- more generally, $S(\rho)$ at
$\rho>\rho_{0}$.

In Fig. 2(d), we plot the symmetry energy corresponding to selected
combinations of $(J,L,K_{0},K_{\rm sym})$ values, indicated in units of MeV,
roughly delimiting the allowed range based on the $R_{1.4}$ constraint in (a).
The upper curves correspond to $R_{1.4}$ closer to the lower bound of $11.8$
km while the lower curves correspond to $R_{1.4}$ closer to the upper bound of
$12.5$ km. A crossing point is observed at roughly $\rho=0.1$ fm, which is
roughly the average density in a heavy nucleus, consistently with other
studies Baldo and Burgio (2016). As indicated on the Figure, the value of
$S(0.1~{}\rm{fm}^{-3})$ is consistent with a constraint derived from giant
dipole resonances Trippa et al. (2008). The symmetry energy at two times the
saturation density is obtained consistent with the range proposed in Ref. Li
et al. (2021), which was extracted from a variety of heavy-ion collision data
and astronomical data.

An important observation is that in all cases the symmetry energy shows and
inflection point at some density above saturation, i.e., the curvature changes
sign from negative to positive. This behavior is mathematically possible
because the higher-order parameters such as $Q_{\rm sym}$ do not vanish in
this scheme. The inflection point is found here consistently within the
interval between $\rho_{0}$ and $2\rho_{0}$.

The above constraints are based solely on bulk nuclear properties and existing
astronomical data. We take the opportunity to comment on the neutron skin
thickness of the nucleus 208Pb, which was extracted recently from parity
violating electron scattering by the PREX collaboration Adhikari et al. (2021)
and found larger than expected from earlier estimates and known systematics
Roca-Maza et al. (2011); Piekarewicz (2021). It is generally thought that a
moderate value of $L$, such as exctracted also in this work, does not favor a
thick neutron skin. However, presently we find a rather weak correlation of
the neutron skin thickness with $L$ compared with a much stronger
anticorrelation with $K_{\tau}$. A thorough investigation of $K_{\tau}$ is
therefore called for and is currently in progress.

Let us further inspect a few EoS sets obtained here which satisfy the
astronomical constraints defined in Fig. 2 but also give a $\Delta R_{np}$
prediction for 208Pb consistent with both the first PREX measurement,
$0.33^{+0.16}_{-0.18}$ fm Abrahamyan et al. (2012), and an earlier broad
estimate $0.195\pm 0.057$ fm Roca-Maza et al. (2011). In Fig. 3 we plot the
density dependence of the symmetry energy for five such sets (a) and the
resulting neutron-star mass-radius relations (b). (One of the EoSs is
consistent also with the PREX-II measurement by giving $\Delta R_{np}=0.212$
fm.)

Figure 3: Symmetry energy (a) and neutron star mass-radius curves (b) for
representative EoSs satisfying astronomical and neutron-skin data as discussed
in the text. The labels show the values of $(L,J,K_{0},K_{\rm sym}$) in units
of MeV.

Astronomical constraints from various sources are displayed in Fig. 3(b)
related to masses observed or to masses and radii of neutron stars Cromartie
et al. (2020); Antoniadis et al. (2013); Steiner et al. (2010); Abbott et al.
(2018, 2020); Riley et al. (2019); Miller et al. (2019, 2021b). What we
conclude from this picture, compared to Fig. 2(d), is that combining both
nuclear data (sub-saturation regime) and astronomical data (high-density
regime) it becomes possible to constrain significantly the density dependence
of the nuclear symmetry energy. Precise astronomical data and more conclusive
measurements of the neutron skin thickness are required.

##  IV Summary

In this work, we attempt to constrain the curvature parameter of the symmetry
energy $K_{\rm sym}$ based on bulk nuclear properties and available
astronomical data. We utilize the KIDS framework for the nuclear EoS and EDF,
which imposes no a priori, spurious correlations among EoS parameters.
Assuming a standard saturation point, we calculate bulk nuclear properties
within KIDS-EDF for different values of the compression modulus of symmetric
nuclear matter ($K_{0}$) and of the leading-order symmetry energy parameters,
i.e., the symmetry energy ($J$) and slope ($L$) at saturation density, each
within a broadly accepted range, as well as $K_{\rm sym}$. The skewness
parameter ($Q_{\rm sym}$) is presently kept fixed at 650 MeV. For all EoS
parameter sets which describe the selected nuclear data within better than
$0.3\%$, we calculate the neutron-star equation of state and mass-radius
relation and analyze the results in terms of Pearson correlation coefficients
$r$.

The curvature parameter is found strongly correlated with neutron-star radii.
By imposing that available measurements of neutron star radii must be
reproduced within their given uncertainties, we arrive at an acceptable value
of $K_{\rm sym}$ between roughly $-150$ and zero MeV. The symmetry energy
consistently shows an inflection point at densities between $\rho_{0}$ and
$2\rho_{0}$. Stronger constraints would be possible with more precise
astronomical data. The neutron skin thickness of 208Pb shows no correlation at
all with neutron star radii, but precise measurements would be useful for
constraining the symmetry energy at sub-saturation densities, further aiding
the evaluation of $K_{\rm sym}$.

## Acknowledgments

This work was supported by the National Research Foundation of Korea (NRF)
grant funded by the Korea govenment (No. 2018R1A5A1025563 and No.
2020R1F1A1052495) and by the Rare Isotope Science Project of the Institute for
Basic Science funded by the Ministry of Science, ICT and Future Planning and
the National Research Foundation (NRF) of Korea (2013M7A1A1075764).

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## Supplementary material

Values of parameters and results analysed in this work are tabulated below.
The EoS parameters $K_{0},~{}J,~{}L,~{}K_{\rm sym}$ and the droplet parameter
$K_{\tau}$ are given in units of MeV. The average deviation per datum ADPD(13)
for 13 data (see Eq. (6) of the main text) is given in percentage points %.
