Shifting Milestones of Natural Sciences:
The Ancient Egyptian Discovery of Algol’s Period Confirmed

Lauri Jetsu1,*, Sebastian Porceddu1

1 Department of Physics, P.O. Box 64, FI-00014 University of Helsinki, Finland
*E-mail<EMAIL_ADDRESS>
## Abstract

The Ancient Egyptians wrote Calendars of Lucky and Unlucky Days that assigned
astronomically influenced prognoses for each day of the year. The best
preserved of these calendars is the Cairo Calendar (hereafter CC) dated to
1244–1163 B.C. We have presented evidence that the 2.85 days period in the
lucky prognoses of CC is equal to that of the eclipsing binary Algol during
this historical era. We wanted to find out the vocabulary that represents
Algol in the mythological texts of CC. Here we show that Algol was represented
as Horus and thus signified both divinity and kingship. The texts describing
the actions of Horus are consistent with the course of events witnessed by any
naked eye observer of Algol. These descriptions support our claim that CC is
the oldest preserved historical document of the discovery of a variable star.
The period of the Moon, 29.6 days, has also been discovered in CC. We show
that the actions of Seth were connected to this period, which also strongly
regulated the times described as lucky for Heaven and for Earth. Now, for the
first time, periodicity is discovered in the descriptions of the days in CC.
Unlike many previous attempts to uncover the reasoning behind the myths of
individual days, we discover the actual rules in the appearance and behaviour
of deities during the whole year.

## Introduction

The Ancient Egyptians referred to celestial events indirectly[1, 2, 3, 4] by
relating them to mythological events. Many prognoses in the Calendars of Lucky
and Unlucky Days have been connected to astronomical observations[1, 5, 6, 7].
Such connections between astronomical events and prognosis texts have been
uncovered in most cases only for individual days[8, 9, 6]. The
$P_{\mathrm{M}}=29.6$ days period of the Moon has been discovered in CC[10].
We have claimed that this document also contains the $P_{\mathrm{A}}=2.85$
days period of the eclipsing binary Algol[11]. However, it not a
straightforward task to identify those indirect mythological references that
are influenced by Algol in CC. Here we present a statistical analysis that
reveals which CC prognosis texts describe Algol’s regular variability.

The Ancient Egyptian year contained 12 months ($M$) of 30 days ($D$) and five
additional “epagomenal” days. CC gives three prognoses for each $D$ of every
$M$ (G = “gut”= “good” and S = “schlecht” = “bad”)[12, 11]. CC also gives
textual descriptions of the daily prognoses (S1 Fig). We study the dates of 28
selected words (hereafter SWs) in these mythological texts of CC. The dates
are transformed into series of time points $t_{\mathrm{i}}$ with equation (2).
The $P_{\mathrm{A}}$ and $P_{\mathrm{M}}$ signals were originally
discovered[11] from six large samples of lucky prognoses ($n=6\times
564=3384$). We use these six samples to determine the zero epochs
$t_{\mathrm{E}}$ of equation (9) for the $P_{\mathrm{A}}$ and $P_{\mathrm{M}}$
signals. The time points leading to the discovery of these signals were close
to phase, $\phi=0$, of equation (5) using the ephemerides of equations (11)
and (12) based on these zero epochs $t_{\mathrm{E}}$. The lucky prognoses of
each SW are a subsample of the above mentioned large samples of lucky
prognoses. We compute an impact parameter $z_{\mathrm{x}}$ for the
$t_{\mathrm{i}}$ of each SW with equation (10). The time points
$t_{\mathrm{i}}$ of the lucky prognoses of any particular SW may strengthen
(if $z_{\mathrm{x}}>0$) or weaken (if $z_{\mathrm{x}}<0$) the $P_{\mathrm{A}}$
and $P_{\mathrm{M}}$ signals. The impact parameter $z_{\mathrm{x}}$ is used
for identifying the SWs having lucky prognoses close to phase, $\phi=0$,
computed with the ephemerides of equations (11) and (12). We will show that
Algol and the Moon were at their brightest close to phase $\phi=0$ with these
two ephemerides. Hence, Algol’s eclipse and the New Moon occurred close to
$\phi=0.5$.

Our statistical analysis also confirms two general things regarding the origin
of the mythological texts of CC. First, the appearances and feasts of various
deities are not independent of the prognoses, or randomly assigned, but
regulated by the same periodic patterns. Second, the deities are used to
represent the same astronomical phenomena that were also used to choose the
prognoses for the days of the year.

## Materials

In this section, we transform the dates of 28 SWs in the mythological texts of
CC into series of time points $t_{\mathrm{i}}$. Our main aim is that all
stages of the production of these data can be replicated. With these
instructions, similar series of time points can be produced for any particular
SW in CC or other similar calendars, where the SW dates are available. We
create the data in two stages: Identification of SW dates and Transformation
of SW dates into series of time points.

### Identification of SW dates

CC is the best preserved Calendar of Lucky and unlucky Days. As in our two
previous studies[10, 11], we use the best preserved continuous calendar found
on pages recto III-XXX and verso I-IX of papyrus Cairo 86637. There are two CC
translations, in English by Bakir[13] and in German by Leitz[12]. Our SWs have
been identified according to the hieroglyphic transcription in Leitz[12] and
the two aforementioned translations. In case of discrepancy we have consulted
the photocopies of the original hieratic text given by Leitz[12]. For the sake
of convenience, we quote sentences according to Bakir’s English translation
despite its imperfections because there is neither space nor reason to discuss
the linguistic details of the text in the present article. This approach
should ascertain that our study of the CC sentences is objective. In other
words, we do not ourself translate any CC sentences into English, but we do
check which individual Ancient Egyptian SWs were also identified by Bakir[13]
and Leitz[12]. There is only one exception to our sentence quotation rule,
i.e. the CC text connected to Horus where Bakir[13] did not identify Horus,
but Leitz[12] and we did (Algol in lucky prognoses: the text at date
$g_{\mathrm{i}}(1,10)$).

Naturally, we can not analyse all words in CC. Our main selection criterion is
to include deities, nouns or locations that could have been used to indirectly
describe periodic phenomena, due to their significant mythological properties
and multiple occurrences in the text. Our list of SWs is not absolute and we
give all the necessary information for other researchers to repeat our
experiment on other SWs we may have ignored. Our 28 SWs in Ancient Egyptian
language are given in Table 1.

Table 1. List of SWs in Ancient Egyptian language.

We do not use the occurrences of our SWs in compound words and composite
deities (e.g. House of Horus or Ra-Horakhti), because it is uncertain to which
word, if not both, the prognosis is connected to. Our identifications of 28
SWs in CC are given in Table 2. It shows that all our 460 SW date
identifications are the same as those made by Leitz[12] (Column 5:
$460\times\\!$ “Yes”). However, 21 of our identifications were not made by
Bakir[13] (Column 6: $21\times\\!$ “No”: $1\times$ “Earth”, $2\times$ “Enemy”,
$4\times$ “Fire”, $12\times$ “Heart”, $1\times$ “Horus” and $1\times$
“Osiris”). Fortunately, most days have combinations “GGG” or “SSS” and we know
that the lucky or unlucky SW prognosis is certainly correct. We ignore the
heterogeneous combinations “HET” (like “SSG”at $D=6$ and $M=1$), because the
correct SW prognosis is uncertain. The dates with an unknown prognosis
combination, “- - -”, are naturally also ignored. Our notations for the number
of lucky and unlucky dates for each SW are $n_{\mathrm{G}}$ and
$n_{\mathrm{S}}$. For example, “Abydos” has $n_{\mathrm{G}}=3$ and
$n_{\mathrm{S}}=2$.

Table 2:  SWs identified in CC.

SW | $D$ | $M$ | Prog | Ltz | Bkr
---|---|---|---|---|---
Abydos | 13 | 3 | SSS | Yes | Yes
Abydos | 17 | 3 | \- - - | Yes | Yes
Abydos | 11 | 4 | GGG | Yes | Yes
Abydos | 18 | 5 | GGG | Yes | Yes
Abydos | 27 | 6 | \- - - | Yes | Yes
Abydos | 28 | 7 | GGG | Yes | Yes
Abydos | 13 | 8 | SSS | Yes | Yes
Abydos | 23 | 8 | \- - - | Yes | Yes
Busiris | 26 | 2 | SSS | Yes | Yes
Busiris | 14 | 5 | SSS | Yes | Yes
Busiris | 26 | 5 | SSS | Yes | Yes

The selected word (SW) identified on day $(D)$ of month $(M)$ in CC. The daily
prognosis combinations (Prog) are “GGG” (All lucky), “SSS” (All unlucky), “- -
-” (All unknown) or “HET” (Heterogeneous). The same SW was identified at the
same date by Leitz[12] (Ltz=”Yes” or “No”) and by Bakir[13] (Bkr=”Yes” or
“No”). The twelve first lines of all 460 lines are shown here for guidance
regarding the contents of this ASCII file which can be downloaded on Dryad
(http://dx.doi.org/10.5061/dryad.tj4qg).

### Transformation of SW dates into series of time points

The dating of CC does not influence the results of our currect analysis,
because we transform the time points to unit vectors with equation (6). The
mutual directions between these unit vectors do not depend on the chosen zero
epoch $t_{0}$ in time. Adding any positive or negative constant value to these
time points rotates all unit vectors with the same constant angle. Hence, our
significance estimates of equations (8) and (13) do not depend on the
connection between Gregorian and Egyptian days. The only assumption made in
our equation (2) below is that the separation between two subsequent days is
exactly one day during the particular year that CC happens to describe.

The transformation relations in equations (2) and (3) of Jetsu et al.[11] were

$\displaystyle t_{\mathrm{i}}=N_{\mathrm{E}}-1+a_{\mathrm{i}},$ (1)

where $N_{\mathrm{E}}=30(M-1)+D$ and $a_{\mathrm{i}}$ was a decimal part. This
decimal part $a_{\mathrm{i}}$ was different for each of the three parts of the
day. The $a_{\mathrm{i}}$ values depended on the chosen transformation between
Egyptian and Gregorian year, and on the chosen day division. The
$P_{\mathrm{A}}$ and $P_{\mathrm{M}}$ signals were discovered in samples of
series of time points SSTP=1, 3, 5, 7, 9 and 11 in Jetsu et al.[11]. The size
of each sample was $n=564$. The period analysis results were the same for all
these six samples, although their $a_{\mathrm{i}}$ values were different for
every $N_{\mathrm{E}}$. The time points $t_{\mathrm{i}}$ of these six samples
are given in Table 3.

Table 3:  The time points $t_{\mathrm{i}}$ of lucky prognoses in Jetsu et
al.[11].

SSTP=1 | SSTP=3 | SSTP=5 | SSTP=7 | SSTP=9 | SSTP=11
---|---|---|---|---|---
0.080 | 0.095 | 0.076 | 0.120 | 0.142 | 0.114
0.239 | 0.284 | 0.227 | 0.359 | 0.426 | 0.341
0.399 | 0.473 | 0.379 | 0.739 | 0.784 | 0.727
1.080 | 1.095 | 1.076 | 1.120 | 1.142 | 1.113
1.240 | 1.284 | 1.227 | 1.360 | 1.425 | 1.340

The $t_{\mathrm{i}}$ values of SSTP=1, 3, 5, 7, 9 and 11 from Table 3 in Jetsu
et al.[11]. The five first lines of all 534 lines are shown here for guidance
regarding the contents of this ASCII file which can be downloaded on Dryad
(http://dx.doi.org/10.5061/dryad.tj4qg).

The mean of the decimal parts $a_{\mathrm{i}}$ of all these $n=6\times
564=3384$ values of $t_{\mathrm{i}}$ is $m_{\mathrm{t}}=0.33$. In this study,
the time point for an SW at the day $D$ of the month $M$ in CC is therefore
computed from

$\displaystyle
t_{\mathrm{i}}=t_{\mathrm{i}}(D,M)=N_{\mathrm{E}}-1+m_{\mathrm{t}}.$ (2)

This accuracy is sufficient, because we do not know to which part or parts of
the day each SW refers to ($\sigma_{\mathrm{t}}\approx\pm 0.^{\mathrm{d}}5$)
and some prognosis texts may refer to the previous or the next day
($\sigma_{\mathrm{t}}\approx\pm 1.^{\mathrm{d}}5$). The $t_{\mathrm{i}}$ of
Table 3 $(n=6\times 564=3384)$ are also later used to determine the zero
epochs $t_{\mathrm{E}}$ for the ephemerides connected to the $P_{\mathrm{A}}$
and $P_{\mathrm{M}}$ signals (equations (11) and (12)). Our “synchronization”
of time points of equations (1) and (2) ensures that these ephemerides enable
us to identify the SWs connected to the $P_{\mathrm{A}}$ and $P_{\mathrm{M}}$
signals. For a given $t$ value, the inverse transformation is

$\displaystyle M$ $\displaystyle=$
$\displaystyle{\mathrm{INT}}[(t+1-m_{\mathrm{t}})/30]+1$ (3) $\displaystyle D$
$\displaystyle=$ $\displaystyle t-m_{\mathrm{t}}+1-30(M-1),$ (4)

where ${\mathrm{INT}}$ removes the decimal part of $(t+1-m_{\mathrm{t}})/30$.
In other words, if the analysis our data gives any particular $t$ value, the
$D$ and $M$ values of this $t$ can be solved from equations (3) and (4).

The time points $t_{\mathrm{i}}$ for all dates with a “GGG” or “SSS” prognosis
combination in CC are given in Table 4. These $t_{\mathrm{i}}$ are needed in
computing the binomial distribution probabilities $Q_{\mathrm{B}}$ of equation
(13).

Table 4:  The time points $t_{\mathrm{i}}$ of all GGG and SSS dates in CC.

$D$ | $M$ | $t_{\mathrm{i}}$ | Prog
---|---|---|---
1 | 1 | 0.33 | GGG
2 | 1 | 1.33 | GGG
5 | 1 | 4.33 | GGG
7 | 1 | 6.33 | GGG
9 | 1 | 8.33 | GGG
10 | 1 | 9.33 | GGG
11 | 1 | 10.33 | SSS
12 | 1 | 11.33 | SSS
16 | 1 | 15.33 | SSS
17 | 1 | 16.33 | SSS

The day ($D$) and month ($M$) values in CC used in computing the time points
($t_{\mathrm{i}}$) for the days with the prognosis (Prog) combinations “GGG”
or “SSS”. There are $N_{\mathrm{G}}=177$ and $N_{\mathrm{S}}=105$ days with a
“GGG” and “SSS” combination, respectively. These data are from Table 1 in
Jetsu et al. 2013[11]. The ten first lines of all 282 lines are shown here for
guidance regarding the contents of this ASCII file which can be downloaded on
Dryad (http://dx.doi.org/10.5061/dryad.tj4qg).

## Methods

Let us assume that time is a straight line, where events are equidistant dots
with a separation of $2\pi$. If this line is wound on a $d=1$ diameter wheel,
the dots line up at the same point on the wheel. Removing some dots produces
gaps in the time line, but the remaining dots will still line up on the wheel.
However, they will not line up on a $d\neq 1$ diameter wheel. This is an
analogy for the Rayleigh test. It projects time points on a unit circle with
the tested period $P$. These points line up in the same direction, if their
time distribution is regular with the tested $P$.

### Analysis

If the Rayleigh method discovers the period $P$ in a series of time points
points t$=[t_{1},t_{2},...,t_{\mathrm{n}}]$, it is possible to identify those
subsamples t∗ of $n^{*}$ time points that strengthen this signal. In other
words, the signal can be separated from noise. The phases of the $n$ time
points $t_{\mathrm{i}}$ are

$\displaystyle\phi_{\mathrm{i}}={\mathrm{FRAC}}[(t_{\mathrm{i}}-t_{0})/P],$
(5)

where $t_{0}$ is an arbitrary zero epoch and ${\mathrm{FRAC}}$ removes the
integer part of $(t_{\mathrm{i}}-t_{0})/P$. The unit vectors are

$\displaystyle{\bf
r}_{\mathrm{i}}=[\cos{\Theta_{\mathrm{i}}},\sin{\Theta_{\mathrm{i}}}],$ (6)

where $\Theta_{\mathrm{i}}=360^{\mathrm{o}}~{}\phi_{\mathrm{i}}$ are the phase
angles. The test statistic of the Rayleigh test is

$\displaystyle z=|{\bf R}|^{2}/n,$ (7)

where vector ${\bf R}=\sum_{\mathrm{i=1}}^{\mathrm{n}}{\bf r}_{\mathrm{i}}$
points to
$\Theta_{\mathrm{R}}={\mathrm{atan}}(R_{\mathrm{y}}/R_{\mathrm{x}})$,
$R_{\mathrm{x}}=\sum_{\mathrm{i=1}}^{\mathrm{n}}\cos{\Theta}_{\mathrm{i}}$ and
$R_{\mathrm{y}}=\sum_{\mathrm{i=1}}^{\mathrm{n}}\sin{\Theta}_{\mathrm{i}}$.
The corresponding phase is
$\phi_{\mathrm{R}}=\Theta_{\mathrm{R}}/(360^{\mathrm{o}})$. Coinciding
directions $\Theta_{\mathrm{i}}$ give $|{\bf R}|=n$, while random
$\Theta_{\mathrm{i}}$ give $|{\bf R}|\approx 0$. The critical level (i.e.
significance) of the Rayleigh test is

$\displaystyle Q_{\mathrm{z}}={\mathrm{e}}^{-z}.$ (8)

We use the ephemeris zero epoch

$\displaystyle t_{\mathrm{E}}=t_{0}+P\phi_{\mathrm{R}}.$ (9)

The mutual directions of ri and the length $|{\bf R}|$ are invariant for any
constant shift of $m_{\mathrm{t}}$, $t_{\mathrm{i}}$, $t_{0}$ or
$t_{\mathrm{E}}$. Using the above $t_{\mathrm{E}}$ of equation (9), vector
${\bf R}$ points to $\Theta=\Theta_{R}=0^{\mathrm{o}}$. All ri with
$-90^{\mathrm{o}}<\Theta_{\mathrm{i}}<90^{\mathrm{o}}$ strengthen the $P$
signal, while the remaining ri weaken it. The test statistic can be divided
into $z=R_{\mathrm{x}}^{2}/n+R_{\mathrm{y}}^{2}/n$. We fix
$t_{0}=t_{\mathrm{E}}$ in equation (5) and compute the “impact” of any
subsample t∗ on the $P$ signal from

$\displaystyle
z_{\mathrm{x}}=(R_{\mathrm{x}}/|R_{\mathrm{x}}|)(R_{\mathrm{x}}^{2}/n),$ (10)

where $R_{\mathrm{x}}$ is computed only for the $n=n^{*}$ time points of t∗.
These t∗ may strengthen ($z_{\mathrm{x}}>0$) or weaken ($z_{\mathrm{x}}<0$)
the $P$ signal, or represent noise ($z_{\mathrm{x}}\approx 0$).

Using the zero epoch $t_{0}=0$ for the $n=6\times 564$ time points
$t_{\mathrm{i}}$ of the G prognoses in Table 3 gives the $t_{\mathrm{E}}$
values of Table 5 for the $P_{\mathrm{A}}$ and $P_{\mathrm{M}}$ signals with
equation (9).

Table 5:  Values of $t_{\mathrm{E}}$ of the six samples $P$ | SSTP=1 | SSTP=3 | SSTP=5 | SSTP=7 | SSTP=9 | SSTP=11
---|---|---|---|---|---|---
2.85 | 0.45 | 0.45 | 0.44 | 0.61 | 0.61 | 0.60
29.6 | 3.42 | 3.42 | 3.42 | 3.58 | 3.58 | 3.58

These six large samples have $t_{\mathrm{E}}=0.53\pm 0.09$ for
$P_{\mathrm{A}}$ and $t_{\mathrm{E}}=3.50\pm 0.09$ for $P_{\mathrm{M}}$.
Hence, we use the following two ephemerides

$\displaystyle t_{0}=t_{\mathrm{E}}=0.53,$ $\displaystyle P=$ $\displaystyle
P_{\mathrm{A}}=2.85{\mathrm{~{}~{}~{}(Algol)}}$ (11) $\displaystyle
t_{0}=t_{\mathrm{E}}=3.50,$ $\displaystyle P=$ $\displaystyle
P_{\mathrm{M}}=29.6{\mathrm{~{}~{}~{}(Moon).}}$ (12)

for computing the phases $\phi_{\mathrm{i}}$ of equation (5). The lucky “GGG”
prognoses of every SW are a subsample of the above six large samples of all
“G” prognoses. We give the $z$ and $z_{\mathrm{x}}$ values of equations (7)
and (8) for any particular SW, if the analysed $t_{\mathrm{i}}$ of this SW
reach $Q_{\mathrm{z}}\leq 0.2$ with the ephemerides of equations (11) or (12).
These periodicities are called weak if $0.05<Q_{\mathrm{z}}\leq 0.2$.

In our Figs. 1–13, we project the $t_{\mathrm{i}}$ of each SW to
r${}_{\mathrm{i}}=[\cos{\Theta_{\mathrm{i}}},\sin{\Theta_{\mathrm{i}}}]$ on a
unit circle, where time runs in the counter clock–wise direction. For the
$P_{\mathrm{A}}$ signal, we define four points Aa, Ab, Ac and Ad. The first
one, Aa, is at $\phi=0\equiv 0^{\mathrm{o}}$ with the ephemeris of equation
(11). The next three points Ab, Ac and Ad are separated by
$\Delta\phi=0.25\equiv 90^{\mathrm{o}}$. Vectors ri pointing between Ad
$\equiv-90^{\mathrm{o}}$ and Ab $\equiv+90^{\mathrm{o}}$ give
$z_{\mathrm{x}}>0$ and strengthen $P_{\mathrm{A}}$ signal, the other ones
weaken it. Because $P_{\mathrm{A}}$ equals $57^{\mathrm{d}}/20$, the
$\phi_{\mathrm{i}}$ of $t_{\mathrm{i}}$ separated by multiples of 57 days are
equal. For clarity, we shift such overlapping $\phi_{\mathrm{i}}$ values by
$\Delta\phi=0.005$ away from each other in our Figs. 1 – 13. However, there
are no such shifts in our computations. Our unambiguous terminology is:

“Connected to the $P_{\mathrm{A}}$ signal” $\equiv$ $t_{\mathrm{i}}$ of an SW
strengthen the $P_{\mathrm{A}}$ signal $\equiv$ $z_{\mathrm{x}}\geq 1.0$ and
$Q_{\mathrm{z}}\leq 0.2$ with the ephemeris of equation (11).
“Connected to Algol” $\equiv$ $t_{\mathrm{i}}$ of an SW show periodicity with
$P_{\mathrm{A}}$, but their contribution to the $P_{\mathrm{A}}$ signal is
insignificant when $0\leq z_{\mathrm{x}}<1.0$ or they weaken this signal when
$z_{\mathrm{x}}<0$ $\equiv$ $z_{\mathrm{x}}<1.0$ and $Q_{\mathrm{z}}\leq 0.2$
with the ephemeris of equation (11).

We use similar terminology for the Moon (equation (12)), and Ma–Md points
similar to Aa–Ad.

Our notations for the lucky and unlucky time points $t_{\mathrm{i}}$ of each
SW are $g_{\mathrm{i}}$ and $s_{\mathrm{i}}$. The notations for their unit
vectors ri of equation (6) are gi and si, respectively. The critical level
$Q_{\mathrm{z}}$ measures the probability for the concentration of all
$n_{\mathrm{G}}$ and $n_{\mathrm{S}}$ directions of gi and si of each SW.
These directions are embedded within the directions of all gi (Table 4:
$N_{\mathrm{G}}=177$) and si (Table 4: $N_{\mathrm{S}}=105$). We first choose
the direction $\Theta_{\mathrm{R}}$ of ${\bf R}$ for some SW. Then we identify
the $n_{1}$ directions of gi or si of this SW that are among the $n_{2}$ of
all $N_{\mathrm{G}}$ or $N_{\mathrm{S}}$ directions closest to
$\Theta_{\mathrm{R}}$. For each SW, this gives the binomial distribution
probability

$\displaystyle
Q_{\mathrm{B}}=P(n_{1},n_{2},N)=\sum_{i=n_{1}}^{n_{2}}{n_{2}\choose
i}q_{\mathrm{B}}^{i}(1-q_{\mathrm{B}})^{n_{2}-i},$ (13)

where $N=N_{\mathrm{G}}$ or $N_{\mathrm{S}}$, and
$q_{\mathrm{B}}=n_{\mathrm{G}}/N_{\mathrm{G}}$ or
$n_{\mathrm{S}}/N_{\mathrm{S}}$. This $Q_{\mathrm{B}}$ is the probability for
that the directions of a particular SW occur $n_{1}$ times, or more, among all
$n_{2}$ directions closest to $\Theta_{\mathrm{R}}$. Many $Q_{\mathrm{z}}$
estimates based on small samples ($n_{\mathrm{G}}$ or $n_{\mathrm{S}}$) are
unreliable, but the $Q_{\mathrm{B}}$ estimates based on large samples (Table
4: $N_{\mathrm{G}}=177$ or $N_{\mathrm{S}}=105$) are not.

All results of our analysis are given in S1 Table, where the results mentioned
in text are marked with bold letters. The structure of S1 Table resembles the
four panel structure of Figs 1–13. We give four separate tables for each SW.
The results for the lucky and unlucky prognoses with $P_{\mathrm{A}}$ are
those shown in figure panels “a” and “b”. The corresponding results for
$P_{\mathrm{M}}$ are shown in figure panels “c” and “d”.

## Results

### Algol in lucky prognoses

Of all 28 SWs, only the lucky prognoses of Horus, Re, Wedjat, Followers,
Sakhmet and Ennead unambiguously strengthen the $P_{\mathrm{A}}$ signal of
Algol, because they have an impact of $z_{\mathrm{x}}\geq 1.0$ and a
significance of $Q_{\mathrm{z}}\leq 0.2$ with the ephemeris of equation (11).
The lucky prognoses of Heliopolis and Enemy are connected to Algol
($Q_{\mathrm{z}}\leq 0.2$), but they are not connected to the $P_{\mathrm{A}}$
signal ($z_{\mathrm{x}}<1.0$). In this section, we discuss these eight SWs in
the order of their impact on the $P_{\mathrm{A}}$ signal, i.e. in the order of
decreasing $z_{\mathrm{x}}$ with the ephemeris of equation (11).

Figure 1: Horus. Time runs in the counter clock–wise direction on these unit
circles. We give the $z$, $Q_{\mathrm{z}}$ and $z_{\mathrm{x}}$ values only
when $Q_{\mathrm{z}}\leq 0.2$. The large black point indicates the
$\Theta_{\mathrm{R}}$ direction. (a) gi with equation (11). Point Aa is at
$\phi=0\equiv 0^{\mathrm{o}}$. The thick line centered on point Ac at
$\phi=0.5\equiv 180^{\mathrm{o}}$ outlines the proposed phase for the 10 hr
eclipse of Algol. (b) si with equation (11). (c) gi with equation (12). Point
Ma at $\phi=0\equiv 0^{\mathrm{o}}$ is close to the proposed Full Moon phase.
(d) si with equation (12)

#### Horus

This SW has the largest impact $z_{\mathrm{x}}=+3.5$ on the $P_{\mathrm{A}}$
signal and the highest significance of the above eight SWs
($Q_{\mathrm{z}}=0.03$, $n_{\mathrm{G}}=14$). The unit vectors gi and si of
lucky and unlucky prognoses with the ephemeris of equation (11) are shown in
Figs 1ab. Point Aa is at $\phi=0\equiv 0^{\mathrm{o}}$. Points Ab, Ac and Ad
are separated by $\Delta\phi=0.25\equiv 90^{\mathrm{o}}$. Only the gi pointing
between Ad $\equiv-90^{\mathrm{o}}$ and Ab $\equiv+90^{\mathrm{o}}$ strengthen
the $P_{\mathrm{A}}$ signal. Twelve out of all fourteen gi are within this
interval (Fig 1a). The four $\Theta_{\mathrm{i}}$ closest to
$\Theta_{\mathrm{R}}=11^{\mathrm{o}}$ reach a high significance of
$Q_{\mathrm{B}}=0.006$ ($n_{1}=4$, $n_{2}=10$, $N_{\mathrm{G}}=177$). The gi
pointing closest to Aa and giving the strongest impact on the $P_{\mathrm{A}}$
signal has the CC text[13]
$g_{\mathrm{i}}(14,2)\equiv+6^{\mathrm{o}}$: “It is the day of receiving the
white crown by the Majesty of Horus; his Ennead is in great festivity.”
The texts[13, 12] for the next best gi closest to Aa are
$g_{\mathrm{i}}(19,12)\equiv+13^{\mathrm{o}}:$ “Horus has returned complete,
nothing is missing in it.”
$g_{\mathrm{i}}(27,1)\equiv+19^{\mathrm{o}}:$ “Peace on the part of Horus with
Seth.”
$g_{\mathrm{i}}(24,3)\equiv+19^{\mathrm{o}}:$ “He has given his throne to his
son, Horus, in front of Re.”
$g_{\mathrm{i}}(1,7)\equiv+32^{\mathrm{o}}:$ “Feast of entering into heaven
and the two banks. Horus is jubilating.”
$g_{\mathrm{i}}(15,11)\equiv+38^{\mathrm{o}}:$ “Horus hears your words in the
presence of every god and goddess on this day.”
$g_{\mathrm{i}}(27,3)\equiv+38^{\mathrm{o}}:$ “Judging Horus and Seth;
stopping the fighting.”
$g_{\mathrm{i}}(18,1)\equiv-38^{\mathrm{o}}:$ “It is the day of magnifying the
majesty of Horus more than his brother, …”
$g_{\mathrm{i}}(1,9)\equiv+51^{\mathrm{o}}:$ “Feast of Horus son of Isis and …
his followers … day”
$g_{\mathrm{i}}(23,7)\equiv-69^{\mathrm{o}}:$ “Feast of Horus … on this day of
his years in his very beautiful images.”
$g_{\mathrm{i}}(29,3)\equiv-69^{\mathrm{o}}:$ “White crown to Horus, and the
red one to Seth.”
$g_{\mathrm{i}}(7,9)\equiv+88^{\mathrm{o}}:$ “The crew follow Horus in the
foreign land, examining its list … therein when he smote him who rebelled
against his master.”
$g_{\mathrm{i}}(1,10)\equiv-120^{\mathrm{o}}:$ “Horus … Osiris … Chentechtai …
land ”
$g_{\mathrm{i}}(28,3)\equiv+164^{\mathrm{o}}:$ “The gods are in jubilation and
in joy when the will is written (lit. made) for Horus, …”
These passages of lucky prognoses are suggestive of Algol at its brightest.
The “white crown”, Horus having “returned complete” and “entering into heaven”
(i.e. into the sky) are not easy to explain as symbols for the eclipse. Among
the $g_{\mathrm{i}}$ of all 28 SWs, the $g_{\mathrm{i}}$ of Horus are the
“best hit” on Aa ($z_{\mathrm{x}}=+3.5$). If these $g_{\mathrm{i}}$ represent
Algol at its brightest, then Aa is in the middle of this brightest phase and
the thick line centered at Ac in Fig 1a outlines Algol’s eclipse. In this
case, the $g_{\mathrm{i}}(7,9)\\!\equiv\\!+88^{\mathrm{o}}$ text may refer to
an imminent eclipse and “the will is written” in
$g_{\mathrm{i}}(28,3)\\!\equiv\\!+164^{\mathrm{o}}$ to the moment when the
beginning of the eclipse is just becoming observable with naked eye. These
passages could certainly describe naked eye observations of the regular
changes of Algol.

Three si of Horus in Fig 1b concentrate close to Ad and reach
$Q_{\mathrm{B}}=0.07$ ($n_{1}=3$, $n_{2}=25$, $N_{\mathrm{S}}=105$). The
fourth vector si points close to Aa. Their CC texts[13] are
$s_{\mathrm{i}}(26,1)\equiv-107^{\mathrm{o}}:$ “… It is the day of Horus
fighting with Seth. …”
$s_{\mathrm{i}}(11,11)\equiv-107^{\mathrm{o}}:$ “Introducing the great ones by
Re to the booth to see what he had observed through the eye of Horus the
elder. They were with heads bent down when they saw the eye of Horus being
angry in front of Re.”
$s_{\mathrm{i}}(20,9)\equiv-69^{\mathrm{o}}:$ “Mat judges in front of these
gods who became angry in the island of the sanctuary of Letopolis. The Majesty
of Horus revised it.”
$s_{\mathrm{i}}(5,8)\equiv 6^{\mathrm{o}}:$ “The Majesty of Horus is well when
the red one sees his form. As for anybody who approaches it, anger will start
on it.”
If the $g_{\mathrm{i}}$ that described feasts were connected to the brightest
phase of Algol, these $s_{\mathrm{i}}$ describing anger would have occurred
after Algol’s eclipse. “Horus is well” for the last $s_{\mathrm{i}}(5,8)$
would seem natural for a lucky prognosis of Horus (as it should be close to
Aa) but it is deemed unlucky for some other reasons. This type of “conflict of
interest” prognoses may explain, why there are significant concentrations of
directions accompanied by a few irregular directions (e.g. Fig 7c).

The $g_{\mathrm{i}}$ and $s_{\mathrm{i}}$ of Horus have $Q_{\mathrm{z}}>0.2$
with the ephemeris of equation (12), and are therefore not connected to the
Moon, except for some $g_{\mathrm{i}}$ texts mentioning both Horus and Seth.
We argue that, as Leitz[12] also did, Mc $\equiv 180^{\mathrm{o}}$ in Fig 1c
coincides with the New Moon (see paragraph Seth). All the aforementioned lucky
prognoses mentioning both Horus and Seth are close to Md
$\equiv-90^{\mathrm{o}}$ in Fig 1c, i.e.
$g_{\mathrm{i}}(27,1)\equiv-82^{\mathrm{o}}$,
$g_{\mathrm{i}}(27,3)\equiv-73^{\mathrm{o}}$ and
$g_{\mathrm{i}}(29,3)\equiv-48^{\mathrm{o}}$ with the ephemeris of equation
(12). The texts of these three days may describe the “luminosity competitions”
between Horus and Seth which come to an end when more than half of the lunar
disk becomes illuminated immediately after Md. The legend of the Contendings
of Horus and Seth[14] (hereafter LE1) has inspired these descriptions. The
text “White crown to Horus, and the red one to Seth” in $g_{\mathrm{i}}(29,3)$
would describe the brightening of Horus with Algol (Fig. 1a:
$\Theta\\!=\\!-69^{\mathrm{o}}$) and the brightening of Seth (Fig. 1c:
$\Theta\\!=\\!-48^{\mathrm{o}}$) with the approaching Full Moon at Ma. The
most simple explanation for the context of these texts is that the lucky
prognoses of Horus are connected to Algol at its brightest.

#### Re

The lucky prognoses reach $Q_{\mathrm{z}}=0.07$ ($n_{\mathrm{G}}=32$) with the
ephemeris of equation (11) and give the second largest impact
$z_{\mathrm{x}}=+2.5$ on the $P_{\mathrm{A}}$ signal (Fig 2a). Absence of
small $Q_{\mathrm{B}}$ values, i.e. gi concentrations, may indicate that Re
(the Sun) was casually following the undertakings of Horus. The si of Re reach
$Q_{\mathrm{z}}=0.2$ ($n_{\mathrm{S}}=26$) with the ephemeris of equation
(12), and explicitly avoid Ma, the proposed Full Moon phase (Fig 2d).

Figure 2: Re. otherwise as in Fig 1

#### Wedjat

The lucky prognoses show weak periodicity ($Q_{\mathrm{z}}=0.1$,
$n_{\mathrm{G}}=4$) with the ephemeris of equation (11). They give the third
largest impact $z_{\mathrm{x}}=+2.0$ on the $P_{\mathrm{A}}$ signal (Fig 3a).
However, their impact on the $P_{\mathrm{M}}$ signal is even larger,
$z_{\mathrm{x}}=+2.9$ (Fig 3c). Wedjat may represent Algol observed at its
brightest close to the Full Moon. The gi and si distributions of Horus and
Wedjat are similar (Figs 1ab and 3ab) with the ephemeris of equation (11).
Wedjat is the Eye of Horus in Ancient Egyptian mythology.

Figure 3: Wedjat. otherwise as in Fig 1

#### Followers

The lucky prognoses have an impact of $z_{\mathrm{x}}=+1.4$ on the
$P_{\mathrm{A}}$ signal (Fig 4a). This periodicity is weak
($Q_{\mathrm{z}}=0.2$, $n_{\mathrm{G}}=15$). Six $s_{\mathrm{i}}$ reach
$Q_{\mathrm{z}}=0.01$ (Fig. 4b). The five si closest to $\Theta_{\mathrm{R}}$
reach a high significance of $Q_{\mathrm{B}}=0.003$ ($n_{1}=5$, $n_{2}=18$,
$N_{\mathrm{S}}=105$) and may refer to an approaching eclipse of Algol. These
$s_{\mathrm{i}}$ also show a weak connection to the Moon (Fig. 4d). It is
tempting to suggest that Followers would be Pleiades following very close
behind Algol in the revolving sky, e.g. in $g_{\mathrm{i}}(7,9)\equiv
88^{\mathrm{o}}$ “The crew follow Horus in the foreign land” (Figs. 1a and
4a).

Figure 4: Followers. otherwise as in Fig 1

#### Sakhmet

The $g_{\mathrm{i}}$ and $s_{\mathrm{i}}$ reach $Q_{\mathrm{z}}=0.06$
($n_{\mathrm{G}}=4$) and 0.05 ($n_{\mathrm{S}}=3$) with the ephemeris of
equation (11). The impact of $g_{\mathrm{i}}$ on the $P_{\mathrm{A}}$ signal
is $z_{\mathrm{x}}=+1.3$ (Fig. 5a). The three $s_{\mathrm{i}}$ at Ad, after
the proposed eclipse at Ac, are strongly connected to Algol, because they
reach the most extreme significance in this study, $Q_{\mathrm{B}}=0.0004$
($n_{1}=3$, $n_{2}=6$, $N_{\mathrm{S}}=105$). The texts[13] are
$s_{\mathrm{i}}(27,8)\equiv-95^{\mathrm{o}}:$ “Re sets because the Majesty of
the goddess Sakhmet is angry in the land of Temhu.”
$s_{\mathrm{i}}(13,6)\equiv-82^{\mathrm{o}}:$ “It is the day of the proceeding
of Sakhmet to Letopolis. Her great executioners passed by the offerings of
Letopolis on this day.”
$s_{\mathrm{i}}(7,10)\equiv-82^{\mathrm{o}}:$ “It is the day of the
executioners of Sakhmet.”
These three unlucky prognoses (Fig. 5b) are immediately followed by lucky ones
(Fig. 5a). The gi and si distributions of Sakhmet (Fig 5ab) resemble those of
Horus (Fig 1ab) with the ephemeris of equation (11). The Eye of Horus (Wedjat)
was transformed into the vengeful goddess Sakhmet in the legend[14] of the
Destruction of Mankind (hereafter LE2). The si vectors of Horus, Wedjat and
Sakhmet point close to Ad which is after Algol’s proposed eclipse at Ac (Figs
1b, 3b and 5b), and may refer to the abrupt pacification of enraged Sakhmet in
LE2.