The spin-orbit and momentum-term couplings $W_{0},t_{1},t_{2}$ and the surface
parameters $C_{12}=\frac{1}{64}[-9t_{1}+5t_{2}]$,
$D_{12}=\frac{1}{64}[3t_{1}+t_{2}]$ are given in units of MeV fm5. For the
above parameters, typical values for the isoscalar and isovector nucleon
effective masses are, respectively, 0.98 and 0.82 times the bare nucleon mass
(with some deviations). $M_{1}\approx 1.4M_{\odot}$ (more precisely in the
range $(1.39-1.41)M_{\odot}$) denotes the mass of a canonical neutron star and
$M_{2}=2.0M_{\odot}$ that of a massive star. The respective radii, $R_{M_{1}}$
and $R_{M_{2}}$ are given in units of km. The neutron skin thickness of 208Pb,
$\Delta R_{np}$, is given in units of fm.

$K_{0}$ | $Q_{0}$ | $J$ | $L$ | $K_{\tau}$ | $K_{\rm sym}$ | ADPD(13) | $W_{0}$ | $t_{1}$ | $t_{2}$ | $C_{12}$ | $D_{12}$ | $R_{M_{1}}$ | $R_{M_{2}}$ | $\Delta R_{np}$
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
240 | -372.65 | 30.5 | 40 | -340 | -162.11 | 0.298 | 100.82 | 293.18 | -172.48 | -54.70 | 11.05 | 11.44 | 10.94 | 0.164
240 | -372.65 | 30.5 | 40 | -360 | -182.11 | 0.296 | 98.44 | 291.85 | -172.81 | -54.54 | 10.98 | 11.31 | 10.83 | 0.174
240 | -372.65 | 31.0 | 40 | -340 | -162.11 | 0.297 | 104.91 | 294.50 | -172.28 | -54.87 | 11.11 | 11.43 | 10.87 | 0.163
240 | -372.65 | 31.0 | 45 | -340 | -139.87 | 0.295 | 102.06 | 293.40 | -172.49 | -54.73 | 11.06 | 11.73 | 11.22 | 0.171
240 | -372.65 | 31.0 | 40 | -360 | -182.11 | 0.291 | 102.70 | 292.57 | -172.84 | -54.65 | 11.01 | 11.30 | 10.76 | 0.173
240 | -372.65 | 31.0 | 45 | -360 | -159.87 | 0.293 | 99.58 | 291.99 | -172.84 | -54.56 | 10.99 | 11.62 | 11.14 | 0.181
240 | -372.65 | 31.0 | 40 | -380 | -202.11 | 0.293 | 100.08 | 291.62 | -173.03 | -54.53 | 10.97 | 11.16 | 10.65 | 0.183
240 | -372.65 | 31.0 | 45 | -380 | -179.87 | 0.297 | 97.14 | 291.21 | -172.97 | -54.47 | 10.95 | 11.51 | 11.06 | 0.192
240 | -372.65 | 31.0 | 40 | -400 | -222.11 | 0.295 | 97.64 | 291.00 | -173.08 | -54.44 | 10.94 | 11.01 | 10.56 | 0.194
240 | -372.65 | 31.5 | 50 | -340 | -117.63 | 0.296 | 103.23 | 293.61 | -172.51 | -54.77 | 11.07 | 11.97 | 11.45 | 0.178
240 | -372.65 | 31.5 | 55 | -340 | -95.40 | 0.300 | 100.28 | 292.77 | -172.62 | -54.66 | 11.03 | 12.17 | 11.67 | 0.186
240 | -372.65 | 31.5 | 45 | -360 | -159.87 | 0.298 | 103.66 | 292.74 | -172.87 | -54.67 | 11.02 | 11.62 | 11.09 | 0.180
240 | -372.65 | 31.5 | 50 | -360 | -137.63 | 0.296 | 100.73 | 292.14 | -172.89 | -54.59 | 10.99 | 11.88 | 11.38 | 0.188
240 | -372.65 | 31.5 | 55 | -360 | -115.40 | 0.298 | 97.68 | 291.64 | -172.87 | -54.52 | 10.97 | 12.10 | 11.61 | 0.197
240 | -372.65 | 31.5 | 45 | -380 | -179.87 | 0.293 | 101.67 | 291.97 | -173.20 | -54.59 | 10.98 | 11.50 | 11.01 | 0.190
240 | -372.65 | 31.5 | 50 | -380 | -157.63 | 0.298 | 98.23 | 291.32 | -173.01 | -54.48 | 10.95 | 11.79 | 11.32 | 0.199
240 | -372.65 | 31.5 | 40 | -400 | -222.11 | 0.297 | 102.09 | 291.69 | -173.32 | -54.56 | 10.96 | 10.98 | 10.47 | 0.192
240 | -372.65 | 32.0 | 55 | -360 | -115.40 | 0.299 | 101.85 | 292.30 | -172.93 | -54.62 | 11.00 | 12.10 | 11.59 | 0.195
245 | -357.65 | 30.0 | 40 | -280 | -98.39 | 0.297 | 100.69 | 262.88 | -181.08 | -51.12 | 9.49 | 11.84 | 11.39 | 0.137
245 | -357.65 | 30.0 | 40 | -300 | -118.39 | 0.294 | 108.07 | 337.85 | -152.07 | -59.39 | 13.46 | 11.75 | 11.32 | 0.136
245 | -357.65 | 30.0 | 40 | -320 | -138.39 | 0.288 | 101.18 | 298.50 | -166.96 | -55.02 | 11.38 | 11.64 | 11.22 | 0.151
245 | -357.65 | 30.0 | 45 | -320 | -115.69 | 0.299 | 98.20 | 295.63 | -167.89 | -54.69 | 11.23 | 11.90 | 11.51 | 0.160
245 | -357.65 | 30.0 | 40 | -340 | -158.39 | 0.289 | 98.33 | 293.02 | -168.92 | -54.40 | 11.10 | 11.53 | 11.12 | 0.162
245 | -357.65 | 30.0 | 45 | -340 | -135.69 | 0.300 | 95.53 | 291.86 | -169.17 | -54.26 | 11.04 | 11.81 | 11.44 | 0.170
245 | -357.65 | 30.0 | 40 | -360 | -178.39 | 0.295 | 95.85 | 290.72 | -169.62 | -54.13 | 10.98 | 11.42 | 11.04 | 0.173
245 | -357.65 | 30.5 | 50 | -280 | -52.99 | 0.298 | 97.38 | 246.51 | -187.42 | -49.31 | 8.63 | 12.26 | 11.83 | 0.154
245 | -357.65 | 30.5 | 45 | -300 | -95.69 | 0.288 | 111.74 | 357.10 | -144.87 | -61.53 | 14.48 | 11.98 | 11.55 | 0.141
245 | -357.65 | 30.5 | 50 | -300 | -72.99 | 0.297 | 103.84 | 313.52 | -161.29 | -56.69 | 12.18 | 12.19 | 11.77 | 0.154
245 | -357.65 | 30.5 | 40 | -320 | -138.39 | 0.279 | 105.91 | 305.24 | -164.68 | -55.79 | 11.73 | 11.64 | 11.17 | 0.150
245 | -357.65 | 30.5 | 45 | -320 | -115.69 | 0.282 | 102.59 | 299.47 | -166.70 | -55.14 | 11.43 | 11.90 | 11.48 | 0.158
245 | -357.65 | 30.5 | 50 | -320 | -92.99 | 0.292 | 99.53 | 296.26 | -167.75 | -54.77 | 11.27 | 12.11 | 11.71 | 0.158
245 | -357.65 | 30.5 | 40 | -340 | -158.39 | 0.281 | 102.55 | 295.03 | -168.46 | -54.65 | 11.20 | 11.53 | 11.07 | 0.161
245 | -357.65 | 30.5 | 45 | -340 | -135.69 | 0.286 | 99.67 | 293.38 | -168.87 | -54.45 | 11.11 | 11.81 | 11.40 | 0.169
245 | -357.65 | 30.5 | 50 | -340 | -112.99 | 0.294 | 96.74 | 292.15 | -169.14 | -54.30 | 11.05 | 12.04 | 11.64 | 0.178
245 | -357.65 | 30.5 | 40 | -360 | -178.39 | 0.283 | 99.95 | 291.81 | -169.51 | -54.28 | 11.03 | 11.41 | 10.97 | 0.172
245 | -357.65 | 30.5 | 45 | -360 | -155.69 | 0.291 | 97.08 | 290.93 | -169.62 | -54.16 | 10.99 | 11.71 | 11.31 | 0.180
245 | -357.65 | 30.5 | 50 | -360 | -132.99 | 0.300 | 94.19 | 290.24 | -169.71 | -54.07 | 10.95 | 11.96 | 11.57 | 0.189
245 | -357.65 | 30.5 | 40 | -380 | -198.39 | 0.287 | 97.50 | 290.17 | -169.98 | -54.08 | 10.95 | 11.28 | 10.88 | 0.182
245 | -357.65 | 30.5 | 45 | -380 | -175.69 | 0.296 | 94.58 | 289.59 | -169.98 | -54.00 | 10.92 | 11.61 | 11.23 | 0.191
245 | -357.65 | 31.0 | 50 | -300 | -72.99 | 0.287 | 117.97 | 398.96 | -129.21 | -66.20 | 16.68 | 12.19 | 11.75 | 0.142
245 | -357.65 | 31.0 | 55 | -300 | -50.29 | 0.293 | 105.68 | 318.19 | -159.61 | -57.21 | 12.42 | 12.37 | 11.92 | 0.160
245 | -357.65 | 31.0 | 40 | -320 | -138.39 | 0.293 | 112.34 | 325.96 | -157.06 | -58.11 | 12.83 | 11.64 | 11.11 | 0.146
245 | -357.65 | 31.0 | 45 | -320 | -115.69 | 0.285 | 107.49 | 307.42 | -163.97 | -56.04 | 11.85 | 11.90 | 11.44 | 0.156
245 | -357.65 | 31.0 | 50 | -320 | -92.99 | 0.284 | 104.01 | 300.57 | -166.39 | -55.27 | 11.49 | 12.12 | 11.69 | 0.165