Figure 5: Sakhmet. otherwise as in Fig 1

#### Ennead

The lucky prognoses show weak periodicity (Fig 6a:
$Q_{\mathrm{z}}=0.1$,$n_{\mathrm{G}}=18$) and an impact of
$z_{\mathrm{x}}=+1.1$ on the $P_{\mathrm{A}}$ signal with the ephemeris of
equation (11), as well as some concentration ($Q_{\mathrm{B}}=0.02$,
$n_{1}=12$, $n_{2}=63$, $N_{\mathrm{G}}=177$). Ennead was a group of nine
deities in Ancient Egyptian mythology. We discussed earlier, why Followers may
have represented Pleiades. Ennead may have been another name for Pleiades,
having the modern name “Seven sisters”. However, the number of Pleiades
members visible with naked eye depends on the observing conditions and the
observer, the maximum number of such members being fourteen [15, 16]. The
unlucky prognoses of Followers could be connected to Pleiades following the
disappearing Algol before eclipse (Fig. 4b), while the unlucky prognoses of
Ennead could be connected to Algol reappearing in front Pleiades after eclipse
(Fig. 6b). Furthermore, the lucky prognosis distributions of Followers and
Ennead are very similar (Figs. 4a and 6a).

Figure 6: Ennead. otherwise as in Fig 1

#### Heliopolis

The lucky prognoses show weak periodicity with ${P_{\mathrm{A}}}$, but their
impact on this signal is insignificant, $z_{\mathrm{x}}=+0.2$, with the
ephemeris of equation (11).

#### Enemy

These lucky prognoses weaken the ${P_{\mathrm{A}}}$ signal, because their
impact is $z_{\mathrm{x}}=-1.0$ with the ephemeris of equation (11).

### The Moon in lucky prognoses

We discuss the remaining other 20 SWs in this section and in sections

  * Algol in unlucky prognoses

  * The Moon in unlucky prognoses

  * No Algol or the Moon in lucky or unlucky prognoses

These SWs are discussed only briefly, because they are not connected to the
$P_{\mathrm{A}}$ signal.

The lucky prognoses of Earth, Heaven, Busiris, Rebel, Thoth and Onnophris are
connected to the ${P_{\mathrm{M}}}$ signal, because they have
$z_{\mathrm{x}}\geq 1.0$ and $Q_{\mathrm{z}}\leq 0.2$ with the ephemeris of
equation (12). The lucky prognoses of Nut are weakly connected to the Moon.

#### Earth

These lucky prognoses reach the highest impact parameter value of this study,
$z_{\mathrm{x}}=+5.3$, on the $P_{\mathrm{M}}$ signal. This periodicity also
reaches the highest Rayleigh test significance of all, $Q_{\mathrm{z}}=0.001$
($n_{\mathrm{G}}=19$). The good moments on Earth occurred before and during
Ma, the proposed Full Moon phase (Fig 7c). The unlucky prognoses also show a
weak connection to Algol (Fig. 7b: $Q_{\mathrm{z}}=0.06$, $n_{\mathrm{S}}=5$)
and an even weaker connection to the Moon (Fig. 7d: $Q_{\mathrm{z}}=0.2$,
$n_{\mathrm{S}}=5$).

Figure 7: Earth. otherwise as in Fig 1

#### Heaven

The second largest impact $z_{\mathrm{x}}=+3.4$ on the $P_{\mathrm{M}}$ signal
comes from these lucky prognoses. Again, the good moments coincide with Ma,
the proposed Full Moon phase (Fig 8c). This is significant periodicity
($Q_{\mathrm{z}}=0.03$, $n_{\mathrm{G}}=19$) combined with a very significant
concentration ($Q_{\mathrm{B}}=0.002$, $n_{1}=12$, $n_{2}=45$,
$N_{\mathrm{G}}=177$). The unlucky prognoses also show a weak connection to
the Moon (Fig. 8d: $Q_{\mathrm{z}}=0.06$, $n_{\mathrm{S}}=4$).

Figure 8: Heaven. otherwise as in Fig 1

#### Busiris

The third largest impact on the $P_{\mathrm{M}}$ signal,
$z_{\mathrm{x}}=+3.0$, comes from the lucky prognoses of Busiris. This
periodicity reaches $Q_{\mathrm{z}}=0.05$ ($n_{\mathrm{G}}=4$) with the
ephemeris of equation (12). And again, the lucky prognoses are close to Ma,
the proposed Full Moon phase (Fig 9c)

Figure 9: Busiris. otherwise as in Fig 1

#### Rebel

The lucky prognoses show weak periodicity ($Q_{\mathrm{z}}=0.2$,
$n_{\mathrm{G}}=3$) with the ephemeris of equation (12) and have an impact of
$z_{\mathrm{x}}=1.6$ on the $P_{\mathrm{M}}$ signal.

#### Thoth and Onnophris

The lucky prognoses of these SW have a weaker impact on the $P_{\mathrm{M}}$
signal, i.e. $1.0\leq z_{\mathrm{x}}\leq 1.3$ with the ephemeris equation
(12).

#### Nut

The lucky prognoses show a weak connection to the Moon. They have no impact on
$P_{\mathrm{M}}$, because $z_{\mathrm{x}}=-0.1$ with the ephemeris of equation
(12).

### Algol in unlucky prognoses

The $P_{\mathrm{A}}$ and $P_{\mathrm{M}}$ signals were detected from the lucky
prognoses $g_{\mathrm{i}}$ [10, 11]. It is therefore self–evident that the
unlucky prognoses $s_{\mathrm{i}}$ had no impact on these two signals.
However, this does not rule out the possibility that the $s_{\mathrm{i}}$ of
some SW may be connected to Algol or the Moon. Most of these si vectors point
away from Aa or Ma, i.e. $z_{\mathrm{x}}<0$ with the ephemerides of equations
(11) or (12). Man and Flame are the only exceptions to this general rule
($z_{\mathrm{x}}\geq 0$).

#### Heart

The unlucky prognoses have $z_{\mathrm{x}}=-3.1$ with the ephemeris of
equation (11). They point towards Ac, the proposed eclipse phase of Algol (Fig
10b). This periodicity reaches a significance of $Q_{\mathrm{z}}=0.04$
($n_{\mathrm{S}}=5$) and $Q_{\mathrm{B}}=0.04$ ($n_{1}=5$, $n_{2}=39$,
$N_{\mathrm{S}}=105$).

Figure 10: Heart. otherwise as in Fig 1

#### Nun

The three unlucky prognoses of this SW reach $Q_{\mathrm{z}}=0.06$ and a high
significance of $Q_{\mathrm{B}}=0.003$ ($n_{1}=3$, $n_{2}=11$,
$N_{\mathrm{S}}=105$) with the ephemeris of equation (11). They also show a
weaker connection to the Moon.

### The Moon in unlucky prognoses

We will first discuss the unlucky prognoses of SWs having negative
$z_{\mathrm{x}}$ values with the ephemeris of equation (12), and then the two
exceptions of Man and Flame.

#### Seth

“See you on the dark side of the Moon” sums up the unlucky prognoses of Seth
(Fig 11d). The significance is $Q_{\mathrm{z}}=0.05$ ($n_{\mathrm{S}}=9$) with
the ephemeris of equation (12). Leitz[12] has argued that the following
texts[13] at two consecutive days
$s_{\mathrm{i}}(16,7)\equiv 173^{\mathrm{o}}$: “Do not look, darkness being on
this day (or, do not see darkness on this day).”
$s_{\mathrm{i}}(17,7)\equiv 185^{\mathrm{o}}$: “Do not pronounce the name of
Seth on this day.”
take place during the New Moon. The si vectors of these two particular texts
point at the opposite sides of Mc $\equiv 180^{\mathrm{o}}$, which supports
both our “prediction” formula of equation (12) and Leitz’ attribution[12] of
the texts to the New Moon. We conclude that Seth is connected to the Moon and
strongly suggest that Mc computed with equation (12) is close to the New Moon.
Hence, the Full Moon is close to Ma.

Figure 11: Seth. otherwise as in Fig 1

#### Osiris

The four unlucky prognoses of this SW also point to the dark side of the Moon,
assuming that Mc is close to the New Moon (Fig 12d). The significance
estimates are $Q_{\mathrm{z}}=0.05$ ($n_{\mathrm{S}}=4$) and
$Q_{\mathrm{B}}=0.02$ ($n_{1}=3$, $n_{2}=15$, $N_{\mathrm{S}}=105$) with the
ephemeris of equation (12).

Figure 12: Osiris. otherwise as in Fig 1

#### Abydos and Lion

These unlucky prognoses show a weak connection to the Moon.

#### Man

The significance estimates for the unlucky prognoses are $Q_{\mathrm{z}}=0.02$
($n_{\mathrm{S}}=6$) and $Q_{\mathrm{B}}=0.009$ ($n_{1}=5$, $n_{2}=23$,
$N_{\mathrm{S}}=105$) with the ephemeris equation (12). These unlucky moments
of Man concentrate on a few days after Ma, the proposed Full Moon phase (Fig
13d).

Figure 13: Man. otherwise as in Fig 1

#### Flame

The significance estimates for these unlucky prognoses are
$Q_{\mathrm{z}}=0.03$ ($n_{\mathrm{S}}=4$) and $Q_{\mathrm{B}}=0.003$
($n_{1}=4$, $n_{2}=17$, $N_{\mathrm{S}}=105$) with the ephemeris of equation
(12).

### No Algol or the Moon in lucky or unlucky prognoses

#### Eye, Fire, Majesty, Shu and Sobek

These SWs are not connected to Algol or the Moon, because their
$g_{\mathrm{i}}$ and $s_{\mathrm{i}}$ have $Q_{\mathrm{z}}>0.2$ with the
ephemerides of equations (11) and (12).

### Some general remarks

This concludes our analysis of 28 SWs. Numerous other[7] SWs in CC need to be
analysed in the future. Combining the inverse relations of equations (3) and
(4) to the ephemerides of equations (11) and (12) will have countless
applications. For example, the first eclipse of Algol would have occurred on
$t(2.6,1)=1.96$ at $D=2.1$ in $M=1$ or the last New Moon on $t(14.6,12)=343.9$
at $D=14.6$ in $M=12$. Any question about CC can now be studied within this
precise framework, e.g. was some meaning given to the nights when an eclipse
of Algol (equation (11): $\phi=0.5$) coincided with the New Moon (equation
(12): $\phi=0.5$)?

## Discussion

Previously, we[11] applied four tests to the astrophysical hypothesis
$H_{1}:$ “Period $P_{\mathrm{A}}=2.^{\mathrm{d}}850$ in CC was
$P_{\mathrm{orb}}$ of Algol.”
This is a summary of those tests:
test i: The mass transfer in this binary system should have increased the
period in the past three millennia. The period value in CC is the first
evidence for such an increase since Goodricke[17] discovered this periodicity
over two centuries ago.
test ii: The period change of 0.017 days from 2.850 to 2.867 days gives a
reasonable estimate for the rate of this mass transfer.
test iii: If eclipses were observed in Ancient Egypt, the orbital plane of the
Algol A–B system must be nearly perpendicular to that of the Algol AB–C
system[18, 19].
test iv: Algol and the Moon are the most probable objects, where naked eye
observers could have discovered periodicity that we could then rediscover in
CC.

tests i and iv supported $H_{1}$, while tests ii and iii indicated that it
could be true.

Algol’s observable night time mid eclipse epochs occur in groups of three
separated with a period of 19 days and we also discovered this period in
CC[11]. This phenomenon is displayed in Fig. 14. First, a mid eclipse epoch
occurs in the end of the night. After three days, the next one occurs close to
midnight. After another three days, a mid eclipse epoch occurs in the
beginning of the night. Then, the next observable night-time mid eclipse epoch
occurs after 13 days. Naked eye observations could easily lead to the
discovery of this $3+3+13$ days regularity. One could speculate that this is
one of the reasons, why the prime number 13 is still considered unlucky. This
would be consistent with our result that, if the brightest phases of Algol
were considered lucky then the eclipses (i.e. the dimmer phases) were
considered unlucky. The 2.85 days period is exactly equal to 57/20 days. This
means that after $57=3\times 19$ days the eclipses returned exactly to the
same moment of the night (see Fig. 14). All $D=1$ days in CC have a prognosis
combination “GGG”, while all $D=20$ days have “SSS”. Perhaps this regular
separation of 19 days was also inspired by Algol.

Figure 14: Eclipses of Algol with $P_{\mathrm{A}}=2.85$ days. The horizontal
continuous lines show the beginnings and ends of 10 hours long nights. The
filled and open circles denote mid eclipse epochs occurring inside and outside
such nights. The $T_{\mathrm{A1}}=10$ hour time intervals of eclipses are
denoted with thick continuous or thin dashed lines. The tilted open and closed
triangles show the $T_{\mathrm{A2}}=7$ and $T_{\mathrm{A3}}=3$ hour limits.

Only a skilled naked eye observer would have been able to discover the minor
exceptions from the $3+3+13$ days regularity. Algol’s eclipses last
$T_{A1}=10$ hours. Naked eye can detect brightness differences of
$0.^{\mathrm{m}}1$ in ideal observing conditions. Hence, an eclipse detection
is theoretically possible for $T_{A2}=7$ hours when Algol is more than
$0.^{\mathrm{m}}1$ dimmer than its brightest suitable comparison star $\gamma$
And (Fig. 14: tilted open triangle limits). This detection could become
certain for $T_{A3}=3$ hours when Algol is also at least $0.^{\mathrm{m}}1$
dimmer than all its other suitable comparison stars $\zeta$ Per, $\epsilon$
Per, $\gamma$ Per, $\delta$ Per and $\beta$ Tri (Fig. 14: tilted closed
triangle limits). During the 57 days eclipse repetition cycle, only two mid
eclipse epochs outside the 10 hour night time limits would qualify as certain
observable eclipses (Fig. 14: open circles at 19th and 48th days). However, a
certain detection of these two events would have been very difficult so close
to dawn and dusk. The same argument is true for three additional possible
eclipse detections (Fig. 14: open circles at 11th, 31st and 54th days).

Here, our statistical analysis of SWs giving the largest impact on the
$P_{\mathrm{A}}$ signal reveals that Algol was represented as Horus. The lucky
prognoses were most likely connected to Algol’s brightest phase. Sakhmet may
have represented Algol after eclipses, and Wedjat during periods close to the
Full Moon. To the Ancient Egyptians, Algol’s cycle may have symbolised the
familiar events of LE1 and LE2. At Aa, Re sends the Eye of Horus (Wedjat) to
destroy the rebels, as in LE2. At Ab, Horus enters the “foreign land” in
$g_{\mathrm{i}}(7,9)$, where he “smote him who rebelled”, as in LE1 or LE2.
The “will is written” for him in $g_{\mathrm{i}}(28,3)$ at the beginning of an
eclipse – the only gi vector of Horus overlapping the thick line centered at
Ac in Fig 1a. After an eclipse, Wedjat returns as Sakhmet who is pacified
immediately after Ad, as in LE2. And a new cycle begins.

Followers and Ennead may have represented Pleiades. Thus, these two, together
with Horus, Re, Wedjat and Sakhmet, give the largest impact on the
$P_{\mathrm{A}}$ signal.

The two periods, $P_{\mathrm{A}}$ and $P_{\mathrm{M}}$, regulate the
assignment of mythological texts to specific days of the year. The Moon
strongly regulates the times described as lucky for Heaven and for Earth (Figs
7c and 8c). The unlucky prognoses of Seth are clearly associated with the
phases of the Moon (Fig 11d). Other SWs follow $P_{\mathrm{A}}$ or
$P_{\mathrm{M}}$, like Busiris, Heart, Osiris and Man (Figs 9, 10, 12 and 13).
We show no figures for Heliopolis, Enemy, Rebel, Thoth, Onnophris, Nut, Nun,
Abydos, Lion and Flame which also reach $Q_{\mathrm{z}}\leq 0.2$ with
$P_{\mathrm{A}}$ or $P_{\mathrm{M}}$. All these regularities can not simply be
dismissed as a coincidence, let alone with the possible errors of
$\sigma_{\mathrm{t}}\approx\pm 0.5$ or $\pm 1.5$ days.

## Conclusions

What was the origin of the phenomenon that occurred every third day, but
always 3 hours and 36 minutes earlier than before, and caught the attention of
Ancient Egyptians? Our statistical analysis leads us to argue that the
mythological texts of CC contain astrophysical information about Algol. In
1596, Fabricius discovered the first variable star, Mira. Holwarda determined
its eleven month period 44 years later. In 1669, Montanari discovered the
second variable star, Algol. Goodricke[17] determined the 2.867 days period of
Algol in 1783. All these astronomical discoveries were made with naked eye.
Since then, they have become milestones of natural sciences. Our statistical
analysis of CC confirms that all these milestones should be shifted about
three millennia backwards in time.

## Acknowledgments

We thank L. Alha, T. Hackman, T. Lindén, K. Muinonen and H. Oja for their
comments on the manuscript. This work has made use of NASA’s Astrophysics Data
System (ADS) services.

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  * 19. Baron F, Monnier JD, Pedretti E, Zhao M, Schaefer G, Parks R, et al.  Imaging the Algol Triple System in the H Band with the CHARA Interferometer.  ApJ. 2012 Jun;752:20.

Data Availability: The authors confirm that all data underlying these findings
are fully available without restriction. Tables 2–4 and the Python 3.0 program
tableS1.py have been deposited to Dryad
(http://dx.doi.org/10.5061/dryad.tj4qg).

## Supporting Information

### S1 Fig

Text of Cairo Calendar page rto VIII. Inside our superimposed rectangle is the
hieratic writing for the word Horus. Reprinted from Leitz[12] under a CC BY
license, with permission from Harrassowitz Verlag, original copyright [1994].

### S1 Table

Analysis results for all SWs Day ($D$), month ($M$) of lucky
($g_{\mathrm{i}}$) and unlucky ($s_{\mathrm{i}}$) time points, their phase
($\phi_{\mathrm{i}}$), phase angle ($\Theta_{\mathrm{i}}$), direction of their
R vector ($\Theta_{\mathrm{R}}$) and differences
$\Delta\Theta_{\mathrm{i}}=\Theta_{\mathrm{i}}-\Theta_{\mathrm{R}}$ with Eq
(11) for $P_{\mathrm{A}}=2.85$ days and Eq (12) for $P_{\mathrm{M}}=29.6$
days. The binomial distribution parameters are $n_{1}$, $n_{2}$, $q_{B}$ for
$Q_{\mathrm{B}}$. Note that the parameters are given in the order of
increasing $\Delta\Theta_{\mathrm{i}}$, $n_{1}$ and $n_{2}$. All values
mentioned in text are marked in bold. We also make available the code of a
Python 3.0 program tableS1.py which can be downloaded on Dryad
(http://dx.doi.org/10.5061/dryad.tj4qg). This program can be used to reproduce
and replicate all analysis results given in S1 Table.