245 | -357.65 | 31.0 | 55 | -320 | -70.29 | 0.287 | 100.83 | 296.93 | -167.59 | -54.85 | 11.30 | 12.30 | 11.87 | 0.173
245 | -357.65 | 31.0 | 40 | -340 | -158.39 | 0.290 | 106.81 | 298.11 | -167.57 | -55.01 | 11.36 | 11.52 | 11.02 | 0.160
245 | -357.65 | 31.0 | 45 | -340 | -135.69 | 0.284 | 103.86 | 295.55 | -168.35 | -54.71 | 11.22 | 11.81 | 11.37 | 0.168
245 | -357.65 | 31.0 | 50 | -340 | -112.99 | 0.287 | 100.95 | 293.78 | -168.83 | -54.50 | 11.13 | 12.04 | 11.62 | 0.176
245 | -357.65 | 31.0 | 55 | -340 | -90.29 | 0.290 | 97.96 | 292.45 | -169.11 | -54.34 | 11.07 | 12.24 | 11.82 | 0.185
245 | -357.65 | 31.0 | 60 | -340 | -67.59 | 0.298 | 94.95 | 291.43 | -169.31 | -54.21 | 11.02 | 12.41 | 11.98 | 0.193
245 | -357.65 | 31.0 | 40 | -360 | -178.39 | 0.287 | 104.06 | 293.18 | -169.29 | -54.45 | 11.10 | 11.40 | 10.92 | 0.170
245 | -357.65 | 31.0 | 45 | -360 | -155.69 | 0.286 | 101.20 | 292.08 | -169.50 | -54.32 | 11.04 | 11.71 | 11.28 | 0.179
245 | -357.65 | 31.0 | 50 | -360 | -132.99 | 0.289 | 98.35 | 291.21 | -169.65 | -54.21 | 11.00 | 11.96 | 11.55 | 0.187
245 | -357.65 | 31.0 | 55 | -360 | -110.29 | 0.294 | 95.34 | 290.44 | -169.72 | -54.10 | 10.96 | 12.17 | 11.76 | 0.196
245 | -357.65 | 31.0 | 40 | -380 | -198.39 | 0.291 | 101.56 | 291.02 | -169.94 | -54.20 | 10.99 | 11.27 | 10.81 | 0.181
245 | -357.65 | 31.0 | 45 | -380 | -175.69 | 0.293 | 98.68 | 290.35 | -169.99 | -54.11 | 10.95 | 11.60 | 11.19 | 0.189
245 | -357.65 | 31.0 | 50 | -380 | -152.99 | 0.295 | 95.73 | 289.75 | -170.01 | -54.03 | 10.93 | 11.87 | 11.48 | 0.198
245 | -357.65 | 31.5 | 60 | -300 | -27.59 | 0.294 | 107.69 | 324.68 | -157.22 | -57.94 | 12.76 | 12.53 | 12.05 | 0.166
245 | -357.65 | 31.5 | 65 | -300 | -4.89 | 0.298 | 102.71 | 306.80 | -163.87 | -55.95 | 11.82 | 12.67 | 12.18 | 0.177
245 | -357.65 | 31.5 | 50 | -320 | -92.99 | 0.294 | 109.08 | 310.08 | -163.05 | -56.34 | 11.99 | 12.12 | 11.65 | 0.163
245 | -357.65 | 31.5 | 55 | -320 | -70.29 | 0.287 | 105.40 | 301.82 | -166.02 | -55.41 | 11.55 | 12.31 | 11.85 | 0.172
245 | -357.65 | 31.5 | 60 | -320 | -47.59 | 0.289 | 102.11 | 297.68 | -167.40 | -54.94 | 11.34 | 12.47 | 12.01 | 0.180
245 | -357.65 | 31.5 | 65 | -320 | -24.89 | 0.292 | 98.92 | 295.13 | -168.17 | -54.64 | 11.21 | 12.62 | 12.13 | 0.189
245 | -357.65 | 31.5 | 70 | -320 | -2.18 | 0.298 | 95.75 | 293.36 | -168.62 | -54.43 | 11.12 | 12.75 | 12.25 | 0.198
245 | -357.65 | 31.5 | 50 | -340 | -112.99 | 0.290 | 105.21 | 296.14 | -168.26 | -54.79 | 11.25 | 12.04 | 11.59 | 0.175
245 | -357.65 | 31.5 | 55 | -340 | -90.29 | 0.289 | 102.17 | 294.19 | -168.76 | -54.56 | 11.15 | 12.24 | 11.79 | 0.183
245 | -357.65 | 31.5 | 60 | -340 | -67.59 | 0.292 | 99.14 | 292.78 | -169.09 | -54.38 | 11.08 | 12.42 | 11.96 | 0.192
245 | -357.65 | 31.5 | 65 | -340 | -44.89 | 0.294 | 96.08 | 291.69 | -169.30 | -54.24 | 11.03 | 12.57 | 12.10 | 0.201
245 | -357.65 | 31.5 | 45 | -360 | -155.69 | 0.294 | 105.32 | 293.53 | -169.26 | -54.50 | 11.11 | 11.71 | 11.24 | 0.177
245 | -357.65 | 31.5 | 50 | -360 | -132.99 | 0.289 | 102.44 | 292.37 | -169.50 | -54.36 | 11.06 | 11.96 | 11.52 | 0.186
245 | -357.65 | 31.5 | 55 | -360 | -110.29 | 0.292 | 99.51 | 291.44 | -169.65 | -54.24 | 11.01 | 12.17 | 11.74 | 0.194
245 | -357.65 | 31.5 | 60 | -360 | -87.59 | 0.294 | 96.47 | 290.65 | -169.73 | -54.13 | 10.97 | 12.35 | 11.92 | 0.203
245 | -357.65 | 31.5 | 65 | -360 | -64.89 | 0.299 | 93.35 | 289.96 | -169.77 | -54.04 | 10.94 | 12.51 | 12.05 | 0.212
245 | -357.65 | 31.5 | 45 | -380 | -175.69 | 0.299 | 102.80 | 291.26 | -169.96 | -54.24 | 11.00 | 11.60 | 11.14 | 0.188
245 | -357.65 | 31.5 | 50 | -380 | -152.99 | 0.299 | 99.86 | 290.55 | -170.01 | -54.14 | 10.96 | 11.87 | 11.44 | 0.196
245 | -357.65 | 32.0 | 65 | -300 | -4.89 | 0.294 | 110.10 | 334.38 | -153.63 | -59.02 | 13.27 | 12.68 | 12.17 | 0.172
245 | -357.65 | 32.0 | 70 | -300 | 17.82 | 0.298 | 104.17 | 309.37 | -162.97 | -56.24 | 11.96 | 12.81 | 12.28 | 0.183
245 | -357.65 | 32.0 | 60 | -320 | -47.59 | 0.293 | 106.77 | 303.26 | -165.56 | -55.58 | 11.63 | 12.48 | 11.99 | 0.178
245 | -357.65 | 32.0 | 65 | -320 | -24.89 | 0.292 | 103.36 | 298.50 | -167.18 | -55.04 | 11.38 | 12.63 | 12.12 | 0.187
245 | -357.65 | 32.0 | 70 | -320 | -2.18 | 0.294 | 100.12 | 295.68 | -168.04 | -54.71 | 11.23 | 12.76 | 12.23 | 0.196
245 | -357.65 | 32.0 | 55 | -340 | -90.29 | 0.298 | 106.47 | 296.74 | -168.11 | -54.86 | 11.28 | 12.25 | 11.77 | 0.181
245 | -357.65 | 32.0 | 60 | -340 | -67.59 | 0.292 | 103.41 | 294.64 | -168.70 | -54.61 | 11.18 | 12.42 | 11.94 | 0.190
245 | -357.65 | 32.0 | 65 | -340 | -44.89 | 0.294 | 100.31 | 293.13 | -169.05 | -54.43 | 11.10 | 12.57 | 12.08 | 0.199
245 | -357.65 | 32.0 | 70 | -340 | -22.18 | 0.297 | 97.19 | 291.96 | -169.28 | -54.28 | 11.04 | 12.71 | 12.20 | 0.208
245 | -357.65 | 32.0 | 55 | -360 | -110.29 | 0.295 | 103.65 | 292.67 | -169.48 | -54.40 | 11.07 | 12.17 | 11.71 | 0.192
245 | -357.65 | 32.0 | 60 | -360 | -87.59 | 0.295 | 100.66 | 291.69 | -169.65 | -54.27 | 11.02 | 12.36 | 11.88 | 0.201
245 | -357.65 | 32.0 | 65 | -360 | -64.89 | 0.299 | 97.56 | 290.84 | -169.73 | -54.16 | 10.98 | 12.52 | 12.03 | 0.210
245 | -357.65 | 32.5 | 70 | -300 | 17.82 | 0.294 | 113.23 | 350.51 | -147.60 | -60.82 | 14.12 | 12.81 | 12.26 | 0.176
245 | -357.65 | 32.5 | 70 | -320 | -2.18 | 0.295 | 104.60 | 299.42 | -166.92 | -55.15 | 11.43 | 12.77 | 12.23 | 0.194
245 | -357.65 | 32.5 | 65 | -340 | -44.89 | 0.298 | 104.60 | 295.13 | -168.62 | -54.68 | 11.20 | 12.58 | 12.06 | 0.197
245 | -357.65 | 32.5 | 70 | -340 | -22.18 | 0.297 | 101.44 | 293.48 | -169.01 | -54.48 | 11.12 | 12.72 | 12.18 | 0.205
250 | -342.65 | 30.0 | 45 | -240 | -31.68 | 0.295 | 104.75 | 273.25 | -173.89 | -52.01 | 10.09 | 12.26 | 11.89 | 0.122
250 | -342.65 | 30.0 | 50 | -240 | -8.53 | 0.295 | 102.17 | 271.48 | -174.40 | -51.80 | 10.00 | 12.43 | 12.08 | 0.129
250 | -342.65 | 30.0 | 40 | -260 | -74.82 | 0.289 | 104.76 | 269.69 | -175.31 | -51.62 | 9.90 | 11.99 | 11.61 | 0.125
250 | -342.65 | 30.0 | 45 | -260 | -51.68 | 0.281 | 102.01 | 266.39 | -176.41 | -51.24 | 9.73 | 12.20 | 11.83 | 0.132
250 | -342.65 | 30.0 | 50 | -260 | -28.53 | 0.290 | 98.95 | 261.25 | -178.23 | -50.66 | 9.46 | 12.37 | 12.02 | 0.140
250 | -342.65 | 30.0 | 40 | -280 | -94.82 | 0.275 | 100.79 | 253.29 | -181.54 | -49.80 | 9.04 | 11.91 | 11.52 | 0.136
250 | -342.65 | 30.0 | 45 | -280 | -71.68 | 0.273 | 95.62 | 232.52 | -189.51 | -47.50 | 7.94 | 12.12 | 11.77 | 0.147
250 | -342.65 | 30.0 | 40 | -300 | -114.82 | 0.269 | 121.35 | 440.33 | -110.21 | -70.53 | 18.92 | 11.82 | 11.44 | 0.122
250 | -342.65 | 30.0 | 45 | -300 | -91.68 | 0.277 | 106.36 | 332.76 | -150.53 | -58.56 | 13.25 | 12.05 | 11.70 | 0.142
250 | -342.65 | 30.0 | 50 | -300 | -68.53 | 0.284 | 101.30 | 312.31 | -158.17 | -56.28 | 12.17 | 12.24 | 11.90 | 0.152
250 | -342.65 | 30.0 | 55 | -300 | -45.38 | 0.294 | 97.61 | 303.55 | -161.34 | -55.29 | 11.71 | 12.41 | 12.07 | 0.161
250 | -342.65 | 30.0 | 40 | -320 | -134.82 | 0.273 | 103.35 | 304.49 | -161.38 | -55.43 | 11.75 | 11.72 | 11.34 | 0.148
250 | -342.65 | 30.0 | 45 | -320 | -111.68 | 0.280 | 100.18 | 299.36 | -163.17 | -54.85 | 11.48 | 11.97 | 11.63 | 0.156
250 | -342.65 | 30.0 | 50 | -320 | -88.53 | 0.288 | 97.14 | 296.06 | -164.25 | -54.46 | 11.31 | 12.17 | 11.84 | 0.165
250 | -342.65 | 30.0 | 40 | -340 | -154.82 | 0.277 | 99.99 | 294.30 | -165.13 | -54.29 | 11.22 | 11.62 | 11.26 | 0.160
250 | -342.65 | 30.0 | 45 | -340 | -131.68 | 0.284 | 97.17 | 292.52 | -165.64 | -54.08 | 11.12 | 11.88 | 11.56 | 0.168
250 | -342.65 | 30.0 | 50 | -340 | -108.53 | 0.298 | 94.29 | 291.10 | -165.98 | -53.90 | 11.05 | 12.10 | 11.78 | 0.176
250 | -342.65 | 30.0 | 40 | -360 | -174.82 | 0.282 | 97.34 | 290.46 | -166.45 | -53.85 | 11.01 | 11.51 | 11.16 | 0.171
250 | -342.65 | 30.0 | 45 | -360 | -151.68 | 0.295 | 94.53 | 289.48 | -166.63 | -53.73 | 10.97 | 11.79 | 11.47 | 0.179
250 | -342.65 | 30.5 | 55 | -240 | 14.62 | 0.295 | 103.67 | 272.16 | -174.26 | -51.89 | 10.03 | 12.58 | 12.20 | 0.135
250 | -342.65 | 30.5 | 60 | -240 | 37.77 | 0.299 | 100.92 | 270.00 | -174.92 | -51.63 | 9.92 | 12.72 | 12.32 | 0.143
250 | -342.65 | 30.5 | 45 | -260 | -51.68 | 0.300 | 106.33 | 270.57 | -175.10 | -51.73 | 9.95 | 12.20 | 11.81 | 0.131
250 | -342.65 | 30.5 | 50 | -260 | -28.53 | 0.289 | 103.58 | 267.63 | -176.05 | -51.39 | 9.79 | 12.38 | 12.00 | 0.138
250 | -342.65 | 30.5 | 55 | -260 | -5.38 | 0.286 | 100.56 | 263.21 | -177.59 | -50.89 | 9.56 | 12.53 | 12.15 | 0.146
250 | -342.65 | 30.5 | 60 | -260 | 17.77 | 0.294 | 97.06 | 255.62 | -180.35 | -50.04 | 9.16 | 12.67 | 12.29 | 0.155
250 | -342.65 | 30.5 | 45 | -280 | -71.68 | 0.287 | 102.65 | 256.79 | -180.30 | -50.20 | 9.22 | 12.13 | 11.75 | 0.143
250 | -342.65 | 30.5 | 50 | -280 | -48.53 | 0.278 | 98.19 | 241.58 | -186.06 | -48.51 | 8.42 | 12.31 | 11.94 | 0.152
250 | -342.65 | 30.5 | 50 | -300 | -68.53 | 0.274 | 109.38 | 346.48 | -145.43 | -60.09 | 13.97 | 12.25 | 11.88 | 0.147
250 | -342.65 | 30.5 | 55 | -300 | -45.38 | 0.280 | 103.16 | 316.75 | -156.57 | -56.78 | 12.40 | 12.42 | 12.06 | 0.158
250 | -342.65 | 30.5 | 60 | -300 | -22.23 | 0.287 | 99.12 | 305.75 | -160.59 | -55.54 | 11.82 | 12.57 | 12.20 | 0.168
250 | -342.65 | 30.5 | 65 | -300 | 0.91 | 0.297 | 95.66 | 299.95 | -162.62 | -54.88 | 11.52 | 12.71 | 12.32 | 0.177
250 | -342.65 | 30.5 | 40 | -320 | -134.82 | 0.272 | 108.96 | 318.57 | -156.30 | -57.01 | 12.49 | 11.72 | 11.31 | 0.146
250 | -342.65 | 30.5 | 45 | -320 | -111.68 | 0.275 | 105.00 | 306.83 | -160.60 | -55.69 | 11.87 | 11.97 | 11.60 | 0.155
250 | -342.65 | 30.5 | 50 | -320 | -88.53 | 0.277 | 101.67 | 300.77 | -162.74 | -55.01 | 11.56 | 12.18 | 11.82 | 0.163
250 | -342.65 | 30.5 | 55 | -320 | -65.38 | 0.283 | 98.55 | 297.02 | -163.99 | -54.58 | 11.36 | 12.36 | 12.00 | 0.172
250 | -342.65 | 30.5 | 60 | -320 | -42.23 | 0.292 | 95.48 | 294.43 | -164.79 | -54.28 | 11.23 | 12.52 | 12.15 | 0.180
250 | -342.65 | 30.5 | 40 | -340 | -154.82 | 0.275 | 104.31 | 297.69 | -164.14 | -54.69 | 11.39 | 11.61 | 11.21 | 0.158
250 | -342.65 | 30.5 | 45 | -340 | -131.68 | 0.277 | 101.42 | 295.03 | -164.97 | -54.38 | 11.25 | 11.88 | 11.52 | 0.166
250 | -342.65 | 30.5 | 50 | -340 | -108.53 | 0.279 | 98.52 | 293.08 | -165.53 | -54.15 | 11.15 | 12.10 | 11.76 | 0.175
250 | -342.65 | 30.5 | 55 | -340 | -85.38 | 0.288 | 95.59 | 291.56 | -165.91 | -53.96 | 11.07 | 12.29 | 11.94 | 0.183
250 | -342.65 | 30.5 | 40 | -360 | -174.82 | 0.283 | 101.48 | 292.10 | -166.13 | -54.05 | 11.10 | 11.50 | 11.11 | 0.169
250 | -342.65 | 30.5 | 45 | -360 | -151.68 | 0.284 | 98.67 | 290.84 | -166.40 | -53.90 | 11.03 | 11.79 | 11.43 | 0.177
250 | -342.65 | 30.5 | 50 | -360 | -128.53 | 0.289 | 95.81 | 289.80 | -166.60 | -53.77 | 10.98 | 12.03 | 11.69 | 0.186
250 | -342.65 | 30.5 | 40 | -380 | -194.82 | 0.295 | 98.92 | 289.41 | -166.98 | -53.74 | 10.96 | 11.38 | 10.99 | 0.180
250 | -342.65 | 30.5 | 45 | -380 | -171.68 | 0.297 | 96.10 | 288.63 | -167.08 | -53.64 | 10.92 | 11.69 | 11.35 | 0.189
250 | -342.65 | 31.0 | 65 | -240 | 60.91 | 0.298 | 102.71 | 270.76 | -174.70 | -51.72 | 9.96 | 12.85 | 12.41 | 0.150
250 | -342.65 | 31.0 | 55 | -260 | -5.38 | 0.300 | 105.09 | 268.73 | -175.74 | -51.52 | 9.85 | 12.54 | 12.13 | 0.145
250 | -342.65 | 31.0 | 60 | -260 | 17.77 | 0.289 | 102.12 | 264.87 | -177.05 | -51.08 | 9.65 | 12.68 | 12.27 | 0.153
250 | -342.65 | 31.0 | 65 | -260 | 40.91 | 0.292 | 98.72 | 258.56 | -179.30 | -50.37 | 9.32 | 12.80 | 12.38 | 0.161
250 | -342.65 | 31.0 | 70 | -260 | 64.06 | 0.296 | 94.45 | 246.14 | -183.96 | -48.99 | 8.66 | 12.92 | 12.49 | 0.171
250 | -342.65 | 31.0 | 50 | -280 | -48.53 | 0.298 | 104.41 | 259.61 | -179.33 | -50.52 | 9.37 | 12.32 | 11.93 | 0.149
250 | -342.65 | 31.0 | 55 | -280 | -25.38 | 0.286 | 100.39 | 247.96 | -183.68 | -49.22 | 8.75 | 12.48 | 12.09 | 0.158
250 | -342.65 | 31.0 | 60 | -280 | -2.23 | 0.282 | 93.42 | 215.04 | -196.45 | -45.59 | 7.01 | 12.63 | 12.22 | 0.171
250 | -342.65 | 31.0 | 70 | -280 | 44.06 | 0.296 | 106.69 | 362.06 | -139.21 | -61.79 | 14.80 | 12.88 | 12.44 | 0.164
250 | -342.65 | 31.0 | 55 | -300 | -45.38 | 0.273 | 113.41 | 370.56 | -136.58 | -62.78 | 15.24 | 12.42 | 12.04 | 0.150
250 | -342.65 | 31.0 | 60 | -300 | -22.23 | 0.279 | 105.19 | 322.66 | -154.42 | -57.44 | 12.71 | 12.58 | 12.18 | 0.164
250 | -342.65 | 31.0 | 65 | -300 | 0.91 | 0.283 | 100.71 | 308.43 | -159.67 | -55.85 | 11.96 | 12.71 | 12.30 | 0.174