Horus:$~{}n_{G}={\bf 14}$,$~{}N_{G}={\bf 177}$,$~{}q_{B}=0.0791$
---
$P=2.85$, $\Theta_{R}=11$ |  |  $P=29.60$, $\Theta_{R}=-75$
Periodicity: $z=3.6$, $Q_{z}={\bf 0.03}$, $z_{x}={\bf 3.5}$ |  | No periodicity
D | M | $g_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$ |  | D | M | $g_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$
19 | 12 | 348.33 | 0.04 | 13 | 1 | 1 | 4 | 0.2808 |  | 27 | 3 | 86.33 | -0.20 | -73 | 2 | 1 | 2 | 0.1519
14 | 2 | 43.33 | 0.02 | 6 | 5 | 2 | 5 | 0.0532 |  | 27 | 1 | 26.33 | -0.23 | -82 | 8 | 2 | 7 | 0.1006
27 | 1 | 26.33 | 0.05 | 19 | 7 | 3 | 9 | 0.0289 |  | 28 | 3 | 87.33 | -0.17 | -60 | 14 | 3 | 16 | 0.1279
24 | 3 | 83.33 | 0.05 | 19 | 7 | 4 | 10 | 0.0056 |  | 29 | 3 | 88.33 | -0.13 | -48 | 26 | 4 | 25 | 0.1311
1 | 7 | 180.33 | 0.09 | 32 | 20 | 5 | 29 | 0.0747 |  | 23 | 7 | 202.33 | -0.28 | -102 | 27 | 5 | 26 | 0.0503
27 | 3 | 86.33 | 0.11 | 38 | 26 | 6 | 40 | 0.0928 |  | 24 | 3 | 83.33 | -0.30 | -109 | 34 | 6 | 36 | 0.0613
15 | 11 | 314.33 | 0.11 | 38 | 26 | 7 | 43 | 0.0503 |  | 19 | 12 | 348.33 | -0.35 | -126 | 51 | 7 | 54 | 0.1322
1 | 9 | 240.33 | 0.14 | 51 | 39 | 8 | 57 | 0.0788 |  | 1 | 7 | 180.33 | -0.03 | -9 | 65 | 8 | 67 | 0.1581
18 | 1 | 17.33 | -0.11 | -38 | 49 | 9 | 68 | 0.0869 |  | 1 | 9 | 240.33 | 0.00 | 0 | 75 | 9 | 79 | 0.1712
7 | 9 | 246.33 | 0.25 | 88 | 77 | 10 | 95 | 0.2180 |  | 1 | 10 | 270.33 | 0.01 | 5 | 80 | 10 | 85 | 0.1337
29 | 3 | 88.33 | -0.19 | -69 | 81 | 11 | 98 | 0.1515 |  | 15 | 11 | 314.33 | -0.50 | -180 | 105 | 11 | 110 | 0.2529
23 | 7 | 202.33 | -0.19 | -69 | 81 | 12 | 99 | 0.0912 |  | 18 | 1 | 17.33 | 0.47 | 168 | 117 | 12 | 119 | 0.2317
1 | 10 | 270.33 | -0.33 | -120 | 131 | 13 | 142 | 0.3332 |  | 7 | 9 | 246.33 | 0.20 | 73 | 148 | 13 | 148 | 0.3890
28 | 3 | 87.33 | 0.46 | 164 | 153 | 14 | 155 | 0.3428 |  | 14 | 2 | 43.33 | 0.35 | 124 | 161 | 14 | 159 | 0.3785
Horus:$~{}n_{S}=4$,$~{}N_{S}={\bf 105}$,$~{}q_{B}=0.0381$
$P=2.85$, $\Theta_{R}=-75$ |  |  $P=29.60$, $\Theta_{R}=-153$
Weak periodicity: $z=2.0$, $Q_{z}=0.1$, $z_{x}=0.1$ |  | No periodicity
D | M | $s_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$ |  | D | M | $s_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$
20 | 9 | 259.33 | -0.19 | -69 | 5 | 1 | 5 | 0.1765 |  | 20 | 9 | 259.33 | -0.36 | -129 | 24 | 1 | 23 | 0.5907
26 | 1 | 25.33 | -0.30 | -107 | 33 | 2 | 21 | 0.1897 |  | 26 | 1 | 25.33 | -0.26 | -95 | 58 | 2 | 42 | 0.4788
11 | 11 | 310.33 | -0.30 | -107 | 33 | 3 | 25 | 0.0681 |  | 11 | 11 | 310.33 | 0.37 | 132 | 76 | 3 | 57 | 0.3705
5 | 8 | 214.33 | 0.02 | 6 | 81 | 4 | 49 | 0.1159 |  | 5 | 8 | 214.33 | 0.12 | 44 | 163 | 4 | 97 | 0.5077

Re:$~{}n_{G}={\bf 31}$,$~{}N_{G}=177$,$~{}q_{B}=0.1751$
---
$P=2.85$, $\Theta_{R}=23$ |  |  $P=29.60$, $\Theta_{R}=-7$
Periodicity: $z=2.9$, $Q_{z}={\bf 0.05}$, $z_{x}={\bf 2.5}$ |  | No periodicity
D | M | $g_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$ |  | D | M | $g_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$
17 | 2 | 46.33 | 0.07 | 25 | 2 | 1 | 1 | 0.1751 |  | 3 | 2 | 32.33 | -0.03 | -9 | 3 | 1 | 6 | 0.6850
24 | 3 | 83.33 | 0.05 | 19 | 4 | 2 | 8 | 0.4217 |  | 2 | 6 | 151.33 | -0.01 | -2 | 5 | 2 | 9 | 0.4854
25 | 10 | 294.33 | 0.09 | 32 | 8 | 3 | 16 | 0.5496 |  | 1 | 6 | 150.33 | -0.04 | -14 | 7 | 3 | 14 | 0.4549
1 | 5 | 120.33 | 0.04 | 13 | 11 | 4 | 19 | 0.4324 |  | 3 | 5 | 122.33 | 0.01 | 5 | 12 | 4 | 20 | 0.4743
27 | 3 | 86.33 | 0.11 | 38 | 15 | 5 | 23 | 0.3766 |  | 1 | 5 | 120.33 | -0.05 | -19 | 12 | 5 | 22 | 0.3390
24 | 5 | 143.33 | 0.11 | 38 | 15 | 6 | 24 | 0.2337 |  | 1 | 4 | 90.33 | -0.07 | -24 | 17 | 6 | 29 | 0.3988
8 | 10 | 277.33 | 0.12 | 44 | 21 | 7 | 31 | 0.2934 |  | 2 | 1 | 1.33 | -0.07 | -26 | 20 | 7 | 32 | 0.3236
21 | 3 | 80.33 | 0.00 | 0 | 23 | 8 | 34 | 0.2350 |  | 6 | 2 | 35.33 | 0.08 | 27 | 34 | 8 | 49 | 0.6446
9 | 11 | 308.33 | 0.00 | 0 | 23 | 9 | 36 | 0.1664 |  | 3 | 10 | 272.33 | 0.08 | 30 | 36 | 9 | 53 | 0.5969
10 | 3 | 69.33 | 0.14 | 51 | 27 | 10 | 37 | 0.0998 |  | 29 | 3 | 88.33 | -0.13 | -48 | 41 | 10 | 61 | 0.6431
25 | 12 | 354.33 | 0.14 | 51 | 27 | 11 | 40 | 0.0783 |  | 25 | 12 | 354.33 | -0.15 | -53 | 46 | 11 | 65 | 0.6006
3 | 2 | 32.33 | 0.16 | 57 | 34 | 12 | 44 | 0.0716 |  | 25 | 10 | 294.33 | -0.17 | -63 | 56 | 12 | 72 | 0.6231
21 | 1 | 20.33 | -0.05 | -19 | 42 | 13 | 55 | 0.1543 |  | 24 | 12 | 353.33 | -0.18 | -65 | 58 | 13 | 76 | 0.5844
19 | 8 | 228.33 | -0.07 | -25 | 48 | 14 | 64 | 0.2209 |  | 9 | 1 | 8.33 | 0.16 | 59 | 66 | 14 | 81 | 0.5673
6 | 2 | 35.33 | 0.21 | 76 | 53 | 15 | 67 | 0.1848 |  | 27 | 3 | 86.33 | -0.20 | -73 | 66 | 15 | 83 | 0.4916
2 | 6 | 151.33 | -0.09 | -32 | 55 | 16 | 72 | 0.1831 |  | 9 | 2 | 38.33 | 0.18 | 64 | 70 | 16 | 87 | 0.4583
19 | 1 | 18.33 | 0.25 | 88 | 65 | 17 | 80 | 0.2275 |  | 9 | 4 | 98.33 | 0.20 | 73 | 80 | 17 | 97 | 0.5405
10 | 12 | 339.33 | -0.12 | -44 | 67 | 18 | 88 | 0.2725 |  | 25 | 5 | 144.33 | -0.24 | -87 | 80 | 18 | 99 | 0.4716
9 | 2 | 38.33 | 0.26 | 95 | 72 | 19 | 89 | 0.2053 |  | 10 | 2 | 39.33 | 0.21 | 76 | 83 | 19 | 101 | 0.4055
2 | 1 | 1.33 | 0.28 | 101 | 78 | 20 | 95 | 0.2164 |  | 10 | 3 | 69.33 | 0.22 | 81 | 87 | 20 | 106 | 0.3955
9 | 4 | 98.33 | 0.32 | 114 | 91 | 21 | 107 | 0.3194 |  | 24 | 5 | 143.33 | -0.28 | -99 | 93 | 21 | 111 | 0.3861
29 | 3 | 88.33 | -0.19 | -69 | 93 | 22 | 110 | 0.2813 |  | 8 | 10 | 277.33 | 0.25 | 90 | 97 | 22 | 116 | 0.3771
24 | 12 | 353.33 | -0.21 | -76 | 99 | 23 | 116 | 0.2904 |  | 24 | 3 | 83.33 | -0.30 | -109 | 102 | 23 | 121 | 0.3684
3 | 10 | 272.33 | 0.37 | 133 | 109 | 24 | 120 | 0.2700 |  | 9 | 11 | 308.33 | 0.30 | 107 | 114 | 24 | 130 | 0.4235
9 | 1 | 8.33 | -0.26 | -95 | 118 | 25 | 127 | 0.2929 |  | 13 | 4 | 102.33 | 0.34 | 122 | 129 | 25 | 139 | 0.4765
3 | 5 | 122.33 | -0.26 | -95 | 118 | 26 | 129 | 0.2460 |  | 10 | 12 | 339.33 | 0.35 | 124 | 131 | 26 | 143 | 0.4508
13 | 4 | 102.33 | -0.28 | -101 | 124 | 27 | 137 | 0.2811 |  | 21 | 3 | 80.33 | -0.40 | -146 | 139 | 27 | 146 | 0.4110
25 | 5 | 144.33 | 0.46 | 164 | 141 | 28 | 147 | 0.3444 |  | 19 | 8 | 228.33 | -0.40 | -146 | 139 | 28 | 147 | 0.3444
1 | 4 | 90.33 | -0.49 | -177 | 160 | 29 | 160 | 0.4516 |  | 21 | 1 | 20.33 | -0.43 | -155 | 148 | 29 | 153 | 0.3512
10 | 2 | 39.33 | -0.39 | -139 | 162 | 30 | 163 | 0.4139 |  | 17 | 2 | 46.33 | 0.45 | 161 | 168 | 30 | 165 | 0.4423
1 | 6 | 150.33 | -0.44 | -158 | 179 | 31 | 175 | 0.5032 |  | 19 | 1 | 18.33 | -0.50 | -180 | 173 | 31 | 172 | 0.4614
Re:$~{}n_{S}={\bf 26}$,$~{}N_{S}=105$,$~{}q_{B}=0.2476$
$P=2.85$, $\Theta_{R}=-124$ |  |  $P=29.60$, $\Theta_{R}=-177$
No periodicity |  | Weak periodicity: $z=1.7$, $Q_{z}={\bf 0.2}$, $z_{x}=-1.7$
D | M | $s_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$ |  | D | M | $s_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$
23 | 1 | 22.33 | -0.35 | -126 | 3 | 1 | 1 | 0.2476 |  | 15 | 12 | 344.33 | -0.49 | -175 | 2 | 1 | 3 | 0.5741
20 | 3 | 79.33 | -0.35 | -126 | 3 | 2 | 2 | 0.0613 |  | 16 | 11 | 315.33 | -0.47 | -167 | 10 | 2 | 13 | 0.8693
15 | 12 | 344.33 | -0.37 | -133 | 9 | 3 | 8 | 0.3155 |  | 19 | 4 | 108.33 | -0.46 | -165 | 12 | 3 | 14 | 0.7120
20 | 5 | 139.33 | -0.30 | -107 | 16 | 4 | 13 | 0.4078 |  | 20 | 2 | 49.33 | -0.45 | -163 | 15 | 4 | 16 | 0.5864
11 | 11 | 310.33 | -0.30 | -107 | 16 | 5 | 15 | 0.3057 |  | 20 | 3 | 79.33 | -0.44 | -158 | 20 | 5 | 19 | 0.5249
10 | 6 | 159.33 | -0.28 | -101 | 23 | 6 | 19 | 0.3233 |  | 20 | 5 | 139.33 | -0.41 | -148 | 29 | 6 | 23 | 0.5209
27 | 2 | 56.33 | -0.42 | -152 | 28 | 7 | 21 | 0.2480 |  | 22 | 1 | 21.33 | -0.40 | -143 | 34 | 7 | 25 | 0.4279
27 | 8 | 236.33 | -0.26 | -95 | 29 | 8 | 24 | 0.2253 |  | 18 | 11 | 317.33 | -0.40 | -143 | 34 | 8 | 27 | 0.3464
7 | 2 | 36.33 | -0.44 | -158 | 34 | 9 | 25 | 0.1428 |  | 11 | 12 | 340.33 | 0.38 | 137 | 46 | 9 | 34 | 0.4737
7 | 10 | 276.33 | -0.23 | -82 | 41 | 10 | 33 | 0.2880 |  | 23 | 1 | 22.33 | -0.36 | -131 | 46 | 10 | 35 | 0.3612
24 | 2 | 53.33 | -0.47 | -171 | 47 | 11 | 34 | 0.2011 |  | 11 | 11 | 310.33 | 0.37 | 132 | 51 | 11 | 39 | 0.3668
12 | 1 | 11.33 | -0.21 | -76 | 48 | 12 | 36 | 0.1586 |  | 11 | 10 | 280.33 | 0.35 | 127 | 56 | 12 | 43 | 0.3715
9 | 3 | 68.33 | -0.21 | -76 | 48 | 13 | 37 | 0.1045 |  | 21 | 9 | 260.33 | -0.32 | -116 | 61 | 13 | 46 | 0.3434
26 | 5 | 145.33 | -0.19 | -69 | 54 | 14 | 40 | 0.0969 |  | 24 | 2 | 53.33 | -0.32 | -114 | 63 | 14 | 48 | 0.2880
19 | 4 | 108.33 | -0.18 | -63 | 60 | 15 | 42 | 0.0751 |  | 22 | 10 | 291.33 | -0.28 | -99 | 78 | 15 | 55 | 0.3824
16 | 11 | 315.33 | 0.46 | 164 | 72 | 16 | 49 | 0.1336 |  | 12 | 1 | 11.33 | 0.26 | 95 | 88 | 16 | 62 | 0.4728
3 | 12 | 332.33 | 0.42 | 152 | 85 | 17 | 58 | 0.2531 |  | 10 | 6 | 159.33 | 0.26 | 95 | 88 | 17 | 63 | 0.3877
22 | 1 | 21.33 | 0.30 | 107 | 129 | 18 | 78 | 0.6766 |  | 27 | 2 | 56.33 | -0.22 | -77 | 100 | 18 | 72 | 0.5265
22 | 10 | 291.33 | 0.04 | 13 | 136 | 19 | 84 | 0.7145 |  | 26 | 5 | 145.33 | -0.21 | -75 | 102 | 19 | 74 | 0.4720
6 | 4 | 95.33 | 0.26 | 95 | 142 | 20 | 85 | 0.6444 |  | 7 | 10 | 276.33 | 0.22 | 78 | 105 | 20 | 75 | 0.3938
11 | 12 | 340.33 | 0.23 | 82 | 154 | 21 | 90 | 0.6623 |  | 9 | 3 | 68.33 | 0.19 | 68 | 114 | 21 | 79 | 0.3955
7 | 7 | 186.33 | 0.19 | 69 | 167 | 22 | 96 | 0.6993 |  | 7 | 7 | 186.33 | 0.18 | 64 | 119 | 22 | 80 | 0.3245
20 | 2 | 49.33 | 0.12 | 44 | 168 | 23 | 98 | 0.6542 |  | 27 | 8 | 236.33 | -0.13 | -48 | 129 | 23 | 87 | 0.3985
11 | 10 | 280.33 | 0.18 | 63 | 173 | 24 | 101 | 0.6295 |  | 7 | 2 | 36.33 | 0.11 | 39 | 143 | 24 | 93 | 0.4470
21 | 9 | 260.33 | 0.16 | 57 | 180 | 25 | 104 | 0.6051 |  | 3 | 12 | 332.33 | 0.11 | 39 | 143 | 25 | 94 | 0.3780
18 | 11 | 317.33 | 0.16 | 57 | 180 | 26 | 105 | 0.5375 |  | 6 | 4 | 95.33 | 0.10 | 37 | 146 | 26 | 97 | 0.3574

Wedjat:$~{}n_{G}=4$,$~{}N_{G}=177$,$~{}q_{B}=0.0226$
---
$P=2.85$, $\Theta_{R}=-8$ |  |  $P=29.60$, $\Theta_{R}=6$
Weak periodicity: $z=2.1$, $Q_{z}=0.1$, $z_{x}={\bf 2.0}$ |  | Periodicity: $z=2.9$, $Q_{z}=0.05$, $z_{x}={\bf 2.9}$
D | M | $g_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$ |  | D | M | $g_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$
1 | 5 | 120.33 | 0.04 | 13 | 21 | 1 | 29 | 0.4846 |  | 30 | 10 | 299.33 | -0.01 | -2 | 8 | 1 | 12 | 0.2399
6 | 9 | 245.33 | -0.11 | -38 | 30 | 2 | 43 | 0.2537 |  | 3 | 2 | 32.33 | -0.03 | -9 | 15 | 2 | 20 | 0.0742
30 | 10 | 299.33 | -0.16 | -57 | 49 | 3 | 73 | 0.2285 |  | 1 | 5 | 120.33 | -0.05 | -19 | 25 | 3 | 36 | 0.0474
3 | 2 | 32.33 | 0.16 | 57 | 65 | 4 | 84 | 0.1228 |  | 6 | 9 | 245.33 | 0.17 | 61 | 55 | 4 | 72 | 0.0804
Wedjat:$~{}n_{S}=1$,$~{}N_{S}=105$,$~{}q_{B}=0.0095$
$P=2.85$, $\Theta_{R}=-101$ |  |  $P=29.60$, $\Theta_{R}=95$
No periodicity |  | No periodicity
D | M | $s_{i}$ | $\phi_{i}$ | $\Theta_{i}$ |  |  |  |  |  | D | M | $s_{i}$ | $\phi_{i}$ | $\Theta_{i}$ |  |  |  |
10 | 6 | 159.33 | -0.28 | -101 |  |  |  |  |  | 10 | 6 | 159.33 | 0.26 | 95 |  |  |  |

Son:$~{}n_{G}=6$,$~{}N_{G}=177$,$~{}q_{B}=0.0339$
---
$P=2.85$, $\Theta_{R}=18$ |  |  $P=29.60$, $\Theta_{R}=-82$
Weak periodicity: $z=2.3$, $Q_{z}=0.1$, $z_{x}={\bf 2.0}$ |  | No periodicity
D | M | $g_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$ |  | D | M | $g_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$
24 | 3 | 83.33 | 0.05 | 19 | 1 | 1 | 2 | 0.0666 |  | 28 | 3 | 87.33 | -0.17 | -60 | 21 | 1 | 22 | 0.5317
1 | 5 | 120.33 | 0.04 | 13 | 6 | 2 | 6 | 0.0157 |  | 24 | 3 | 83.33 | -0.30 | -109 | 27 | 2 | 27 | 0.2325
21 | 3 | 80.33 | 0.00 | 0 | 18 | 3 | 27 | 0.0622 |  | 1 | 5 | 120.33 | -0.05 | -19 | 63 | 3 | 59 | 0.3233
1 | 9 | 240.33 | 0.14 | 51 | 32 | 4 | 47 | 0.0745 |  | 21 | 3 | 80.33 | -0.40 | -146 | 64 | 4 | 61 | 0.1523
13 | 12 | 342.33 | -0.07 | -25 | 44 | 5 | 62 | 0.0590 |  | 1 | 9 | 240.33 | 0.00 | 0 | 82 | 5 | 84 | 0.1566
28 | 3 | 87.33 | 0.46 | 164 | 146 | 6 | 151 | 0.4052 |  | 13 | 12 | 342.33 | 0.45 | 161 | 117 | 6 | 122 | 0.2340
Son:$~{}n_{S}=4$,$~{}N_{S}=105$,$~{}q_{B}=0.0381$
$P=2.85$, $\Theta_{R}=85$ |  |  $P=29.60$, $\Theta_{R}=-167$
No periodicity |  | No periodicity
D | M | $s_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$ |  | D | M | $s_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$
17 | 8 | 226.33 | 0.23 | 82 | 3 | 1 | 3 | 0.1100 |  | 17 | 8 | 226.33 | -0.47 | -170 | 2 | 1 | 5 | 0.1765
12 | 2 | 41.33 | 0.32 | 114 | 29 | 2 | 23 | 0.2179 |  | 20 | 2 | 49.33 | -0.45 | -163 | 5 | 2 | 7 | 0.0268
20 | 2 | 49.33 | 0.12 | 44 | 40 | 3 | 29 | 0.0970 |  | 26 | 1 | 25.33 | -0.26 | -95 | 73 | 3 | 53 | 0.3285
26 | 1 | 25.33 | -0.30 | -107 | 168 | 4 | 95 | 0.4914 |  | 12 | 2 | 41.33 | 0.28 | 100 | 92 | 4 | 66 | 0.2434

Sakhmet:$~{}n_{G}={\bf 3}$,$~{}N_{G}=177$,$~{}q_{B}=0.0169$
---
$P=2.85$, $\Theta_{R}=-33$ |  |  $P=29.60$, $\Theta_{R}=1$
Weak periodicity: $z=2.2$, $Q_{z}={\bf 0.1}$, $z_{x}={\bf 1.6}$ |  | No periodicity
D | M | $g_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$ |  | D | M | $g_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$
29 | 5 | 148.33 | -0.14 | -51 | 18 | 1 | 25 | 0.3478 |  | 1 | 5 | 120.33 | -0.05 | -19 | 20 | 1 | 29 | 0.3909
9 | 5 | 128.33 | -0.16 | -57 | 24 | 2 | 33 | 0.1075 |  | 29 | 5 | 148.33 | -0.11 | -39 | 39 | 2 | 56 | 0.2454
1 | 5 | 120.33 | 0.04 | 13 | 45 | 3 | 56 | 0.0696 |  | 9 | 5 | 128.33 | 0.22 | 78 | 77 | 3 | 97 | 0.2273
Sakhmet:$~{}n_{S}={\bf 3}$,$~{}N_{S}={\bf 105}$,$~{}q_{B}=0.0286$
$P=2.85$, $\Theta_{R}=-86$ |  |  $P=29.60$, $\Theta_{R}=78$
Periodicity: $z=3.0$, $Q_{z}={\bf 0.05}$, $z_{x}=0.0$ |  | No periodicity
D | M | $s_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$ |  | D | M | $s_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$
13 | 6 | 162.33 | -0.23 | -82 | 4 | 1 | 3 | 0.0833 |  | 7 | 10 | 276.33 | 0.22 | 78 | 0 | 1 | 1 | 0.0286
7 | 10 | 276.33 | -0.23 | -82 | 4 | 2 | 4 | 0.0047 |  | 13 | 6 | 162.33 | 0.37 | 132 | 54 | 2 | 32 | 0.2323
27 | 8 | 236.33 | -0.26 | -95 | 8 | 3 | 6 | 0.0004 |  | 27 | 8 | 236.33 | -0.13 | -48 | 126 | 3 | 70 | 0.3233

Followers:$~{}n_{G}={\bf 15}$,$~{}N_{G}=177$,$~{}q_{B}=0.0847$
---
$P=2.85$, $\Theta_{R}=22$ |  |  $P=29.60$, $\Theta_{R}=57$
Weak periodicity: $z=1.6$, $Q_{z}={\bf 0.2}$, $z_{x}={\bf 1.4}$ |  | No periodicity
D | M | $g_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$ |  | D | M | $g_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$
21 | 5 | 140.33 | 0.05 | 19 | 3 | 1 | 3 | 0.2333 |  | 6 | 9 | 245.33 | 0.17 | 61 | 4 | 1 | 5 | 0.3577
1 | 5 | 120.33 | 0.04 | 13 | 9 | 2 | 12 | 0.2705 |  | 10 | 2 | 39.33 | 0.21 | 76 | 18 | 2 | 20 | 0.5148
29 | 11 | 328.33 | 0.02 | 6 | 15 | 3 | 25 | 0.3567 |  | 3 | 10 | 272.33 | 0.08 | 30 | 28 | 3 | 30 | 0.4731
8 | 10 | 277.33 | 0.12 | 44 | 23 | 4 | 35 | 0.3447 |  | 8 | 10 | 277.33 | 0.25 | 90 | 33 | 4 | 38 | 0.4041
1 | 9 | 240.33 | 0.14 | 51 | 29 | 5 | 41 | 0.2651 |  | 9 | 10 | 278.33 | 0.28 | 103 | 45 | 5 | 48 | 0.3849
3 | 2 | 32.33 | 0.16 | 57 | 35 | 6 | 50 | 0.2472 |  | 1 | 9 | 240.33 | 0.00 | 0 | 57 | 6 | 62 | 0.4305
21 | 1 | 20.33 | -0.05 | -19 | 40 | 7 | 53 | 0.1591 |  | 3 | 2 | 32.33 | -0.03 | -9 | 67 | 7 | 73 | 0.4249
6 | 9 | 245.33 | -0.11 | -38 | 59 | 8 | 77 | 0.3277 |  | 29 | 11 | 328.33 | -0.03 | -9 | 67 | 8 | 75 | 0.3020
16 | 8 | 225.33 | -0.12 | -44 | 66 | 9 | 81 | 0.2468 |  | 1 | 5 | 120.33 | -0.05 | -19 | 76 | 9 | 86 | 0.3047
13 | 10 | 282.33 | -0.12 | -44 | 66 | 10 | 82 | 0.1551 |  | 1 | 4 | 90.33 | -0.07 | -24 | 81 | 10 | 91 | 0.2413
19 | 1 | 18.33 | 0.25 | 88 | 67 | 11 | 84 | 0.0976 |  | 13 | 10 | 282.33 | 0.42 | 151 | 94 | 11 | 106 | 0.2865
3 | 10 | 272.33 | 0.37 | 133 | 111 | 12 | 123 | 0.3491 |  | 16 | 8 | 225.33 | 0.49 | 178 | 121 | 12 | 131 | 0.4333
9 | 10 | 278.33 | 0.47 | 171 | 149 | 13 | 154 | 0.5476 |  | 19 | 1 | 18.33 | -0.50 | -180 | 123 | 13 | 134 | 0.3475
10 | 2 | 39.33 | -0.39 | -139 | 160 | 14 | 160 | 0.4909 |  | 21 | 1 | 20.33 | -0.43 | -155 | 147 | 14 | 156 | 0.4522
1 | 4 | 90.33 | -0.49 | -177 | 162 | 15 | 163 | 0.4088 |  | 21 | 5 | 140.33 | -0.38 | -136 | 167 | 15 | 171 | 0.4838
Followers:$~{}n_{S}={\bf 6}$,$~{}N_{S}={\bf 105}$,$~{}q_{B}=0.0571$
$P=2.85$, $\Theta_{R}=82$ |  |  $P=29.60$, $\Theta_{R}=134$
Periodicity: $z=4.3$, $Q_{z}={\bf 0.01}$, $z_{x}=0.1$ |  | Weak periodicity: $z=1.7$, $Q_{z}=0.2$, $z_{x}=-0.8$
D | M | $s_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$ |  | D | M | $s_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$
17 | 8 | 226.33 | 0.23 | 82 | 0 | 1 | 3 | 0.1618 |  | 11 | 12 | 340.33 | 0.38 | 137 | 3 | 1 | 3 | 0.1618
11 | 12 | 340.33 | 0.23 | 82 | 0 | 2 | 4 | 0.0181 |  | 11 | 10 | 280.33 | 0.35 | 127 | 7 | 2 | 7 | 0.0566
7 | 7 | 186.33 | 0.19 | 69 | 13 | 3 | 11 | 0.0218 |  | 11 | 1 | 10.33 | 0.23 | 83 | 50 | 3 | 31 | 0.2598
11 | 10 | 280.33 | 0.18 | 63 | 19 | 4 | 15 | 0.0087 |  | 17 | 8 | 226.33 | -0.47 | -170 | 57 | 4 | 37 | 0.1590
21 | 9 | 260.33 | 0.16 | 57 | 25 | 5 | 18 | 0.0028 |  | 7 | 7 | 186.33 | 0.18 | 64 | 70 | 5 | 48 | 0.1378
11 | 1 | 10.33 | 0.44 | 158 | 76 | 6 | 42 | 0.0311 |  | 21 | 9 | 260.33 | -0.32 | -116 | 110 | 6 | 74 | 0.2477

Ennead:$~{}n_{G}=18$,$~{}N_{G}={\bf 177}$,$~{}q_{B}=0.1017$
---
$P=2.85$, $\Theta_{R}=46$ |  |  $P=29.60$, $\Theta_{R}=64$
Weak periodicity: $z=2.2$, $Q_{z}=0.1$, $z_{x}={\bf 1.1}$ |  | No periodicity
D | M | $g_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$ |  | D | M | $g_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$
10 | 3 | 69.33 | 0.14 | 51 | 4 | 1 | 3 | 0.2751 |  | 9 | 2 | 38.33 | 0.18 | 64 | 0 | 1 | 1 | 0.1017
24 | 5 | 143.33 | 0.11 | 38 | 9 | 2 | 9 | 0.2310 |  | 10 | 3 | 69.33 | 0.22 | 81 | 17 | 2 | 19 | 0.5893
18 | 9 | 257.33 | 0.11 | 38 | 9 | 3 | 10 | 0.0731 |  | 8 | 8 | 217.33 | 0.22 | 81 | 17 | 3 | 20 | 0.3327
17 | 2 | 46.33 | 0.07 | 25 | 21 | 4 | 24 | 0.2231 |  | 6 | 2 | 35.33 | 0.08 | 27 | 37 | 4 | 39 | 0.5701
8 | 8 | 217.33 | 0.07 | 25 | 21 | 5 | 27 | 0.1334 |  | 5 | 4 | 94.33 | 0.07 | 25 | 39 | 5 | 42 | 0.4267
6 | 2 | 35.33 | 0.21 | 76 | 29 | 6 | 36 | 0.1539 |  | 13 | 4 | 102.33 | 0.34 | 122 | 58 | 6 | 60 | 0.5799
30 | 5 | 149.33 | 0.21 | 76 | 29 | 7 | 37 | 0.0764 |  | 14 | 2 | 43.33 | 0.35 | 124 | 61 | 7 | 63 | 0.4622
14 | 2 | 43.33 | 0.02 | 6 | 40 | 8 | 44 | 0.0735 |  | 16 | 2 | 45.33 | 0.41 | 149 | 85 | 8 | 91 | 0.7184
19 | 1 | 18.33 | 0.25 | 88 | 42 | 9 | 48 | 0.0506 |  | 1 | 4 | 90.33 | -0.07 | -24 | 88 | 9 | 96 | 0.6511
9 | 2 | 38.33 | 0.26 | 95 | 48 | 10 | 57 | 0.0601 |  | 2 | 1 | 1.33 | -0.07 | -26 | 90 | 10 | 99 | 0.5577
16 | 12 | 345.33 | -0.02 | -6 | 53 | 11 | 62 | 0.0468 |  | 30 | 5 | 149.33 | -0.07 | -26 | 90 | 11 | 100 | 0.4392
2 | 1 | 1.33 | 0.28 | 101 | 55 | 12 | 63 | 0.0237 |  | 30 | 4 | 119.33 | -0.09 | -31 | 95 | 12 | 105 | 0.3801
5 | 4 | 94.33 | -0.09 | -32 | 78 | 13 | 91 | 0.1317 |  | 17 | 2 | 46.33 | 0.45 | 161 | 97 | 13 | 106 | 0.2802
1 | 2 | 30.33 | 0.46 | 164 | 118 | 14 | 126 | 0.4052 |  | 1 | 2 | 30.33 | -0.09 | -34 | 97 | 14 | 108 | 0.2069
1 | 4 | 90.33 | -0.49 | -177 | 137 | 15 | 143 | 0.4899 |  | 19 | 1 | 18.33 | -0.50 | -180 | 117 | 15 | 126 | 0.2993
16 | 2 | 45.33 | -0.28 | -101 | 147 | 16 | 154 | 0.5029 |  | 16 | 12 | 345.33 | -0.45 | -163 | 134 | 16 | 144 | 0.3934
13 | 4 | 102.33 | -0.28 | -101 | 147 | 17 | 155 | 0.4091 |  | 18 | 9 | 257.33 | -0.42 | -153 | 143 | 17 | 150 | 0.3564
30 | 4 | 119.33 | -0.32 | -114 | 160 | 18 | 166 | 0.4238 |  | 24 | 5 | 143.33 | -0.28 | -99 | 163 | 18 | 165 | 0.4135
Ennead:$~{}n_{S}=3$,$~{}N_{S}=105$,$~{}q_{B}=0.0286$
$P=2.85$, $\Theta_{R}=-117$ |  |  $P=29.60$, $\Theta_{R}=-171$
No periodicity |  | No periodicity
D | M | $s_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$ |  | D | M | $s_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$
15 | 12 | 344.33 | -0.37 | -133 | 16 | 1 | 16 | 0.3711 |  | 15 | 12 | 344.33 | -0.49 | -175 | 4 | 1 | 7 | 0.1837
7 | 2 | 36.33 | -0.44 | -158 | 41 | 2 | 32 | 0.2323 |  | 19 | 10 | 288.33 | -0.38 | -136 | 35 | 2 | 29 | 0.2006
19 | 10 | 288.33 | -0.02 | -6 | 110 | 3 | 66 | 0.2920 |  | 7 | 2 | 36.33 | 0.11 | 39 | 150 | 3 | 98 | 0.5333

Heliopolis:$~{}n_{G}=4$,$~{}N_{G}=177$,$~{}q_{B}=0.0226$
---
$P=2.85$, $\Theta_{R}=-70$ |  |  $P=29.60$, $\Theta_{R}=138$
Weak periodicity: $z=2.1$, $Q_{z}=0.1$, $z_{x}={\bf 0.2}$ |  | No periodicity
D | M | $g_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$ |  | D | M | $g_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$
26 | 3 | 85.33 | -0.25 | -88 | 18 | 1 | 14 | 0.2739 |  | 9 | 7 | 188.33 | 0.24 | 88 | 50 | 1 | 44 | 0.6342
9 | 7 | 188.33 | -0.11 | -38 | 32 | 2 | 34 | 0.1789 |  | 10 | 2 | 39.33 | 0.21 | 76 | 62 | 2 | 53 | 0.3374
19 | 8 | 228.33 | -0.07 | -25 | 45 | 3 | 47 | 0.0900 |  | 19 | 8 | 228.33 | -0.40 | -146 | 76 | 3 | 67 | 0.1933
10 | 2 | 39.33 | -0.39 | -139 | 69 | 4 | 69 | 0.0711 |  | 26 | 3 | 85.33 | -0.24 | -85 | 137 | 4 | 121 | 0.2928
Heliopolis:$~{}n_{S}=4$,$~{}N_{S}=105$,$~{}q_{B}=0.0381$
$P=2.85$, $\Theta_{R}=-168$ |  |  $P=29.60$, $\Theta_{R}=132$
Weak periodicity: $z=2.3$, $Q_{z}=0.1$, $z_{x}=-2.2$ |  | No periodicity
D | M | $s_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$ |  | D | M | $s_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$
22 | 11 | 321.33 | -0.44 | -158 | 10 | 1 | 8 | 0.2671 |  | 10 | 6 | 159.33 | 0.26 | 95 | 37 | 1 | 22 | 0.5745
16 | 11 | 315.33 | 0.46 | 164 | 27 | 2 | 18 | 0.1487 |  | 16 | 11 | 315.33 | -0.47 | -167 | 61 | 2 | 41 | 0.4662
3 | 12 | 332.33 | 0.42 | 152 | 40 | 3 | 27 | 0.0820 |  | 3 | 12 | 332.33 | 0.11 | 39 | 93 | 3 | 64 | 0.4424
10 | 6 | 159.33 | -0.28 | -101 | 67 | 4 | 45 | 0.0915 |  | 22 | 11 | 321.33 | -0.26 | -95 | 134 | 4 | 85 | 0.4070

Enemy:$~{}n_{G}=6$,$~{}N_{G}=177$,$~{}q_{B}=0.0339$
---
$P=2.85$, $\Theta_{R}=140$ |  |  $P=29.60$, $\Theta_{R}=77$
Weak periodicity: $z=1.7$, $Q_{z}=0.2$, $z_{x}={\bf-1.0}$ |  | No periodicity
D | M | $g_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$ |  | D | M | $g_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$
23 | 10 | 292.33 | 0.39 | 139 | 1 | 1 | 2 | 0.0666 |  | 9 | 4 | 98.33 | 0.20 | 73 | 3 | 1 | 4 | 0.1289
9 | 4 | 98.33 | 0.32 | 114 | 27 | 2 | 19 | 0.1345 |  | 9 | 2 | 38.33 | 0.18 | 64 | 13 | 2 | 16 | 0.1007
9 | 2 | 38.33 | 0.26 | 95 | 46 | 3 | 36 | 0.1219 |  | 13 | 2 | 42.33 | 0.31 | 112 | 35 | 3 | 36 | 0.1219
19 | 1 | 18.33 | 0.25 | 88 | 52 | 4 | 42 | 0.0533 |  | 1 | 8 | 210.33 | -0.01 | -5 | 81 | 4 | 81 | 0.2950
1 | 8 | 210.33 | -0.39 | -139 | 81 | 5 | 66 | 0.0732 |  | 19 | 1 | 18.33 | -0.50 | -180 | 104 | 5 | 111 | 0.3241
13 | 2 | 42.33 | -0.33 | -120 | 100 | 6 | 77 | 0.0467 |  | 23 | 10 | 292.33 | -0.24 | -87 | 164 | 6 | 164 | 0.4829
Enemy:$~{}n_{S}=5$,$~{}N_{S}=105$,$~{}q_{B}=0.0476$
$P=2.85$, $\Theta_{R}=-121$ |  |  $P=29.60$, $\Theta_{R}=-146$
No periodicity |  | No periodicity
D | M | $s_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$ |  | D | M | $s_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$
23 | 1 | 22.33 | -0.35 | -126 | 5 | 1 | 2 | 0.0930 |  | 23 | 1 | 22.33 | -0.36 | -131 | 15 | 1 | 12 | 0.4432
26 | 1 | 25.33 | -0.30 | -107 | 14 | 2 | 10 | 0.0791 |  | 26 | 1 | 25.33 | -0.26 | -95 | 51 | 2 | 40 | 0.5739
14 | 3 | 73.33 | -0.46 | -164 | 43 | 3 | 32 | 0.1941 |  | 25 | 8 | 234.33 | -0.20 | -73 | 73 | 3 | 55 | 0.4901
25 | 8 | 234.33 | 0.04 | 13 | 134 | 4 | 82 | 0.5521 |  | 14 | 3 | 73.33 | 0.36 | 129 | 85 | 4 | 61 | 0.3309
13 | 3 | 72.33 | 0.19 | 69 | 170 | 5 | 96 | 0.4840 |  | 13 | 3 | 72.33 | 0.33 | 117 | 97 | 5 | 68 | 0.2228