250 | -342.65 | 31.0 | 70 | -300 | 24.06 | 0.291 | 97.06 | 301.51 | -162.14 | -55.07 | 11.60 | 12.84 | 12.41 | 0.184
250 | -342.65 | 31.0 | 40 | -320 | -134.82 | 0.277 | 120.24 | 380.32 | -133.16 | -63.89 | 15.75 | 11.72 | 11.26 | 0.137
250 | -342.65 | 31.0 | 45 | -320 | -111.68 | 0.279 | 111.15 | 325.02 | -153.96 | -57.73 | 12.83 | 11.97 | 11.56 | 0.151
250 | -342.65 | 31.0 | 50 | -320 | -88.53 | 0.277 | 106.71 | 309.69 | -159.64 | -56.02 | 12.02 | 12.18 | 11.80 | 0.161
250 | -342.65 | 31.0 | 55 | -320 | -65.38 | 0.279 | 103.17 | 302.38 | -162.23 | -55.20 | 11.64 | 12.36 | 11.98 | 0.170
250 | -342.65 | 31.0 | 60 | -320 | -42.23 | 0.282 | 99.92 | 298.07 | -163.68 | -54.70 | 11.41 | 12.52 | 12.13 | 0.178
250 | -342.65 | 31.0 | 65 | -320 | -19.09 | 0.287 | 96.77 | 295.17 | -164.58 | -54.37 | 11.26 | 12.67 | 12.27 | 0.187
250 | -342.65 | 31.0 | 70 | -320 | 4.06 | 0.297 | 93.62 | 293.07 | -165.18 | -54.12 | 11.16 | 12.80 | 12.37 | 0.196
250 | -342.65 | 31.0 | 40 | -340 | -154.82 | 0.285 | 108.98 | 303.34 | -162.34 | -55.34 | 11.68 | 11.61 | 11.16 | 0.157
250 | -342.65 | 31.0 | 45 | -340 | -131.68 | 0.280 | 105.79 | 298.80 | -163.83 | -54.82 | 11.45 | 11.88 | 11.49 | 0.165
250 | -342.65 | 31.0 | 50 | -340 | -108.53 | 0.280 | 102.79 | 295.82 | -164.77 | -54.47 | 11.29 | 12.11 | 11.74 | 0.173
250 | -342.65 | 31.0 | 55 | -340 | -85.38 | 0.282 | 99.83 | 293.67 | -165.39 | -54.22 | 11.18 | 12.30 | 11.92 | 0.181
250 | -342.65 | 31.0 | 60 | -340 | -62.23 | 0.284 | 96.85 | 292.03 | -165.83 | -54.02 | 11.10 | 12.47 | 12.09 | 0.190
250 | -342.65 | 31.0 | 65 | -340 | -39.09 | 0.292 | 93.83 | 290.72 | -166.12 | -53.86 | 11.03 | 12.62 | 12.22 | 0.199
250 | -342.65 | 31.0 | 40 | -360 | -174.82 | 0.294 | 105.64 | 294.26 | -165.60 | -54.32 | 11.21 | 11.49 | 11.05 | 0.168
250 | -342.65 | 31.0 | 45 | -360 | -151.68 | 0.289 | 102.84 | 292.59 | -166.04 | -54.12 | 11.12 | 11.79 | 11.40 | 0.176
250 | -342.65 | 31.0 | 50 | -360 | -128.53 | 0.291 | 99.99 | 291.25 | -166.35 | -53.95 | 11.05 | 12.03 | 11.67 | 0.184
250 | -342.65 | 31.0 | 55 | -360 | -105.38 | 0.293 | 97.08 | 290.15 | -166.57 | -53.82 | 11.00 | 12.23 | 11.86 | 0.193
250 | -342.65 | 31.0 | 60 | -360 | -82.23 | 0.298 | 94.10 | 289.21 | -166.72 | -53.70 | 10.95 | 12.41 | 12.04 | 0.202
250 | -342.65 | 31.5 | 65 | -260 | 40.91 | 0.295 | 103.82 | 266.44 | -176.68 | -51.27 | 9.73 | 12.81 | 12.36 | 0.159
250 | -342.65 | 31.5 | 70 | -260 | 64.06 | 0.292 | 100.32 | 260.98 | -178.47 | -50.64 | 9.44 | 12.93 | 12.47 | 0.168
250 | -342.65 | 31.5 | 60 | -280 | -2.23 | 0.297 | 102.30 | 252.67 | -181.93 | -49.75 | 9.00 | 12.64 | 12.20 | 0.164
250 | -342.65 | 31.5 | 65 | -280 | 20.91 | 0.287 | 96.78 | 230.45 | -190.46 | -47.29 | 7.83 | 12.77 | 12.33 | 0.175
250 | -342.65 | 31.5 | 60 | -300 | -22.23 | 0.275 | 120.95 | 422.60 | -117.00 | -68.57 | 17.98 | 12.58 | 12.17 | 0.151
250 | -342.65 | 31.5 | 65 | -300 | 0.91 | 0.281 | 107.46 | 330.96 | -151.36 | -58.37 | 13.15 | 12.72 | 12.28 | 0.170
250 | -342.65 | 31.5 | 70 | -300 | 24.06 | 0.284 | 102.34 | 311.74 | -158.50 | -56.22 | 12.14 | 12.85 | 12.40 | 0.181
250 | -342.65 | 31.5 | 45 | -320 | -111.68 | 0.274 | 129.58 | 448.96 | -107.61 | -71.54 | 19.36 | 11.97 | 11.53 | 0.136
250 | -342.65 | 31.5 | 50 | -320 | -88.53 | 0.285 | 113.62 | 334.21 | -150.57 | -58.76 | 13.31 | 12.19 | 11.77 | 0.157
250 | -342.65 | 31.5 | 55 | -320 | -65.38 | 0.282 | 108.42 | 313.20 | -158.38 | -56.42 | 12.21 | 12.37 | 11.96 | 0.167
250 | -342.65 | 31.5 | 60 | -320 | -42.23 | 0.282 | 104.67 | 304.28 | -161.61 | -55.42 | 11.74 | 12.53 | 12.11 | 0.176
250 | -342.65 | 31.5 | 65 | -320 | -19.09 | 0.285 | 101.30 | 299.27 | -163.33 | -54.84 | 11.48 | 12.67 | 12.25 | 0.185
250 | -342.65 | 31.5 | 70 | -320 | 4.06 | 0.287 | 98.05 | 296.01 | -164.36 | -54.47 | 11.31 | 12.80 | 12.37 | 0.194
250 | -342.65 | 31.5 | 45 | -340 | -131.68 | 0.297 | 110.46 | 305.26 | -161.66 | -55.56 | 11.78 | 11.88 | 11.45 | 0.163
250 | -342.65 | 31.5 | 50 | -340 | -108.53 | 0.289 | 107.23 | 300.04 | -163.46 | -54.96 | 11.51 | 12.11 | 11.70 | 0.171
250 | -342.65 | 31.5 | 55 | -340 | -85.38 | 0.284 | 104.19 | 296.70 | -164.55 | -54.58 | 11.34 | 12.30 | 11.90 | 0.180
250 | -342.65 | 31.5 | 60 | -340 | -62.23 | 0.286 | 101.15 | 294.32 | -165.25 | -54.30 | 11.21 | 12.47 | 12.07 | 0.188
250 | -342.65 | 31.5 | 65 | -340 | -39.09 | 0.289 | 98.09 | 292.54 | -165.73 | -54.09 | 11.12 | 12.62 | 12.20 | 0.197
250 | -342.65 | 31.5 | 70 | -340 | -15.94 | 0.293 | 95.00 | 291.12 | -166.05 | -53.91 | 11.05 | 12.76 | 12.32 | 0.206
250 | -342.65 | 31.5 | 50 | -360 | -128.53 | 0.296 | 104.15 | 293.11 | -165.94 | -54.18 | 11.15 | 12.03 | 11.64 | 0.183
250 | -342.65 | 31.5 | 55 | -360 | -105.38 | 0.298 | 101.27 | 291.68 | -166.29 | -54.01 | 11.07 | 12.24 | 11.84 | 0.191
250 | -342.65 | 32.0 | 70 | -300 | 24.06 | 0.284 | 110.22 | 343.49 | -146.69 | -59.76 | 13.81 | 12.85 | 12.38 | 0.175
250 | -342.65 | 32.0 | 55 | -320 | -65.38 | 0.290 | 116.67 | 348.43 | -145.28 | -60.35 | 14.06 | 12.37 | 11.95 | 0.161
250 | -342.65 | 32.0 | 60 | -320 | -42.23 | 0.288 | 110.29 | 317.75 | -156.77 | -56.93 | 12.45 | 12.54 | 12.10 | 0.173
250 | -342.65 | 32.0 | 65 | -320 | -19.09 | 0.285 | 106.18 | 306.51 | -160.85 | -55.67 | 11.85 | 12.68 | 12.23 | 0.183
250 | -342.65 | 32.0 | 70 | -320 | 4.06 | 0.287 | 102.65 | 300.62 | -162.90 | -55.00 | 11.55 | 12.81 | 12.35 | 0.192
250 | -342.65 | 32.0 | 55 | -340 | -85.38 | 0.299 | 108.69 | 301.47 | -163.03 | -55.13 | 11.58 | 12.31 | 11.89 | 0.178
250 | -342.65 | 32.0 | 60 | -340 | -62.23 | 0.292 | 105.54 | 297.65 | -164.28 | -54.69 | 11.39 | 12.48 | 12.06 | 0.186
250 | -342.65 | 32.0 | 65 | -340 | -39.09 | 0.292 | 102.42 | 295.02 | -165.07 | -54.38 | 11.25 | 12.63 | 12.18 | 0.195
250 | -342.65 | 32.0 | 70 | -340 | -15.94 | 0.297 | 99.32 | 293.07 | -165.61 | -54.15 | 11.15 | 12.76 | 12.32 | 0.204
250 | -342.65 | 32.5 | 60 | -320 | -42.23 | 0.295 | 120.97 | 373.46 | -135.93 | -63.14 | 15.38 | 12.54 | 12.08 | 0.165
250 | -342.65 | 32.5 | 70 | -320 | 4.06 | 0.289 | 107.74 | 309.24 | -159.91 | -55.98 | 12.00 | 12.82 | 12.33 | 0.189
250 | -342.65 | 33.0 | 65 | -320 | -19.09 | 0.295 | 128.82 | 429.49 | -115.03 | -69.38 | 18.34 | 12.69 | 12.20 | 0.164