Earth:$~{}n_{G}={\bf 19}$,$~{}N_{G}=177$,$~{}q_{B}=0.1073$
---
$P=2.85$, $\Theta_{R}=-61$ |  |  $P=29.60$, $\Theta_{R}=-27$
No periodicity |  | Periodicity: $z=6.6$, $Q_{z}={\bf 0.001}$, $z_{x}={\bf 5.3}$
D | M | $g_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$ |  | D | M | $g_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$
2 | 4 | 91.33 | -0.14 | -51 | 10 | 1 | 9 | 0.6401 |  | 1 | 1 | 0.33 | -0.11 | -39 | 12 | 1 | 17 | 0.8549
29 | 5 | 148.33 | -0.14 | -51 | 10 | 2 | 10 | 0.2924 |  | 29 | 5 | 148.33 | -0.11 | -39 | 12 | 2 | 18 | 0.5902
26 | 3 | 85.33 | -0.25 | -88 | 28 | 3 | 25 | 0.5119 |  | 1 | 6 | 150.33 | -0.04 | -14 | 13 | 3 | 19 | 0.3344
2 | 6 | 151.33 | -0.09 | -32 | 29 | 4 | 30 | 0.4046 |  | 30 | 2 | 59.33 | -0.11 | -41 | 14 | 4 | 21 | 0.1824
6 | 3 | 65.33 | -0.26 | -95 | 34 | 5 | 34 | 0.2989 |  | 2 | 4 | 91.33 | -0.03 | -12 | 15 | 5 | 23 | 0.0930
1 | 1 | 0.33 | -0.07 | -25 | 36 | 6 | 38 | 0.2186 |  | 1 | 7 | 180.33 | -0.03 | -9 | 17 | 6 | 26 | 0.0535
1 | 10 | 270.33 | -0.33 | -120 | 59 | 7 | 67 | 0.5884 |  | 28 | 5 | 147.33 | -0.14 | -51 | 24 | 7 | 37 | 0.0957
30 | 2 | 59.33 | -0.37 | -133 | 72 | 8 | 76 | 0.5780 |  | 2 | 6 | 151.33 | -0.01 | -2 | 25 | 8 | 38 | 0.0457
21 | 5 | 140.33 | 0.05 | 19 | 80 | 9 | 86 | 0.5835 |  | 1 | 10 | 270.33 | 0.01 | 5 | 32 | 9 | 47 | 0.0599
12 | 12 | 341.33 | -0.42 | -152 | 91 | 10 | 95 | 0.5750 |  | 28 | 3 | 87.33 | -0.17 | -60 | 34 | 10 | 48 | 0.0292
1 | 7 | 180.33 | 0.09 | 32 | 92 | 11 | 99 | 0.4993 |  | 1 | 11 | 300.33 | 0.03 | 10 | 37 | 11 | 54 | 0.0266
1 | 6 | 150.33 | -0.44 | -158 | 97 | 12 | 104 | 0.4413 |  | 27 | 3 | 86.33 | -0.20 | -73 | 46 | 12 | 63 | 0.0343
27 | 3 | 86.33 | 0.11 | 38 | 99 | 13 | 108 | 0.3748 |  | 3 | 10 | 272.33 | 0.08 | 30 | 56 | 13 | 74 | 0.0506
24 | 5 | 143.33 | 0.11 | 38 | 99 | 14 | 109 | 0.2794 |  | 26 | 3 | 85.33 | -0.24 | -85 | 58 | 14 | 75 | 0.0275
28 | 5 | 147.33 | -0.49 | -177 | 116 | 15 | 125 | 0.3645 |  | 6 | 3 | 65.33 | 0.09 | 32 | 59 | 15 | 76 | 0.0143
1 | 11 | 300.33 | 0.19 | 69 | 130 | 16 | 137 | 0.4000 |  | 24 | 5 | 143.33 | -0.28 | -99 | 73 | 16 | 88 | 0.0244
28 | 3 | 87.33 | 0.46 | 164 | 135 | 17 | 140 | 0.3330 |  | 7 | 9 | 246.33 | 0.20 | 73 | 100 | 17 | 115 | 0.1084
7 | 9 | 246.33 | 0.25 | 88 | 149 | 18 | 153 | 0.3774 |  | 21 | 5 | 140.33 | -0.38 | -136 | 109 | 18 | 122 | 0.1023
3 | 10 | 272.33 | 0.37 | 133 | 167 | 19 | 170 | 0.4623 |  | 12 | 12 | 341.33 | 0.41 | 149 | 176 | 19 | 174 | 0.5045
Earth:$~{}n_{S}={\bf 5}$,$~{}N_{S}=105$,$~{}q_{B}=0.0476$
$P=2.85$, $\Theta_{R}=-75$ |  |  $P=29.60$, $\Theta_{R}=-119$
Weak periodicity: $z=2.9$, $Q_{z}={\bf 0.06}$, $z_{x}=0.2$ |  | Weak periodicity: $z=1.8$, $Q_{z}={\bf 0.2}$, $z_{x}=-0.4$
D | M | $s_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$ |  | D | M | $s_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$
26 | 5 | 145.33 | -0.19 | -69 | 5 | 1 | 4 | 0.1773 |  | 19 | 10 | 288.33 | -0.38 | -136 | 17 | 1 | 12 | 0.4432
27 | 12 | 356.33 | -0.16 | -57 | 18 | 2 | 12 | 0.1091 |  | 20 | 5 | 139.33 | -0.41 | -148 | 29 | 2 | 23 | 0.3000
20 | 5 | 139.33 | -0.30 | -107 | 33 | 3 | 23 | 0.0941 |  | 26 | 5 | 145.33 | -0.21 | -75 | 44 | 3 | 33 | 0.2065
17 | 5 | 136.33 | -0.35 | -126 | 52 | 4 | 33 | 0.0702 |  | 17 | 5 | 136.33 | 0.49 | 175 | 66 | 4 | 49 | 0.2040
19 | 10 | 288.33 | -0.02 | -6 | 68 | 5 | 42 | 0.0483 |  | 27 | 12 | 356.33 | -0.08 | -29 | 90 | 5 | 62 | 0.1725

Heaven:$~{}n_{G}={\bf 19}$,$~{}N_{G}={\bf 177}$,$~{}q_{B}=0.1073$
---
$P=2.85$, $\Theta_{R}=10$ |  |  $P=29.60$, $\Theta_{R}=0$
No periodicity |  | Periodicity: $z=3.4$, $Q_{z}={\bf 0.03}$, $z_{x}={\bf 3.4}$
D | M | $g_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$ |  | D | M | $g_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$
2 | 12 | 331.33 | 0.07 | 25 | 15 | 1 | 22 | 0.9178 |  | 1 | 8 | 210.33 | -0.01 | -5 | 4 | 1 | 7 | 0.5484
1 | 3 | 60.33 | -0.02 | -6 | 16 | 2 | 23 | 0.7236 |  | 1 | 7 | 180.33 | -0.03 | -9 | 9 | 2 | 16 | 0.5247
1 | 7 | 180.33 | 0.09 | 32 | 22 | 3 | 29 | 0.6153 |  | 5 | 1 | 4.33 | 0.03 | 10 | 10 | 3 | 18 | 0.3036
24 | 5 | 143.33 | 0.11 | 38 | 28 | 4 | 41 | 0.6547 |  | 1 | 11 | 300.33 | 0.03 | 10 | 10 | 4 | 19 | 0.1396
19 | 8 | 228.33 | -0.07 | -25 | 35 | 5 | 53 | 0.6854 |  | 2 | 4 | 91.33 | -0.03 | -12 | 12 | 5 | 20 | 0.0559
10 | 3 | 69.33 | 0.14 | 51 | 41 | 6 | 56 | 0.5654 |  | 1 | 6 | 150.33 | -0.04 | -14 | 14 | 6 | 23 | 0.0309
1 | 11 | 300.33 | 0.19 | 69 | 59 | 7 | 78 | 0.7449 |  | 1 | 12 | 330.33 | 0.04 | 15 | 15 | 7 | 25 | 0.0138
2 | 4 | 91.33 | -0.14 | -51 | 61 | 8 | 80 | 0.6372 |  | 2 | 2 | 31.33 | -0.06 | -22 | 22 | 8 | 31 | 0.0144
6 | 2 | 35.33 | 0.21 | 76 | 66 | 9 | 83 | 0.5393 |  | 6 | 2 | 35.33 | 0.08 | 27 | 27 | 9 | 41 | 0.0275
19 | 1 | 18.33 | 0.25 | 88 | 78 | 10 | 92 | 0.5328 |  | 2 | 12 | 331.33 | 0.08 | 27 | 27 | 10 | 42 | 0.0118
2 | 2 | 31.33 | -0.19 | -69 | 79 | 11 | 97 | 0.4713 |  | 1 | 3 | 60.33 | -0.08 | -29 | 29 | 11 | 43 | 0.0048
26 | 3 | 85.33 | -0.25 | -88 | 98 | 12 | 115 | 0.5857 |  | 3 | 10 | 272.33 | 0.08 | 30 | 30 | 12 | 45 | 0.0022
5 | 1 | 4.33 | 0.33 | 120 | 110 | 13 | 125 | 0.5907 |  | 10 | 3 | 69.33 | 0.22 | 81 | 81 | 13 | 99 | 0.2628
13 | 4 | 102.33 | -0.28 | -101 | 111 | 14 | 128 | 0.5123 |  | 26 | 3 | 85.33 | -0.24 | -85 | 85 | 14 | 104 | 0.2238
1 | 12 | 330.33 | -0.28 | -101 | 111 | 15 | 130 | 0.4244 |  | 24 | 5 | 143.33 | -0.28 | -99 | 99 | 15 | 117 | 0.2724
3 | 10 | 272.33 | 0.37 | 133 | 123 | 16 | 132 | 0.3425 |  | 13 | 4 | 102.33 | 0.34 | 122 | 122 | 16 | 136 | 0.3884
1 | 8 | 210.33 | -0.39 | -139 | 149 | 17 | 153 | 0.4783 |  | 19 | 8 | 228.33 | -0.40 | -146 | 146 | 17 | 150 | 0.4446
1 | 6 | 150.33 | -0.44 | -158 | 168 | 18 | 166 | 0.5188 |  | 15 | 8 | 224.33 | 0.46 | 166 | 166 | 18 | 167 | 0.5294
15 | 8 | 224.33 | -0.47 | -171 | 179 | 19 | 175 | 0.5150 |  | 19 | 1 | 18.33 | -0.50 | -180 | 180 | 19 | 175 | 0.5150
Heaven:$~{}n_{S}={\bf 4}$,$~{}N_{S}=105$,$~{}q_{B}=0.0381$
$P=2.85$, $\Theta_{R}=103$ |  |  $P=29.60$, $\Theta_{R}=-132$
No periodicity |  | Weak periodicity: $z=2.9$, $Q_{z}={\bf 0.06}$, $z_{x}=-1.3$
D | M | $s_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$ |  | D | M | $s_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$
22 | 1 | 21.33 | 0.30 | 107 | 5 | 1 | 2 | 0.0747 |  | 22 | 1 | 21.33 | -0.40 | -143 | 11 | 1 | 7 | 0.2381
20 | 6 | 169.33 | 0.23 | 82 | 20 | 2 | 13 | 0.0857 |  | 20 | 6 | 169.33 | -0.40 | -143 | 11 | 2 | 8 | 0.0349
19 | 5 | 138.33 | 0.35 | 126 | 24 | 3 | 16 | 0.0213 |  | 19 | 5 | 138.33 | -0.44 | -160 | 28 | 3 | 20 | 0.0388
26 | 5 | 145.33 | -0.19 | -69 | 172 | 4 | 99 | 0.5237 |  | 26 | 5 | 145.33 | -0.21 | -75 | 57 | 4 | 48 | 0.1096

Busiris:$~{}n_{G}={\bf 4}$,$~{}N_{G}=177$,$~{}q_{B}=0.0226$
---
$P=2.85$, $\Theta_{R}=19$ |  |  $P=29.60$, $\Theta_{R}=3$
No periodicity |  | Periodicity: $z=3.0$, $Q_{z}={\bf 0.05}$, $z_{x}={\bf 3.0}$
D | M | $g_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$ |  | D | M | $g_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$
2 | 8 | 211.33 | -0.04 | -13 | 32 | 1 | 43 | 0.6258 |  | 2 | 8 | 211.33 | 0.02 | 8 | 5 | 1 | 6 | 0.1282
28 | 10 | 297.33 | 0.14 | 51 | 32 | 2 | 48 | 0.2957 |  | 30 | 7 | 209.33 | -0.05 | -17 | 20 | 2 | 29 | 0.1391
6 | 7 | 185.33 | -0.16 | -57 | 76 | 3 | 93 | 0.3511 |  | 28 | 10 | 297.33 | -0.07 | -26 | 29 | 3 | 45 | 0.0813
30 | 7 | 209.33 | 0.26 | 95 | 76 | 4 | 97 | 0.1773 |  | 6 | 7 | 185.33 | 0.14 | 51 | 48 | 4 | 63 | 0.0543
Busiris:$~{}n_{S}=3$,$~{}N_{S}=105$,$~{}q_{B}=0.0286$
$P=2.85$, $\Theta_{R}=-123$ |  |  $P=29.60$, $\Theta_{R}=-111$
No periodicity |  | No periodicity
D | M | $s_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$ |  | D | M | $s_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$
14 | 5 | 133.33 | -0.40 | -145 | 22 | 1 | 19 | 0.4235 |  | 26 | 2 | 55.33 | -0.25 | -90 | 21 | 1 | 16 | 0.3711
26 | 5 | 145.33 | -0.19 | -69 | 53 | 2 | 39 | 0.3068 |  | 26 | 5 | 145.33 | -0.21 | -75 | 35 | 2 | 27 | 0.1798
26 | 2 | 55.33 | 0.23 | 82 | 155 | 3 | 87 | 0.4543 |  | 14 | 5 | 133.33 | 0.39 | 139 | 110 | 3 | 68 | 0.3076

Rebel:$~{}n_{G}=3$,$~{}N_{G}=177$,$~{}q_{B}=0.0169$
---
$P=2.85$, $\Theta_{R}=125$ |  |  $P=29.60$, $\Theta_{R}=11$
No periodicity |  | Weak periodicity: $z=1.6$, $Q_{z}=0.2$, $z_{x}={\bf 1.6}$
D | M | $g_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$ |  | D | M | $g_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$
2 | 1 | 1.33 | 0.28 | 101 | 24 | 1 | 16 | 0.2393 |  | 1 | 8 | 210.33 | -0.01 | -5 | 16 | 1 | 20 | 0.2896
7 | 9 | 246.33 | 0.25 | 88 | 36 | 2 | 30 | 0.0915 |  | 2 | 1 | 1.33 | -0.07 | -26 | 38 | 2 | 49 | 0.2017
1 | 8 | 210.33 | -0.39 | -139 | 96 | 3 | 87 | 0.1837 |  | 7 | 9 | 246.33 | 0.20 | 73 | 62 | 3 | 81 | 0.1587
Rebel:$~{}n_{S}=3$,$~{}N_{S}=105$,$~{}q_{B}=0.0286$
$P=2.85$, $\Theta_{R}=107$ |  |  $P=29.60$, $\Theta_{R}=-162$
No periodicity |  | No periodicity
D | M | $s_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$ |  | D | M | $s_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$
12 | 2 | 41.33 | 0.32 | 114 | 7 | 1 | 5 | 0.1349 |  | 20 | 2 | 49.33 | -0.45 | -163 | 0 | 1 | 1 | 0.0286
23 | 12 | 352.33 | 0.44 | 158 | 51 | 2 | 38 | 0.2962 |  | 23 | 12 | 352.33 | -0.22 | -77 | 85 | 2 | 63 | 0.5406
20 | 2 | 49.33 | 0.12 | 44 | 63 | 3 | 42 | 0.1180 |  | 12 | 2 | 41.33 | 0.28 | 100 | 98 | 3 | 69 | 0.3155

Thoth:$~{}n_{G}=10$,$~{}N_{G}=177$,$~{}q_{B}=0.0565$
---
$P=2.85$, $\Theta_{R}=115$ |  |  $P=29.60$, $\Theta_{R}=-39$
No periodicity |  | Weak periodicity: $z=2.1$, $Q_{z}=0.1$, $z_{x}={\bf 1.3}$
D | M | $g_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$ |  | D | M | $g_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$
9 | 4 | 98.33 | 0.32 | 114 | 1 | 1 | 1 | 0.0565 |  | 29 | 5 | 148.33 | -0.11 | -39 | 1 | 1 | 2 | 0.1098
13 | 7 | 192.33 | 0.30 | 107 | 8 | 2 | 6 | 0.0411 |  | 28 | 5 | 147.33 | -0.14 | -51 | 11 | 2 | 15 | 0.2066
26 | 4 | 115.33 | 0.28 | 101 | 14 | 3 | 9 | 0.0117 |  | 1 | 4 | 90.33 | -0.07 | -24 | 15 | 3 | 21 | 0.1124
19 | 9 | 258.33 | 0.46 | 164 | 49 | 4 | 41 | 0.1998 |  | 3 | 2 | 32.33 | -0.03 | -9 | 30 | 4 | 39 | 0.1766
3 | 2 | 32.33 | 0.16 | 57 | 58 | 5 | 45 | 0.1087 |  | 27 | 3 | 86.33 | -0.20 | -73 | 33 | 5 | 46 | 0.1166
1 | 4 | 90.33 | -0.49 | -177 | 68 | 6 | 56 | 0.0953 |  | 30 | 10 | 299.33 | -0.01 | -2 | 37 | 6 | 52 | 0.0720
28 | 5 | 147.33 | -0.49 | -177 | 68 | 7 | 57 | 0.0409 |  | 26 | 4 | 115.33 | -0.22 | -80 | 41 | 7 | 54 | 0.0317
27 | 3 | 86.33 | 0.11 | 38 | 77 | 8 | 65 | 0.0297 |  | 19 | 9 | 258.33 | -0.39 | -141 | 101 | 8 | 110 | 0.2827
29 | 5 | 148.33 | -0.14 | -51 | 166 | 9 | 165 | 0.5908 |  | 9 | 4 | 98.33 | 0.20 | 73 | 113 | 9 | 120 | 0.2381
30 | 10 | 299.33 | -0.16 | -57 | 172 | 10 | 173 | 0.5164 |  | 13 | 7 | 192.33 | 0.38 | 137 | 176 | 10 | 176 | 0.5384
Thoth:$~{}n_{S}=2$,$~{}N_{S}=105$,$~{}q_{B}=0.0190$
$P=2.85$, $\Theta_{R}=66$ |  |  $P=29.60$, $\Theta_{R}=149$
Weak periodicity: $z=1.7$, $Q_{z}=0.2$, $z_{x}=0.3$ |  | No periodicity
D | M | $s_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$ |  | D | M | $s_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$
20 | 2 | 49.33 | 0.12 | 44 | 22 | 1 | 18 | 0.2926 |  | 20 | 2 | 49.33 | -0.45 | -163 | 49 | 1 | 34 | 0.4800
10 | 7 | 189.33 | 0.25 | 88 | 22 | 2 | 19 | 0.0501 |  | 10 | 7 | 189.33 | 0.28 | 100 | 49 | 2 | 35 | 0.1432