255 | -327.65 | 30.0 | 45 | -240 | -27.82 | 0.275 | 105.28 | 267.34 | -172.94 | -51.11 | 9.83 | 12.32 | 12.01 | 0.120
255 | -327.65 | 30.0 | 50 | -240 | -4.24 | 0.270 | 102.78 | 265.44 | -173.51 | -50.88 | 9.73 | 12.48 | 12.17 | 0.127
255 | -327.65 | 30.0 | 65 | -240 | 66.48 | 0.296 | 94.20 | 254.87 | -177.08 | -49.68 | 9.18 | 12.87 | 12.54 | 0.150
255 | -327.65 | 30.0 | 40 | -260 | -71.40 | 0.279 | 105.17 | 263.03 | -174.64 | -50.63 | 9.60 | 12.06 | 11.73 | 0.123
255 | -327.65 | 30.0 | 45 | -260 | -47.82 | 0.267 | 102.45 | 259.57 | -175.80 | -50.24 | 9.42 | 12.25 | 11.94 | 0.131
255 | -327.65 | 30.0 | 50 | -260 | -24.24 | 0.265 | 99.48 | 254.56 | -177.58 | -49.67 | 9.16 | 12.42 | 12.12 | 0.138
255 | -327.65 | 30.0 | 55 | -260 | -0.67 | 0.270 | 96.05 | 246.53 | -180.55 | -48.77 | 8.73 | 12.57 | 12.26 | 0.147
255 | -327.65 | 30.0 | 60 | -260 | 22.91 | 0.278 | 91.56 | 231.28 | -186.36 | -47.08 | 7.93 | 12.71 | 12.40 | 0.157
255 | -327.65 | 30.0 | 65 | -260 | 46.48 | 0.287 | 83.51 | 190.61 | -202.34 | -42.61 | 5.77 | 12.83 | 12.50 | 0.172
255 | -327.65 | 30.0 | 40 | -280 | -91.40 | 0.274 | 101.08 | 245.65 | -181.28 | -48.71 | 8.68 | 11.98 | 11.64 | 0.135
255 | -327.65 | 30.0 | 45 | -280 | -67.82 | 0.271 | 96.54 | 228.98 | -187.65 | -46.86 | 7.80 | 12.18 | 11.88 | 0.145
255 | -327.65 | 30.0 | 50 | -280 | -44.24 | 0.278 | 87.59 | 181.50 | -206.37 | -41.65 | 5.28 | 12.36 | 12.06 | 0.161
255 | -327.65 | 30.0 | 60 | -280 | 2.91 | 0.282 | 109.39 | 392.75 | -124.20 | -64.93 | 16.47 | 12.66 | 12.35 | 0.143
255 | -327.65 | 30.0 | 65 | -280 | 26.48 | 0.296 | 99.78 | 333.47 | -146.45 | -58.34 | 13.34 | 12.79 | 12.47 | 0.159
255 | -327.65 | 30.0 | 45 | -300 | -87.82 | 0.264 | 113.52 | 380.91 | -129.06 | -63.65 | 15.84 | 12.11 | 11.80 | 0.133
255 | -327.65 | 30.0 | 50 | -300 | -64.24 | 0.271 | 105.11 | 330.94 | -147.82 | -58.09 | 13.20 | 12.30 | 12.00 | 0.147
255 | -327.65 | 30.0 | 55 | -300 | -40.67 | 0.278 | 100.45 | 313.74 | -154.20 | -56.17 | 12.30 | 12.46 | 12.17 | 0.157
255 | -327.65 | 30.0 | 60 | -300 | -17.09 | 0.290 | 96.77 | 304.97 | -157.37 | -55.18 | 11.84 | 12.61 | 12.30 | 0.166
255 | -327.65 | 30.0 | 40 | -320 | -131.40 | 0.266 | 105.81 | 312.97 | -154.90 | -56.11 | 12.25 | 11.80 | 11.46 | 0.144
255 | -327.65 | 30.0 | 45 | -320 | -107.82 | 0.268 | 102.32 | 304.71 | -157.87 | -55.18 | 11.82 | 12.03 | 11.73 | 0.153
255 | -327.65 | 30.0 | 50 | -320 | -84.24 | 0.275 | 99.14 | 299.59 | -159.65 | -54.60 | 11.55 | 12.23 | 11.94 | 0.161
255 | -327.65 | 30.0 | 55 | -320 | -60.67 | 0.286 | 96.12 | 296.08 | -160.82 | -54.20 | 11.37 | 12.41 | 12.12 | 0.170
255 | -327.65 | 30.0 | 40 | -340 | -151.40 | 0.274 | 101.67 | 296.20 | -161.17 | -54.24 | 11.37 | 11.70 | 11.37 | 0.157
255 | -327.65 | 30.0 | 45 | -340 | -127.82 | 0.276 | 98.84 | 293.68 | -161.95 | -53.95 | 11.24 | 11.95 | 11.66 | 0.165
255 | -327.65 | 30.0 | 50 | -340 | -104.24 | 0.288 | 96.00 | 291.73 | -162.51 | -53.72 | 11.14 | 12.16 | 11.88 | 0.173
255 | -327.65 | 30.0 | 40 | -360 | -171.40 | 0.293 | 98.82 | 290.44 | -163.22 | -53.59 | 11.06 | 11.59 | 11.27 | 0.168
255 | -327.65 | 30.5 | 50 | -240 | -4.24 | 0.288 | 106.86 | 268.06 | -172.80 | -51.20 | 9.87 | 12.49 | 12.16 | 0.127
255 | -327.65 | 30.5 | 55 | -240 | 19.33 | 0.276 | 104.34 | 266.30 | -173.29 | -50.99 | 9.78 | 12.63 | 12.30 | 0.133
255 | -327.65 | 30.5 | 60 | -240 | 42.91 | 0.275 | 101.68 | 264.09 | -173.98 | -50.73 | 9.66 | 12.76 | 12.42 | 0.141
255 | -327.65 | 30.5 | 65 | -240 | 66.48 | 0.280 | 98.86 | 261.15 | -174.92 | -50.39 | 9.51 | 12.88 | 12.53 | 0.148
255 | -327.65 | 30.5 | 70 | -240 | 90.06 | 0.289 | 95.84 | 257.06 | -176.34 | -49.93 | 9.29 | 12.99 | 12.63 | 0.157
255 | -327.65 | 30.5 | 45 | -260 | -47.82 | 0.293 | 106.81 | 264.19 | -174.32 | -50.77 | 9.66 | 12.26 | 11.93 | 0.130
255 | -327.65 | 30.5 | 50 | -260 | -24.24 | 0.278 | 104.12 | 261.15 | -175.32 | -50.42 | 9.50 | 12.43 | 12.10 | 0.137
255 | -327.65 | 30.5 | 55 | -260 | -0.67 | 0.269 | 101.21 | 256.87 | -176.80 | -49.94 | 9.28 | 12.58 | 12.25 | 0.144
255 | -327.65 | 30.5 | 60 | -260 | 22.91 | 0.270 | 97.92 | 250.31 | -179.18 | -49.20 | 8.93 | 12.72 | 12.38 | 0.153
255 | -327.65 | 30.5 | 65 | -260 | 46.48 | 0.272 | 93.91 | 238.81 | -183.50 | -47.92 | 8.33 | 12.84 | 12.50 | 0.162
255 | -327.65 | 30.5 | 70 | -260 | 70.06 | 0.280 | 87.88 | 213.07 | -193.47 | -45.08 | 6.96 | 12.96 | 12.59 | 0.175
255 | -327.65 | 30.5 | 45 | -280 | -67.82 | 0.286 | 103.05 | 249.71 | -179.81 | -49.16 | 8.90 | 12.19 | 11.85 | 0.141
255 | -327.65 | 30.5 | 50 | -280 | -44.24 | 0.278 | 99.07 | 237.30 | -184.49 | -47.78 | 8.24 | 12.37 | 12.04 | 0.150
255 | -327.65 | 30.5 | 55 | -280 | -20.67 | 0.278 | 92.72 | 208.28 | -195.77 | -44.58 | 6.70 | 12.53 | 12.21 | 0.162
255 | -327.65 | 30.5 | 70 | -280 | 50.06 | 0.285 | 102.81 | 347.95 | -141.04 | -59.95 | 14.11 | 12.92 | 12.56 | 0.164
255 | -327.65 | 30.5 | 50 | -300 | -64.24 | 0.263 | 122.28 | 445.09 | -105.14 | -70.80 | 19.22 | 12.30 | 11.98 | 0.132
255 | -327.65 | 30.5 | 55 | -300 | -40.67 | 0.270 | 108.03 | 343.71 | -143.07 | -59.51 | 13.88 | 12.47 | 12.16 | 0.152
255 | -327.65 | 30.5 | 60 | -300 | -17.09 | 0.274 | 102.45 | 319.13 | -152.25 | -56.77 | 12.58 | 12.62 | 12.30 | 0.163
255 | -327.65 | 30.5 | 65 | -300 | 6.48 | 0.281 | 98.44 | 307.96 | -156.34 | -55.52 | 11.99 | 12.75 | 12.42 | 0.172
255 | -327.65 | 30.5 | 70 | -300 | 30.06 | 0.294 | 94.91 | 301.52 | -158.61 | -54.79 | 11.66 | 12.88 | 12.51 | 0.182
255 | -327.65 | 30.5 | 40 | -320 | -131.40 | 0.266 | 112.96 | 340.06 | -144.86 | -59.14 | 13.68 | 11.80 | 11.43 | 0.140
255 | -327.65 | 30.5 | 50 | -320 | -84.24 | 0.271 | 104.05 | 307.55 | -156.91 | -55.51 | 11.96 | 12.24 | 11.92 | 0.159
255 | -327.65 | 30.5 | 55 | -320 | -60.67 | 0.272 | 100.73 | 301.44 | -159.06 | -54.82 | 11.64 | 12.41 | 12.10 | 0.168
255 | -327.65 | 30.5 | 60 | -320 | -37.09 | 0.277 | 97.58 | 297.38 | -160.42 | -54.35 | 11.43 | 12.57 | 12.25 | 0.177
255 | -327.65 | 30.5 | 65 | -320 | -13.52 | 0.291 | 94.49 | 294.46 | -161.35 | -54.01 | 11.28 | 12.71 | 12.37 | 0.185
255 | -327.65 | 30.5 | 40 | -340 | -151.40 | 0.282 | 106.16 | 301.36 | -159.49 | -54.84 | 11.63 | 11.69 | 11.33 | 0.155
255 | -327.65 | 30.5 | 45 | -340 | -127.82 | 0.284 | 103.20 | 297.46 | -160.79 | -54.39 | 11.43 | 11.95 | 11.63 | 0.164