Onnophris:$~{}n_{G}=7$,$~{}N_{G}=177$,$~{}q_{B}=0.0395$
---
$P=2.85$, $\Theta_{R}=-138$ |  |  $P=29.60$, $\Theta_{R}=-47$
No periodicity |  | Weak periodicity: $z=2.1$, $Q_{z}=0.1$, $z_{x}={\bf 1.0}$
D | M | $g_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$ |  | D | M | $g_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$
28 | 7 | 207.33 | -0.44 | -158 | 20 | 1 | 14 | 0.4316 |  | 28 | 6 | 177.33 | -0.13 | -46 | 1 | 1 | 2 | 0.0775
16 | 2 | 45.33 | -0.28 | -101 | 37 | 2 | 24 | 0.2451 |  | 28 | 7 | 207.33 | -0.11 | -41 | 6 | 2 | 7 | 0.0288
1 | 12 | 330.33 | -0.28 | -101 | 37 | 3 | 27 | 0.0894 |  | 28 | 3 | 87.33 | -0.17 | -60 | 14 | 3 | 16 | 0.0235
28 | 3 | 87.33 | 0.46 | 164 | 58 | 4 | 47 | 0.1144 |  | 29 | 8 | 238.33 | -0.07 | -24 | 23 | 4 | 29 | 0.0264
29 | 8 | 238.33 | 0.44 | 158 | 64 | 5 | 54 | 0.0619 |  | 1 | 12 | 330.33 | 0.04 | 15 | 62 | 5 | 78 | 0.1959
28 | 6 | 177.33 | 0.04 | 13 | 151 | 6 | 141 | 0.4861 |  | 24 | 3 | 83.33 | -0.30 | -109 | 62 | 6 | 79 | 0.0928
24 | 3 | 83.33 | 0.05 | 19 | 157 | 7 | 146 | 0.3567 |  | 16 | 2 | 45.33 | 0.41 | 149 | 164 | 7 | 167 | 0.4918
Onnophris:$~{}n_{S}=3$,$~{}N_{S}=105$,$~{}q_{B}=0.0286$
$P=2.85$, $\Theta_{R}=-32$ |  |  $P=29.60$, $\Theta_{R}=-102$
No periodicity |  | No periodicity
D | M | $s_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$ |  | D | M | $s_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$
23 | 11 | 322.33 | -0.09 | -32 | 1 | 1 | 1 | 0.0286 |  | 24 | 8 | 233.33 | -0.24 | -85 | 17 | 1 | 13 | 0.3140
24 | 8 | 233.33 | -0.32 | -114 | 82 | 2 | 39 | 0.3068 |  | 23 | 11 | 322.33 | -0.23 | -82 | 20 | 2 | 15 | 0.0670
13 | 3 | 72.33 | 0.19 | 69 | 102 | 3 | 55 | 0.2077 |  | 13 | 3 | 72.33 | 0.33 | 117 | 141 | 3 | 82 | 0.4166

Nut:$~{}n_{G}=3$,$~{}N_{G}=177$,$~{}q_{B}=0.0169$
---
$P=2.85$, $\Theta_{R}=55$ |  |  $P=29.60$, $\Theta_{R}=-105$
No periodicity |  | Weak periodicity: $z=1.8$, $Q_{z}=0.2$, $z_{x}={\bf-0.1}$
D | M | $g_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$ |  | D | M | $g_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$
22 | 12 | 351.33 | 0.09 | 32 | 24 | 1 | 28 | 0.3804 |  | 22 | 12 | 351.33 | -0.25 | -90 | 16 | 1 | 13 | 0.1993
18 | 7 | 197.33 | 0.05 | 19 | 37 | 2 | 44 | 0.1711 |  | 28 | 1 | 27.33 | -0.19 | -70 | 35 | 2 | 26 | 0.0714
28 | 1 | 27.33 | 0.40 | 145 | 90 | 3 | 100 | 0.2407 |  | 18 | 7 | 197.33 | -0.45 | -163 | 57 | 3 | 45 | 0.0408
Nut:$~{}n_{S}=4$,$~{}N_{S}=105$,$~{}q_{B}=0.0381$
$P=2.85$, $\Theta_{R}=81$ |  |  $P=29.60$, $\Theta_{R}=139$
No periodicity |  | No periodicity
D | M | $s_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$ |  | D | M | $s_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$
17 | 8 | 226.33 | 0.23 | 82 | 1 | 1 | 3 | 0.1100 |  | 12 | 2 | 41.33 | 0.28 | 100 | 39 | 1 | 24 | 0.6063
12 | 2 | 41.33 | 0.32 | 114 | 33 | 2 | 24 | 0.2321 |  | 17 | 8 | 226.33 | -0.47 | -170 | 51 | 2 | 34 | 0.3735
20 | 2 | 49.33 | 0.12 | 44 | 37 | 3 | 27 | 0.0820 |  | 20 | 2 | 49.33 | -0.45 | -163 | 58 | 3 | 41 | 0.2046
4 | 10 | 273.33 | -0.28 | -101 | 178 | 4 | 105 | 0.5703 |  | 4 | 10 | 273.33 | 0.12 | 42 | 98 | 4 | 66 | 0.2434

Heart:$~{}n_{G}=27$,$~{}N_{G}=177$,$~{}q_{B}=0.1525$
---
$P=2.85$, $\Theta_{R}=-91$ |  |  $P=29.60$, $\Theta_{R}=47$
No periodicity |  | No periodicity
D | M | $g_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$ |  | D | M | $g_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$
9 | 1 | 8.33 | -0.26 | -95 | 4 | 1 | 4 | 0.4842 |  | 9 | 1 | 8.33 | 0.16 | 59 | 11 | 1 | 8 | 0.7340
6 | 3 | 65.33 | -0.26 | -95 | 4 | 2 | 5 | 0.1695 |  | 6 | 3 | 65.33 | 0.09 | 32 | 15 | 2 | 14 | 0.6531
16 | 2 | 45.33 | -0.28 | -101 | 10 | 3 | 11 | 0.2289 |  | 9 | 2 | 38.33 | 0.18 | 64 | 16 | 3 | 16 | 0.4502
13 | 4 | 102.33 | -0.28 | -101 | 10 | 4 | 12 | 0.0969 |  | 7 | 8 | 216.33 | 0.19 | 68 | 21 | 4 | 22 | 0.4383
7 | 8 | 216.33 | -0.28 | -101 | 10 | 5 | 13 | 0.0365 |  | 4 | 6 | 153.33 | 0.06 | 22 | 25 | 5 | 27 | 0.3959
29 | 3 | 88.33 | -0.19 | -69 | 22 | 6 | 19 | 0.0576 |  | 7 | 9 | 246.33 | 0.20 | 73 | 26 | 6 | 30 | 0.3034
30 | 4 | 119.33 | -0.32 | -114 | 23 | 7 | 22 | 0.0399 |  | 10 | 2 | 39.33 | 0.21 | 76 | 29 | 7 | 31 | 0.1841
13 | 2 | 42.33 | -0.33 | -120 | 29 | 8 | 24 | 0.0218 |  | 9 | 5 | 128.33 | 0.22 | 78 | 31 | 8 | 34 | 0.1361
9 | 5 | 128.33 | -0.16 | -57 | 34 | 9 | 29 | 0.0247 |  | 4 | 4 | 93.33 | 0.03 | 13 | 35 | 9 | 38 | 0.1145
29 | 5 | 148.33 | -0.14 | -51 | 41 | 10 | 34 | 0.0267 |  | 9 | 10 | 278.33 | 0.28 | 103 | 55 | 10 | 64 | 0.5202
10 | 2 | 39.33 | -0.39 | -139 | 48 | 11 | 41 | 0.0396 |  | 9 | 11 | 308.33 | 0.30 | 107 | 60 | 11 | 71 | 0.5281
4 | 6 | 153.33 | -0.39 | -139 | 48 | 12 | 42 | 0.0201 |  | 13 | 2 | 42.33 | 0.31 | 112 | 65 | 12 | 76 | 0.4969
12 | 12 | 341.33 | -0.42 | -152 | 60 | 13 | 54 | 0.0594 |  | 2 | 1 | 1.33 | -0.07 | -26 | 74 | 13 | 86 | 0.5601
4 | 4 | 93.33 | -0.44 | -158 | 67 | 14 | 61 | 0.0729 |  | 13 | 4 | 102.33 | 0.34 | 122 | 75 | 14 | 89 | 0.4952
16 | 12 | 345.33 | -0.02 | -6 | 85 | 15 | 83 | 0.2791 |  | 30 | 4 | 119.33 | -0.09 | -31 | 79 | 15 | 95 | 0.4857
24 | 1 | 23.33 | 0.00 | 0 | 91 | 16 | 87 | 0.2470 |  | 29 | 5 | 148.33 | -0.11 | -39 | 86 | 16 | 101 | 0.4769
9 | 11 | 308.33 | 0.00 | 0 | 91 | 17 | 90 | 0.2048 |  | 14 | 4 | 103.33 | 0.37 | 134 | 87 | 17 | 102 | 0.3864
9 | 10 | 278.33 | 0.47 | 171 | 98 | 18 | 99 | 0.2457 |  | 29 | 3 | 88.33 | -0.13 | -48 | 96 | 18 | 110 | 0.4127
28 | 3 | 87.33 | 0.46 | 164 | 105 | 19 | 105 | 0.2447 |  | 25 | 12 | 354.33 | -0.15 | -53 | 100 | 19 | 113 | 0.3605
24 | 3 | 83.33 | 0.05 | 19 | 110 | 20 | 109 | 0.2182 |  | 16 | 2 | 45.33 | 0.41 | 149 | 101 | 20 | 114 | 0.2842
14 | 4 | 103.33 | 0.07 | 25 | 116 | 21 | 115 | 0.2178 |  | 12 | 12 | 341.33 | 0.41 | 149 | 101 | 21 | 115 | 0.2178
25 | 10 | 294.33 | 0.09 | 32 | 123 | 22 | 126 | 0.2795 |  | 28 | 3 | 87.33 | -0.17 | -60 | 108 | 22 | 120 | 0.2056
25 | 3 | 84.33 | 0.40 | 145 | 124 | 23 | 129 | 0.2401 |  | 25 | 10 | 294.33 | -0.17 | -63 | 110 | 23 | 122 | 0.1631
25 | 12 | 354.33 | 0.14 | 51 | 142 | 24 | 147 | 0.3929 |  | 25 | 3 | 84.33 | -0.27 | -97 | 144 | 24 | 154 | 0.4888
2 | 1 | 1.33 | 0.28 | 101 | 168 | 25 | 164 | 0.5347 |  | 16 | 12 | 345.33 | -0.45 | -163 | 150 | 25 | 160 | 0.4816
9 | 2 | 38.33 | 0.26 | 95 | 174 | 26 | 170 | 0.5269 |  | 24 | 3 | 83.33 | -0.30 | -109 | 156 | 26 | 164 | 0.4484
7 | 9 | 246.33 | 0.25 | 88 | 180 | 27 | 176 | 0.5193 |  | 24 | 1 | 23.33 | -0.33 | -119 | 166 | 27 | 169 | 0.4293
Heart:$~{}n_{S}={\bf 5}$,$~{}N_{S}={\bf 105}$,$~{}q_{B}=0.0476$
$P=2.85$, $\Theta_{R}=-172$ |  |  $P=29.60$, $\Theta_{R}=154$
Periodicity: $z=3.2$, $Q_{z}={\bf 0.04}$, $z_{x}={\bf-3.1}$ |  | No periodicity
D | M | $s_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$ |  | D | M | $s_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$
14 | 3 | 73.33 | -0.46 | -164 | 8 | 1 | 5 | 0.2165 |  | 14 | 3 | 73.33 | 0.36 | 129 | 24 | 1 | 15 | 0.5190
22 | 7 | 201.33 | 0.46 | 164 | 24 | 2 | 14 | 0.1414 |  | 10 | 11 | 309.33 | 0.33 | 120 | 34 | 2 | 22 | 0.2821
5 | 11 | 304.33 | -0.40 | -145 | 26 | 3 | 18 | 0.0516 |  | 23 | 1 | 22.33 | -0.36 | -131 | 75 | 3 | 54 | 0.4779
23 | 1 | 22.33 | -0.35 | -126 | 45 | 4 | 28 | 0.0423 |  | 22 | 7 | 201.33 | -0.32 | -114 | 92 | 4 | 65 | 0.3746
10 | 11 | 309.33 | 0.35 | 126 | 62 | 5 | 39 | 0.0367 |  | 5 | 11 | 304.33 | 0.16 | 59 | 95 | 5 | 66 | 0.2055

Nun:$~{}n_{G}=7$,$~{}N_{G}=177$,$~{}q_{B}=0.0395$
---
$P=2.85$, $\Theta_{R}=-38$ |  |  $P=29.60$, $\Theta_{R}=-52$
No periodicity |  | No periodicity
D | M | $g_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$ |  | D | M | $g_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$
1 | 1 | 0.33 | -0.07 | -25 | 13 | 1 | 14 | 0.4316 |  | 30 | 2 | 59.33 | -0.11 | -41 | 11 | 1 | 10 | 0.3320
12 | 7 | 191.33 | -0.05 | -19 | 19 | 2 | 25 | 0.2599 |  | 1 | 1 | 0.33 | -0.11 | -39 | 13 | 2 | 14 | 0.1039
19 | 2 | 48.33 | -0.23 | -82 | 44 | 3 | 55 | 0.3715 |  | 30 | 5 | 149.33 | -0.07 | -26 | 25 | 3 | 30 | 0.1140
17 | 2 | 46.33 | 0.07 | 25 | 63 | 4 | 73 | 0.3269 |  | 1 | 4 | 90.33 | -0.07 | -24 | 28 | 4 | 32 | 0.0364
30 | 2 | 59.33 | -0.37 | -133 | 95 | 5 | 111 | 0.4484 |  | 19 | 2 | 48.33 | -0.49 | -175 | 123 | 5 | 127 | 0.5671
30 | 5 | 149.33 | 0.21 | 76 | 114 | 6 | 121 | 0.3456 |  | 17 | 2 | 46.33 | 0.45 | 161 | 147 | 6 | 151 | 0.5529
1 | 4 | 90.33 | -0.49 | -177 | 139 | 7 | 148 | 0.3696 |  | 12 | 7 | 191.33 | 0.35 | 124 | 176 | 7 | 175 | 0.5412
Nun:$~{}n_{S}={\bf 3}$,$~{}N_{S}={\bf 105}$,$~{}q_{B}=0.0286$
$P=2.85$, $\Theta_{R}=-122$ |  |  $P=29.60$, $\Theta_{R}=-161$
Weak periodicity: $z=2.9$, $Q_{z}={\bf 0.06}$, $z_{x}=-0.8$ |  | Weak periodicity: $z=2.4$, $Q_{z}=0.1$, $z_{x}=-2.1$
D | M | $s_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$ |  | D | M | $s_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$
17 | 5 | 136.33 | -0.35 | -126 | 4 | 1 | 4 | 0.1095 |  | 15 | 12 | 344.33 | -0.49 | -175 | 14 | 1 | 15 | 0.3526
15 | 12 | 344.33 | -0.37 | -133 | 10 | 2 | 9 | 0.0257 |  | 17 | 5 | 136.33 | 0.49 | 175 | 24 | 2 | 22 | 0.1295
23 | 3 | 82.33 | -0.30 | -107 | 15 | 3 | 11 | 0.0032 |  | 23 | 3 | 82.33 | -0.34 | -121 | 40 | 3 | 33 | 0.0674

Seth:$~{}n_{G}=5$,$~{}N_{G}=177$,$~{}q_{B}=0.0282$
---
$P=2.85$, $\Theta_{R}=11$ |  |  $P=29.60$, $\Theta_{R}=-73$
No periodicity |  | No periodicity
D | M | $g_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$ |  | D | M | $g_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$
27 | 1 | 26.33 | 0.05 | 19 | 8 | 1 | 9 | 0.2273 |  | 27 | 3 | 86.33 | -0.20 | -73 | 0 | 1 | 1 | 0.0282
27 | 3 | 86.33 | 0.11 | 38 | 27 | 2 | 40 | 0.3126 |  | 27 | 1 | 26.33 | -0.23 | -82 | 10 | 2 | 9 | 0.0252
13 | 12 | 342.33 | -0.07 | -25 | 36 | 3 | 55 | 0.2031 |  | 29 | 3 | 88.33 | -0.13 | -48 | 24 | 3 | 24 | 0.0293
29 | 3 | 88.33 | -0.19 | -69 | 80 | 4 | 98 | 0.3003 |  | 13 | 12 | 342.33 | 0.45 | 161 | 126 | 4 | 128 | 0.4900
9 | 4 | 98.33 | 0.32 | 114 | 103 | 5 | 118 | 0.2417 |  | 9 | 4 | 98.33 | 0.20 | 73 | 146 | 5 | 146 | 0.3958
Seth:$~{}n_{S}={\bf 9}$,$~{}N_{S}=105$,$~{}q_{B}=0.0857$
$P=2.85$, $\Theta_{R}=57$ |  |  $P=29.60$, $\Theta_{R}=-180$
No periodicity |  | Periodicity: $z=3.1$, $Q_{z}={\bf 0.05}$, $z_{x}=-3.1$
D | M | $s_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$ |  | D | M | $s_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$
13 | 3 | 72.33 | 0.19 | 69 | 12 | 1 | 8 | 0.5117 |  | 18 | 3 | 77.33 | 0.49 | 178 | 2 | 1 | 1 | 0.0857
20 | 2 | 49.33 | 0.12 | 44 | 13 | 2 | 12 | 0.2750 |  | 17 | 7 | 196.33 | -0.49 | -175 | 6 | 2 | 5 | 0.0617
17 | 8 | 226.33 | 0.23 | 82 | 25 | 3 | 18 | 0.1964 |  | 17 | 8 | 226.33 | -0.47 | -170 | 11 | 3 | 10 | 0.0478
11 | 12 | 340.33 | 0.23 | 82 | 25 | 4 | 19 | 0.0739 |  | 20 | 2 | 49.33 | -0.45 | -163 | 18 | 4 | 16 | 0.0425
12 | 2 | 41.33 | 0.32 | 114 | 56 | 5 | 29 | 0.0977 |  | 11 | 12 | 340.33 | 0.38 | 137 | 43 | 5 | 33 | 0.1483
18 | 3 | 77.33 | -0.05 | -19 | 76 | 6 | 43 | 0.1593 |  | 13 | 3 | 72.33 | 0.33 | 117 | 62 | 6 | 47 | 0.2122
26 | 1 | 25.33 | -0.30 | -107 | 165 | 7 | 92 | 0.6831 |  | 12 | 2 | 41.33 | 0.28 | 100 | 79 | 7 | 56 | 0.2014
17 | 7 | 196.33 | -0.30 | -107 | 165 | 8 | 95 | 0.5739 |  | 26 | 1 | 25.33 | -0.26 | -95 | 86 | 8 | 62 | 0.1591
24 | 8 | 233.33 | -0.32 | -114 | 171 | 9 | 100 | 0.4902 |  | 24 | 8 | 233.33 | -0.24 | -85 | 96 | 9 | 68 | 0.1260