255 | -327.65 | 30.5 | 50 | -340 | -104.24 | 0.287 | 100.28 | 294.63 | -161.68 | -54.06 | 11.28 | 12.17 | 11.86 | 0.172
255 | -327.65 | 30.5 | 55 | -340 | -80.67 | 0.290 | 97.39 | 292.49 | -162.32 | -53.81 | 11.17 | 12.35 | 12.04 | 0.180
255 | -327.65 | 31.0 | 60 | -240 | 42.91 | 0.288 | 105.87 | 267.11 | -173.11 | -51.09 | 9.82 | 12.77 | 12.42 | 0.140
255 | -327.65 | 31.0 | 65 | -240 | 66.48 | 0.278 | 103.21 | 265.09 | -173.70 | -50.85 | 9.71 | 12.89 | 12.51 | 0.147
255 | -327.65 | 31.0 | 70 | -240 | 90.06 | 0.281 | 100.39 | 262.48 | -174.53 | -50.55 | 9.58 | 13.00 | 12.61 | 0.155
255 | -327.65 | 31.0 | 55 | -260 | -0.67 | 0.291 | 105.74 | 262.54 | -174.91 | -50.59 | 9.57 | 12.59 | 12.23 | 0.143
255 | -327.65 | 31.0 | 60 | -260 | 22.91 | 0.277 | 102.87 | 258.84 | -176.17 | -50.16 | 9.38 | 12.72 | 12.37 | 0.151
255 | -327.65 | 31.0 | 65 | -260 | 46.48 | 0.272 | 99.67 | 253.36 | -178.10 | -49.54 | 9.09 | 12.85 | 12.48 | 0.159
255 | -327.65 | 31.0 | 70 | -260 | 70.06 | 0.275 | 95.96 | 244.37 | -181.43 | -48.54 | 8.62 | 12.96 | 12.59 | 0.168
255 | -327.65 | 31.0 | 50 | -280 | -44.24 | 0.299 | 104.93 | 252.97 | -178.67 | -49.53 | 9.07 | 12.37 | 12.03 | 0.147
255 | -327.65 | 31.0 | 55 | -280 | -20.67 | 0.286 | 101.27 | 243.34 | -182.24 | -48.46 | 8.56 | 12.53 | 12.19 | 0.156
255 | -327.65 | 31.0 | 60 | -280 | 2.91 | 0.282 | 96.18 | 223.65 | -189.80 | -46.28 | 7.52 | 12.68 | 12.32 | 0.166
255 | -327.65 | 31.0 | 65 | -280 | 26.48 | 0.294 | 84.57 | 159.25 | -215.43 | -39.23 | 4.10 | 12.81 | 12.43 | 0.186
255 | -327.65 | 31.0 | 60 | -300 | -17.09 | 0.271 | 111.90 | 364.71 | -135.22 | -61.85 | 14.98 | 12.63 | 12.28 | 0.155
255 | -327.65 | 31.0 | 65 | -300 | 6.48 | 0.274 | 104.61 | 326.40 | -149.58 | -57.59 | 12.96 | 12.76 | 12.40 | 0.168
255 | -327.65 | 31.0 | 70 | -300 | 30.06 | 0.277 | 100.17 | 311.64 | -155.02 | -55.94 | 12.19 | 12.88 | 12.51 | 0.179
255 | -327.65 | 31.0 | 45 | -320 | -107.82 | 0.274 | 116.57 | 358.11 | -138.14 | -61.15 | 14.63 | 12.04 | 11.68 | 0.144
255 | -327.65 | 31.0 | 50 | -320 | -84.24 | 0.274 | 110.03 | 324.63 | -150.67 | -57.42 | 12.86 | 12.24 | 11.91 | 0.156
255 | -327.65 | 31.0 | 55 | -320 | -60.67 | 0.277 | 105.84 | 311.03 | -155.68 | -55.90 | 12.15 | 12.42 | 12.08 | 0.165
255 | -327.65 | 31.0 | 60 | -320 | -37.09 | 0.280 | 102.30 | 303.59 | -158.34 | -55.06 | 11.76 | 12.57 | 12.23 | 0.174
255 | -327.65 | 31.0 | 65 | -320 | -13.52 | 0.284 | 99.04 | 298.86 | -159.96 | -54.52 | 11.51 | 12.72 | 12.37 | 0.183
255 | -327.65 | 31.0 | 70 | -320 | 10.06 | 0.290 | 95.85 | 295.53 | -161.02 | -54.14 | 11.34 | 12.84 | 12.47 | 0.192
255 | -327.65 | 31.0 | 45 | -340 | -127.82 | 0.297 | 107.83 | 303.43 | -158.81 | -55.08 | 11.74 | 11.95 | 11.61 | 0.162
255 | -327.65 | 31.0 | 50 | -340 | -104.24 | 0.295 | 104.75 | 298.91 | -160.36 | -54.56 | 11.51 | 12.17 | 11.84 | 0.170
255 | -327.65 | 31.0 | 55 | -340 | -80.67 | 0.297 | 101.75 | 295.71 | -161.39 | -54.19 | 11.34 | 12.36 | 12.02 | 0.178
255 | -327.65 | 31.5 | 65 | -240 | 66.48 | 0.300 | 107.38 | 267.84 | -172.95 | -51.18 | 9.85 | 12.90 | 12.51 | 0.146
255 | -327.65 | 31.5 | 70 | -240 | 90.06 | 0.286 | 104.70 | 266.00 | -173.47 | -50.96 | 9.76 | 13.01 | 12.59 | 0.154
255 | -327.65 | 31.5 | 65 | -260 | 46.48 | 0.288 | 104.45 | 260.52 | -175.63 | -50.36 | 9.47 | 12.86 | 12.46 | 0.157
255 | -327.65 | 31.5 | 70 | -260 | 70.06 | 0.279 | 101.36 | 255.88 | -177.24 | -49.83 | 9.23 | 12.97 | 12.57 | 0.165
255 | -327.65 | 31.5 | 60 | -280 | 2.91 | 0.297 | 103.25 | 247.92 | -180.56 | -48.97 | 8.80 | 12.68 | 12.32 | 0.162
255 | -327.65 | 31.5 | 65 | -280 | 26.48 | 0.288 | 98.85 | 233.62 | -185.97 | -47.38 | 8.05 | 12.81 | 12.43 | 0.171
255 | -327.65 | 31.5 | 70 | -280 | 50.06 | 0.291 | 91.30 | 197.21 | -200.22 | -43.37 | 6.12 | 12.93 | 12.52 | 0.185
255 | -327.65 | 31.5 | 65 | -300 | 6.48 | 0.274 | 118.05 | 405.81 | -119.86 | -66.43 | 17.15 | 12.77 | 12.39 | 0.157
255 | -327.65 | 31.5 | 70 | -300 | 30.06 | 0.279 | 107.24 | 336.80 | -145.72 | -58.75 | 13.51 | 12.89 | 12.50 | 0.173
255 | -327.65 | 31.5 | 50 | -320 | -84.24 | 0.285 | 121.94 | 391.37 | -125.72 | -64.86 | 16.38 | 12.25 | 11.89 | 0.147
255 | -327.65 | 31.5 | 55 | -320 | -60.67 | 0.287 | 112.57 | 334.00 | -147.22 | -58.47 | 13.36 | 12.43 | 12.07 | 0.161
255 | -327.65 | 31.5 | 60 | -320 | -37.09 | 0.288 | 107.71 | 315.43 | -154.11 | -56.40 | 12.38 | 12.58 | 12.21 | 0.171
255 | -327.65 | 31.5 | 65 | -320 | -13.52 | 0.291 | 103.93 | 306.17 | -157.46 | -55.36 | 11.89 | 12.72 | 12.35 | 0.181
255 | -327.65 | 31.5 | 70 | -320 | 10.06 | 0.295 | 100.49 | 300.55 | -159.40 | -54.72 | 11.60 | 12.85 | 12.47 | 0.190
255 | -327.65 | 32.0 | 70 | -280 | 50.06 | 0.297 | 101.12 | 240.67 | -183.34 | -48.17 | 8.42 | 12.94 | 12.52 | 0.177
255 | -327.65 | 32.0 | 70 | -300 | 30.06 | 0.279 | 132.41 | 523.18 | -76.42 | -79.54 | 23.33 | 12.90 | 12.48 | 0.149
255 | -327.65 | 32.0 | 55 | -320 | -60.67 | 0.290 | 132.68 | 473.38 | -95.25 | -74.01 | 20.70 | 12.43 | 12.05 | 0.144
255 | -327.65 | 32.0 | 65 | -320 | -13.52 | 0.298 | 109.73 | 321.19 | -152.03 | -57.04 | 12.68 | 12.73 | 12.34 | 0.177
260 | -312.65 | 30.0 | 40 | -240 | -48.10 | 0.293 | 108.14 | 263.41 | -171.42 | -50.43 | 9.67 | 12.19 | 11.91 | 0.112
260 | -312.65 | 30.0 | 45 | -240 | -24.11 | 0.278 | 105.82 | 261.81 | -171.88 | -50.25 | 9.59 | 12.37 | 12.10 | 0.119
260 | -312.65 | 30.0 | 50 | -240 | -0.12 | 0.268 | 103.39 | 259.86 | -172.47 | -50.02 | 9.49 | 12.52 | 12.27 | 0.125
260 | -312.65 | 30.0 | 55 | -240 | 23.86 | 0.266 | 100.80 | 257.44 | -173.24 | -49.74 | 9.36 | 12.67 | 12.40 | 0.132
260 | -312.65 | 30.0 | 60 | -240 | 47.85 | 0.266 | 98.08 | 254.31 | -174.28 | -49.38 | 9.20 | 12.80 | 12.53 | 0.140
260 | -312.65 | 30.0 | 65 | -240 | 71.84 | 0.272 | 95.14 | 250.08 | -175.75 | -48.90 | 8.98 | 12.91 | 12.63 | 0.148
260 | -312.65 | 30.0 | 70 | -240 | 95.83 | 0.279 | 91.89 | 244.02 | -177.94 | -48.22 | 8.66 | 13.02 | 12.73 | 0.156
260 | -312.65 | 30.0 | 40 | -260 | -68.10 | 0.284 | 105.57 | 256.90 | -173.81 | -49.71 | 9.33 | 12.11 | 11.83 | 0.122
260 | -312.65 | 30.0 | 45 | -260 | -44.11 | 0.273 | 102.96 | 253.47 | -174.98 | -49.31 | 9.15 | 12.30 | 12.04 | 0.129
260 | -312.65 | 30.0 | 50 | -260 | -20.12 | 0.267 | 100.11 | 248.77 | -176.65 | -48.78 | 8.90 | 12.47 | 12.22 | 0.137
260 | -312.65 | 30.0 | 55 | -260 | 3.86 | 0.268 | 96.87 | 241.81 | -179.19 | -48.00 | 8.54 | 12.62 | 12.36 | 0.145
260 | -312.65 | 30.0 | 60 | -260 | 27.85 | 0.270 | 92.99 | 230.47 | -183.47 | -46.74 | 7.94 | 12.75 | 12.48 | 0.154
260 | -312.65 | 30.0 | 65 | -260 | 51.84 | 0.278 | 87.57 | 208.38 | -192.02 | -44.30 | 6.77 | 12.87 | 12.60 | 0.165
260 | -312.65 | 30.0 | 40 | -280 | -88.10 | 0.282 | 101.44 | 239.14 | -180.61 | -47.74 | 8.39 | 12.04 | 11.74 | 0.134
260 | -312.65 | 30.0 | 45 | -280 | -64.11 | 0.279 | 97.39 | 225.37 | -185.86 | -46.21 | 7.66 | 12.24 | 11.98 | 0.143
260 | -312.65 | 30.0 | 50 | -280 | -40.12 | 0.284 | 91.05 | 196.05 | -197.31 | -42.98 | 6.11 | 12.41 | 12.16 | 0.156
260 | -312.65 | 30.0 | 70 | -280 | 55.83 | 0.296 | 99.39 | 337.98 | -141.36 | -58.57 | 13.63 | 12.94 | 12.66 | 0.163
260 | -312.65 | 30.0 | 50 | -300 | -60.12 | 0.265 | 110.72 | 365.54 | -131.48 | -61.68 | 15.08 | 12.35 | 12.10 | 0.139
260 | -312.65 | 30.0 | 55 | -300 | -36.14 | 0.272 | 104.07 | 330.54 | -144.59 | -57.78 | 13.23 | 12.51 | 12.26 | 0.151
260 | -312.65 | 30.0 | 60 | -300 | -12.15 | 0.282 | 99.66 | 315.03 | -150.33 | -56.04 | 12.42 | 12.66 | 12.40 | 0.161
260 | -312.65 | 30.0 | 65 | -300 | 11.84 | 0.297 | 95.98 | 306.23 | -153.52 | -55.06 | 11.96 | 12.79 | 12.52 | 0.171
260 | -312.65 | 30.0 | 40 | -320 | -128.10 | 0.280 | 108.59 | 324.84 | -147.14 | -57.18 | 12.93 | 11.87 | 11.58 | 0.140
260 | -312.65 | 30.0 | 45 | -320 | -104.11 | 0.282 | 104.68 | 312.20 | -151.81 | -55.76 | 12.26 | 12.09 | 11.84 | 0.149
260 | -312.65 | 30.0 | 50 | -320 | -80.12 | 0.285 | 101.30 | 304.63 | -154.53 | -54.91 | 11.87 | 12.29 | 12.04 | 0.158
260 | -312.65 | 30.0 | 55 | -320 | -56.14 | 0.292 | 98.14 | 299.56 | -156.28 | -54.34 | 11.60 | 12.46 | 12.22 | 0.166
260 | -312.65 | 30.5 | 50 | -240 | -0.12 | 0.293 | 107.48 | 262.70 | -171.68 | -50.35 | 9.63 | 12.53 | 12.26 | 0.125
260 | -312.65 | 30.5 | 55 | -240 | 23.86 | 0.277 | 105.03 | 260.93 | -172.19 | -50.15 | 9.54 | 12.67 | 12.40 | 0.132
260 | -312.65 | 30.5 | 60 | -240 | 47.85 | 0.270 | 102.45 | 258.75 | -172.85 | -49.89 | 9.43 | 12.80 | 12.51 | 0.139
260 | -312.65 | 30.5 | 65 | -240 | 71.84 | 0.270 | 99.76 | 256.00 | -173.74 | -49.57 | 9.29 | 12.92 | 12.62 | 0.146
260 | -312.65 | 30.5 | 70 | -240 | 95.83 | 0.271 | 96.85 | 252.38 | -174.97 | -49.16 | 9.10 | 13.03 | 12.71 | 0.154
260 | -312.65 | 30.5 | 45 | -260 | -44.11 | 0.298 | 107.32 | 258.35 | -173.39 | -49.88 | 9.40 | 12.31 | 12.03 | 0.128
260 | -312.65 | 30.5 | 50 | -260 | -20.12 | 0.283 | 104.70 | 255.34 | -174.38 | -49.53 | 9.24 | 12.48 | 12.20 | 0.135
260 | -312.65 | 30.5 | 55 | -260 | 3.86 | 0.275 | 101.91 | 251.34 | -175.76 | -49.08 | 9.04 | 12.63 | 12.35 | 0.143
260 | -312.65 | 30.5 | 60 | -260 | 27.85 | 0.272 | 98.83 | 245.67 | -177.80 | -48.44 | 8.74 | 12.76 | 12.47 | 0.151
260 | -312.65 | 30.5 | 65 | -260 | 51.84 | 0.274 | 95.26 | 236.92 | -181.06 | -47.46 | 8.28 | 12.88 | 12.58 | 0.159
260 | -312.65 | 30.5 | 70 | -260 | 75.83 | 0.278 | 90.71 | 221.50 | -186.93 | -45.75 | 7.46 | 12.99 | 12.68 | 0.170
260 | -312.65 | 30.5 | 45 | -280 | -64.11 | 0.298 | 103.56 | 243.64 | -178.97 | -48.24 | 8.62 | 12.24 | 11.95 | 0.140
260 | -312.65 | 30.5 | 50 | -280 | -40.12 | 0.291 | 99.90 | 233.29 | -182.85 | -47.09 | 8.08 | 12.42 | 12.14 | 0.148
260 | -312.65 | 30.5 | 55 | -280 | -16.14 | 0.290 | 94.97 | 213.89 | -190.34 | -44.95 | 7.05 | 12.57 | 12.29 | 0.159
260 | -312.65 | 30.5 | 55 | -300 | -36.14 | 0.273 | 117.02 | 407.16 | -115.94 | -66.32 | 17.27 | 12.52 | 12.24 | 0.140
260 | -312.65 | 30.5 | 60 | -300 | -12.15 | 0.278 | 107.10 | 343.78 | -139.68 | -59.26 | 13.93 | 12.66 | 12.38 | 0.156
260 | -312.65 | 30.5 | 65 | -300 | 11.84 | 0.282 | 101.81 | 321.52 | -147.96 | -56.77 | 12.76 | 12.80 | 12.50 | 0.167
260 | -312.65 | 30.5 | 70 | -300 | 35.83 | 0.292 | 97.78 | 310.09 | -152.14 | -55.49 | 12.16 | 12.91 | 12.61 | 0.177
260 | -312.65 | 30.5 | 40 | -320 | -128.10 | 0.288 | 118.72 | 377.17 | -127.61 | -63.01 | 15.69 | 11.87 | 11.55 | 0.133
260 | -312.65 | 30.5 | 45 | -320 | -104.11 | 0.290 | 111.35 | 335.07 | -143.40 | -58.32 | 13.47 | 12.10 | 11.82 | 0.146
260 | -312.65 | 30.5 | 50 | -320 | -80.12 | 0.293 | 106.79 | 317.61 | -149.86 | -56.37 | 12.55 | 12.29 | 12.02 | 0.155
260 | -312.65 | 30.5 | 55 | -320 | -56.14 | 0.296 | 103.11 | 307.99 | -153.35 | -55.29 | 12.04 | 12.46 | 12.20 | 0.164
260 | -312.65 | 30.5 | 60 | -320 | -32.15 | 0.299 | 99.81 | 301.87 | -155.51 | -54.60 | 11.72 | 12.61 | 12.33 | 0.173
260 | -312.65 | 31.0 | 60 | -240 | 47.85 | 0.291 | 106.64 | 261.89 | -171.95 | -50.26 | 9.59 | 12.81 | 12.50 | 0.138
260 | -312.65 | 31.0 | 65 | -240 | 71.84 | 0.279 | 104.07 | 259.92 | -172.52 | -50.03 | 9.49 | 12.93 | 12.61 | 0.145
260 | -312.65 | 31.0 | 70 | -240 | 95.83 | 0.273 | 101.36 | 257.48 | -173.28 | -49.75 | 9.36 | 13.04 | 12.69 | 0.152
260 | -312.65 | 31.0 | 60 | -260 | 27.85 | 0.288 | 103.65 | 253.52 | -175.03 | -49.33 | 9.15 | 12.77 | 12.47 | 0.149
260 | -312.65 | 31.0 | 65 | -260 | 51.84 | 0.282 | 100.64 | 248.78 | -176.70 | -48.79 | 8.90 | 12.89 | 12.58 | 0.156
260 | -312.65 | 31.0 | 70 | -260 | 75.83 | 0.282 | 97.28 | 241.80 | -179.24 | -48.01 | 8.53 | 13.00 | 12.67 | 0.165
260 | -312.65 | 31.0 | 60 | -280 | 7.85 | 0.300 | 97.92 | 225.30 | -185.94 | -46.21 | 7.66 | 12.72 | 12.42 | 0.163
260 | -312.65 | 31.0 | 60 | -300 | -12.15 | 0.285 | 131.04 | 520.76 | -73.89 | -79.00 | 23.26 | 12.67 | 12.37 | 0.134
260 | -312.65 | 31.0 | 65 | -300 | 11.84 | 0.285 | 111.27 | 365.52 | -131.73 | -61.69 | 15.08 | 12.81 | 12.50 | 0.159
260 | -312.65 | 31.0 | 70 | -300 | 35.83 | 0.293 | 104.26 | 330.45 | -144.66 | -57.77 | 13.23 | 12.93 | 12.60 | 0.172
260 | -312.65 | 31.0 | 45 | -320 | -104.11 | 0.297 | 126.66 | 432.79 | -106.89 | -69.21 | 18.62 | 12.10 | 11.79 | 0.133
260 | -312.65 | 31.5 | 70 | -240 | 95.83 | 0.292 | 105.62 | 260.98 | -172.24 | -50.16 | 9.54 | 13.05 | 12.69 | 0.151
260 | -312.65 | 31.5 | 70 | -260 | 75.83 | 0.295 | 102.35 | 251.37 | -175.81 | -49.08 | 9.04 | 13.01 | 12.65 | 0.162
260 | -312.65 | 31.5 | 70 | -300 | 35.83 | 0.298 | 117.23 | 406.47 | -116.24 | -66.24 | 17.24 | 12.93 | 12.60 | 0.160