Osiris:$~{}n_{G}=8$,$~{}N_{G}=177$,$~{}q_{B}=0.0452$
---
$P=2.85$, $\Theta_{R}=-82$ |  |  $P=29.60$, $\Theta_{R}=93$
No periodicity |  | No periodicity
D | M | $g_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$ |  | D | M | $g_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$
16 | 2 | 45.33 | -0.28 | -101 | 19 | 1 | 18 | 0.5650 |  | 11 | 4 | 100.33 | 0.27 | 98 | 4 | 1 | 3 | 0.1296
6 | 7 | 185.33 | -0.16 | -57 | 25 | 2 | 23 | 0.2791 |  | 6 | 7 | 185.33 | 0.14 | 51 | 42 | 2 | 43 | 0.5846
1 | 10 | 270.33 | -0.33 | -120 | 38 | 3 | 39 | 0.2579 |  | 16 | 2 | 45.33 | 0.41 | 149 | 56 | 3 | 50 | 0.3949
13 | 12 | 342.33 | -0.07 | -25 | 57 | 4 | 55 | 0.2368 |  | 13 | 12 | 342.33 | 0.45 | 161 | 68 | 4 | 64 | 0.3281
28 | 7 | 207.33 | -0.44 | -158 | 76 | 5 | 76 | 0.2598 |  | 17 | 6 | 166.33 | -0.50 | -180 | 87 | 5 | 83 | 0.3216
11 | 4 | 100.33 | 0.02 | 6 | 88 | 6 | 86 | 0.1935 |  | 1 | 10 | 270.33 | 0.01 | 5 | 88 | 6 | 86 | 0.1935
28 | 3 | 87.33 | 0.46 | 164 | 114 | 7 | 122 | 0.3144 |  | 28 | 7 | 207.33 | -0.11 | -41 | 134 | 7 | 137 | 0.4252
17 | 6 | 166.33 | 0.18 | 63 | 145 | 8 | 148 | 0.3540 |  | 28 | 3 | 87.33 | -0.17 | -60 | 154 | 8 | 151 | 0.3746
Osiris:$~{}n_{S}={\bf 4}$,$~{}N_{S}={\bf 105}$,$~{}q_{B}=0.0381$
$P=2.85$, $\Theta_{R}=-141$ |  |  $P=29.60$, $\Theta_{R}=144$
No periodicity |  | Periodicity: $z=3.0$, $Q_{z}={\bf 0.05}$, $z_{x}=-2.0$
D | M | $s_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$ |  | D | M | $s_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$
14 | 5 | 133.33 | -0.40 | -145 | 4 | 1 | 3 | 0.1100 |  | 14 | 5 | 133.33 | 0.39 | 139 | 5 | 1 | 4 | 0.1439
14 | 3 | 73.33 | -0.46 | -164 | 23 | 2 | 18 | 0.1487 |  | 14 | 3 | 73.33 | 0.36 | 129 | 14 | 2 | 9 | 0.0437
19 | 4 | 108.33 | -0.18 | -63 | 78 | 3 | 52 | 0.3180 |  | 13 | 3 | 72.33 | 0.33 | 117 | 27 | 3 | 15 | 0.0178
13 | 3 | 72.33 | 0.19 | 69 | 150 | 4 | 92 | 0.4665 |  | 19 | 4 | 108.33 | -0.46 | -165 | 51 | 4 | 37 | 0.0513

Abydos:$~{}n_{G}=3$,$~{}N_{G}=177$,$~{}q_{B}=0.0169$
---
$P=2.85$, $\Theta_{R}=-14$ |  |  $P=29.60$, $\Theta_{R}=151$
No periodicity |  | No periodicity
D | M | $g_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$ |  | D | M | $g_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$
18 | 5 | 137.33 | 0.00 | 0 | 14 | 1 | 22 | 0.3135 |  | 18 | 5 | 137.33 | -0.48 | -172 | 36 | 1 | 29 | 0.3909
11 | 4 | 100.33 | 0.02 | 6 | 20 | 2 | 30 | 0.0915 |  | 11 | 4 | 100.33 | 0.27 | 98 | 54 | 2 | 43 | 0.1650
28 | 7 | 207.33 | -0.44 | -158 | 144 | 3 | 146 | 0.4507 |  | 28 | 7 | 207.33 | -0.11 | -41 | 168 | 3 | 159 | 0.5066
Abydos:$~{}n_{S}=2$,$~{}N_{S}=105$,$~{}q_{B}=0.0190$
$P=2.85$, $\Theta_{R}=3$ |  |  $P=29.60$, $\Theta_{R}=129$
No periodicity |  | Weak periodicity: $z=1.9$, $Q_{z}=0.1$, $z_{x}=-0.8$
D | M | $s_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$ |  | D | M | $s_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$
13 | 3 | 72.33 | 0.19 | 69 | 66 | 1 | 26 | 0.3935 |  | 13 | 3 | 72.33 | 0.33 | 117 | 12 | 1 | 9 | 0.1589
13 | 8 | 222.33 | -0.18 | -63 | 66 | 2 | 28 | 0.0990 |  | 13 | 8 | 222.33 | 0.39 | 141 | 12 | 2 | 12 | 0.0211

Lion:$~{}n_{G}=1$,$~{}N_{G}=177$,$~{}q_{B}=0.0056$
---
$P=2.85$, $\Theta_{R}=-177$ |  |  $P=29.60$, $\Theta_{R}=-24$
No periodicity |  | No periodicity
D | M | $g_{i}$ | $\phi_{i}$ | $\Theta_{i}$ |  |  |  |  |  | D | M | $g_{i}$ | $\phi_{i}$ | $\Theta_{i}$ |  |  |  |
1 | 4 | 90.33 | -0.49 | -177 |  |  |  |  |  | 1 | 4 | 90.33 | -0.07 | -24 |  |  |  |
Lion:$~{}n_{S}=6$,$~{}N_{S}=105$,$~{}q_{B}=0.0571$
$P=2.85$, $\Theta_{R}=-162$ |  |  $P=29.60$, $\Theta_{R}=-100$
No periodicity |  | Weak periodicity: $z=2.2$, $Q_{z}=0.1$, $z_{x}=-0.1$
D | M | $s_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$ |  | D | M | $s_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$
24 | 2 | 53.33 | -0.47 | -171 | 8 | 1 | 6 | 0.2975 |  | 25 | 2 | 54.33 | -0.28 | -102 | 2 | 1 | 2 | 0.1110
18 | 10 | 287.33 | -0.37 | -133 | 29 | 2 | 19 | 0.2966 |  | 24 | 2 | 53.33 | -0.32 | -114 | 14 | 2 | 9 | 0.0899
26 | 10 | 295.33 | 0.44 | 158 | 40 | 3 | 28 | 0.2135 |  | 19 | 10 | 288.33 | -0.38 | -136 | 36 | 3 | 25 | 0.1692
3 | 8 | 212.33 | 0.32 | 114 | 84 | 4 | 56 | 0.3987 |  | 18 | 10 | 287.33 | -0.41 | -148 | 48 | 4 | 33 | 0.1172
25 | 2 | 54.33 | -0.12 | -44 | 118 | 5 | 79 | 0.4735 |  | 26 | 10 | 295.33 | -0.14 | -51 | 49 | 5 | 34 | 0.0425
19 | 10 | 288.33 | -0.02 | -6 | 156 | 6 | 101 | 0.5207 |  | 3 | 8 | 212.33 | 0.06 | 20 | 119 | 6 | 70 | 0.2102

Man:$~{}n_{G}=5$,$~{}N_{G}=177$,$~{}q_{B}=0.0282$
---
$P=2.85$, $\Theta_{R}=-27$ |  |  $P=29.60$, $\Theta_{R}=3$
No periodicity |  | No periodicity
D | M | $g_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$ |  | D | M | $g_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$
16 | 10 | 285.33 | -0.07 | -25 | 2 | 1 | 5 | 0.1335 |  | 3 | 5 | 122.33 | 0.01 | 5 | 2 | 1 | 3 | 0.0824
6 | 5 | 125.33 | -0.21 | -76 | 49 | 2 | 60 | 0.5083 |  | 4 | 5 | 123.33 | 0.05 | 17 | 14 | 2 | 22 | 0.1272
4 | 5 | 123.33 | 0.09 | 32 | 59 | 3 | 73 | 0.3404 |  | 6 | 5 | 125.33 | 0.12 | 42 | 39 | 3 | 53 | 0.1886
3 | 5 | 122.33 | -0.26 | -95 | 68 | 4 | 88 | 0.2378 |  | 29 | 2 | 58.33 | -0.15 | -53 | 56 | 4 | 72 | 0.1465
29 | 2 | 58.33 | 0.28 | 101 | 128 | 5 | 134 | 0.3287 |  | 16 | 10 | 285.33 | -0.48 | -172 | 175 | 5 | 172 | 0.5366
Man:$~{}n_{S}={\bf 6}$,$~{}N_{S}={\bf 105}$,$~{}q_{B}=0.0571$
$P=2.85$, $\Theta_{R}=-165$ |  |  $P=29.60$, $\Theta_{R}=54$
No periodicity |  | Periodicity: $z=3.9$, $Q_{z}={\bf 0.02}$, $z_{x}=1.4$
D | M | $s_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$ |  | D | M | $s_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$
8 | 11 | 307.33 | -0.35 | -126 | 39 | 1 | 29 | 0.8185 |  | 7 | 5 | 126.33 | 0.15 | 54 | 0 | 1 | 1 | 0.0571
6 | 8 | 215.33 | 0.37 | 133 | 62 | 2 | 41 | 0.6878 |  | 6 | 8 | 215.33 | 0.16 | 56 | 2 | 2 | 2 | 0.0033
4 | 10 | 273.33 | -0.28 | -101 | 64 | 3 | 43 | 0.4486 |  | 4 | 10 | 273.33 | 0.12 | 42 | 12 | 3 | 7 | 0.0055
30 | 6 | 179.33 | -0.26 | -95 | 70 | 4 | 47 | 0.2806 |  | 7 | 11 | 306.33 | 0.23 | 83 | 29 | 4 | 17 | 0.0139
7 | 11 | 306.33 | 0.30 | 107 | 88 | 5 | 60 | 0.2579 |  | 8 | 11 | 307.33 | 0.26 | 95 | 41 | 5 | 23 | 0.0086
7 | 5 | 126.33 | 0.14 | 51 | 144 | 6 | 95 | 0.4610 |  | 30 | 6 | 179.33 | -0.06 | -22 | 76 | 6 | 35 | 0.0135

Flame:$~{}n_{S}={\bf 4}$,$~{}N_{S}={\bf 105}$,$~{}q_{B}=0.0381$
---
$P=2.85$, $\Theta_{R}=123$ |  |  $P=29.60$, $\Theta_{R}=85$
No periodicity |  | Periodicity: $z=3.6$, $Q_{z}={\bf 0.03}$, $z_{x}=0.0$
D | M | $s_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$ |  | D | M | $s_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$
10 | 7 | 189.33 | 0.25 | 88 | 35 | 1 | 19 | 0.5219 |  | 11 | 1 | 10.33 | 0.23 | 83 | 2 | 1 | 1 | 0.0381
11 | 1 | 10.33 | 0.44 | 158 | 35 | 2 | 20 | 0.1759 |  | 10 | 7 | 189.33 | 0.28 | 100 | 15 | 2 | 10 | 0.0533
11 | 5 | 130.33 | -0.46 | -164 | 73 | 3 | 47 | 0.2657 |  | 11 | 5 | 130.33 | 0.28 | 103 | 17 | 3 | 12 | 0.0094
7 | 5 | 126.33 | 0.14 | 51 | 73 | 4 | 50 | 0.1224 |  | 7 | 5 | 126.33 | 0.15 | 54 | 31 | 4 | 17 | 0.0034

Eye:$~{}n_{G}=4$,$~{}N_{G}=177$,$~{}q_{B}=0.0226$
---
$P=2.85$, $\Theta_{R}=-24$ |  |  $P=29.60$, $\Theta_{R}=115$
No periodicity |  | No periodicity
D | M | $g_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$ |  | D | M | $g_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$
10 | 12 | 339.33 | -0.12 | -44 | 21 | 1 | 32 | 0.5188 |  | 10 | 12 | 339.33 | 0.35 | 124 | 10 | 1 | 11 | 0.2223
19 | 12 | 348.33 | 0.04 | 13 | 36 | 2 | 51 | 0.3208 |  | 10 | 4 | 99.33 | 0.24 | 85 | 29 | 2 | 24 | 0.1016
8 | 8 | 217.33 | 0.07 | 25 | 49 | 3 | 63 | 0.1706 |  | 8 | 8 | 217.33 | 0.22 | 81 | 34 | 3 | 27 | 0.0225
10 | 4 | 99.33 | -0.33 | -120 | 96 | 4 | 111 | 0.2430 |  | 19 | 12 | 348.33 | -0.35 | -126 | 119 | 4 | 110 | 0.2381
Eye:$~{}n_{S}=5$,$~{}N_{S}=105$,$~{}q_{B}=0.0476$
$P=2.85$, $\Theta_{R}=81$ |  |  $P=29.60$, $\Theta_{R}=124$
No periodicity |  | No periodicity
D | M | $s_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$ |  | D | M | $s_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$
7 | 7 | 186.33 | 0.19 | 69 | 11 | 1 | 11 | 0.4153 |  | 11 | 11 | 310.33 | 0.37 | 132 | 8 | 1 | 8 | 0.3232
20 | 4 | 109.33 | 0.18 | 63 | 18 | 2 | 14 | 0.1414 |  | 14 | 11 | 313.33 | 0.47 | 168 | 45 | 2 | 26 | 0.3531
3 | 8 | 212.33 | 0.32 | 114 | 33 | 3 | 25 | 0.1141 |  | 7 | 7 | 186.33 | 0.18 | 64 | 60 | 3 | 36 | 0.2446
14 | 11 | 313.33 | -0.25 | -88 | 169 | 4 | 96 | 0.6759 |  | 20 | 4 | 109.33 | -0.42 | -153 | 84 | 4 | 55 | 0.2660
11 | 11 | 310.33 | -0.30 | -107 | 172 | 5 | 101 | 0.5291 |  | 3 | 8 | 212.33 | 0.06 | 20 | 104 | 5 | 68 | 0.2228

Fire:$~{}n_{G}=4$,$~{}N_{G}=177$,$~{}q_{B}=0.0226$
---
$P=2.85$, $\Theta_{R}=122$ |  |  $P=29.60$, $\Theta_{R}=4$
No periodicity |  | No periodicity
D | M | $g_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$ |  | D | M | $g_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$
19 | 1 | 18.33 | 0.25 | 88 | 33 | 1 | 25 | 0.4353 |  | 29 | 8 | 238.33 | -0.07 | -24 | 28 | 1 | 40 | 0.5992
29 | 8 | 238.33 | 0.44 | 158 | 36 | 2 | 31 | 0.1548 |  | 30 | 5 | 149.33 | -0.07 | -26 | 30 | 2 | 44 | 0.2621
30 | 5 | 149.33 | 0.21 | 76 | 46 | 3 | 38 | 0.0542 |  | 7 | 8 | 216.33 | 0.19 | 68 | 65 | 3 | 81 | 0.2770
7 | 8 | 216.33 | -0.28 | -101 | 137 | 4 | 129 | 0.3336 |  | 19 | 1 | 18.33 | -0.50 | -180 | 177 | 4 | 173 | 0.5508
Fire:$~{}n_{S}=7$,$~{}N_{S}=105$,$~{}q_{B}=0.0667$
$P=2.85$, $\Theta_{R}=171$ |  |  $P=29.60$, $\Theta_{R}=143$
No periodicity |  | No periodicity
D | M | $s_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$ |  | D | M | $s_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$
11 | 1 | 10.33 | 0.44 | 158 | 13 | 1 | 6 | 0.3390 |  | 14 | 11 | 313.33 | 0.47 | 168 | 25 | 1 | 14 | 0.6194
29 | 4 | 118.33 | 0.33 | 120 | 51 | 2 | 30 | 0.6033 |  | 10 | 5 | 129.33 | 0.25 | 90 | 53 | 2 | 38 | 0.7301
7 | 11 | 306.33 | 0.30 | 107 | 63 | 3 | 41 | 0.5207 |  | 11 | 1 | 10.33 | 0.23 | 83 | 60 | 3 | 43 | 0.5533
23 | 1 | 22.33 | -0.35 | -126 | 63 | 4 | 42 | 0.3064 |  | 7 | 11 | 306.33 | 0.23 | 83 | 60 | 4 | 44 | 0.3372
23 | 3 | 82.33 | -0.30 | -107 | 82 | 5 | 52 | 0.2647 |  | 23 | 1 | 22.33 | -0.36 | -131 | 86 | 5 | 58 | 0.3441
10 | 5 | 129.33 | 0.19 | 69 | 101 | 6 | 68 | 0.2999 |  | 23 | 3 | 82.33 | -0.34 | -121 | 96 | 6 | 65 | 0.2649
14 | 11 | 313.33 | -0.25 | -88 | 101 | 7 | 72 | 0.2033 |  | 29 | 4 | 118.33 | -0.12 | -43 | 173 | 7 | 102 | 0.5243

Majesty:$~{}n_{G}=13$,$~{}N_{G}=177$,$~{}q_{B}=0.0734$
---
$P=2.85$, $\Theta_{R}=-64$ |  |  $P=29.60$, $\Theta_{R}=10$
No periodicity |  | No periodicity
D | M | $g_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$ |  | D | M | $g_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$
2 | 2 | 31.33 | -0.19 | -69 | 6 | 1 | 2 | 0.1415 |  | 2 | 8 | 211.33 | 0.02 | 8 | 3 | 1 | 4 | 0.2630
18 | 1 | 17.33 | -0.11 | -38 | 26 | 2 | 24 | 0.5348 |  | 5 | 4 | 94.33 | 0.07 | 25 | 15 | 2 | 17 | 0.3582
9 | 1 | 8.33 | -0.26 | -95 | 31 | 3 | 28 | 0.3391 |  | 2 | 2 | 31.33 | -0.06 | -22 | 32 | 3 | 44 | 0.6364
5 | 4 | 94.33 | -0.09 | -32 | 32 | 4 | 34 | 0.2375 |  | 1 | 4 | 90.33 | -0.07 | -24 | 34 | 4 | 46 | 0.4401
19 | 8 | 228.33 | -0.07 | -25 | 38 | 5 | 45 | 0.2333 |  | 9 | 1 | 8.33 | 0.16 | 59 | 49 | 5 | 61 | 0.4676
2 | 8 | 211.33 | -0.04 | -13 | 51 | 6 | 57 | 0.2394 |  | 28 | 7 | 207.33 | -0.11 | -41 | 51 | 6 | 68 | 0.3829
24 | 1 | 23.33 | 0.00 | 0 | 64 | 7 | 68 | 0.2312 |  | 9 | 4 | 98.33 | 0.20 | 73 | 63 | 7 | 80 | 0.3729
14 | 2 | 43.33 | 0.02 | 6 | 70 | 8 | 73 | 0.1662 |  | 10 | 2 | 39.33 | 0.21 | 76 | 66 | 8 | 84 | 0.2750
10 | 2 | 39.33 | -0.39 | -139 | 75 | 9 | 77 | 0.1111 |  | 25 | 5 | 144.33 | -0.24 | -87 | 97 | 9 | 116 | 0.4823
28 | 7 | 207.33 | -0.44 | -158 | 94 | 10 | 98 | 0.1826 |  | 14 | 2 | 43.33 | 0.35 | 124 | 114 | 10 | 130 | 0.4871
1 | 4 | 90.33 | -0.49 | -177 | 113 | 11 | 120 | 0.2667 |  | 24 | 1 | 23.33 | -0.33 | -119 | 129 | 11 | 142 | 0.4725
25 | 5 | 144.33 | 0.46 | 164 | 132 | 12 | 139 | 0.3236 |  | 19 | 8 | 228.33 | -0.40 | -146 | 156 | 12 | 161 | 0.5219
9 | 4 | 98.33 | 0.32 | 114 | 177 | 13 | 176 | 0.5327 |  | 18 | 1 | 17.33 | 0.47 | 168 | 158 | 13 | 162 | 0.4119
Majesty:$~{}n_{S}=7$,$~{}N_{S}=105$,$~{}q_{B}=0.0667$
$P=2.85$, $\Theta_{R}=-138$ |  |  $P=29.60$, $\Theta_{R}=-169$
No periodicity |  | No periodicity
D | M | $s_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$ |  | D | M | $s_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$
26 | 1 | 25.33 | -0.30 | -107 | 31 | 1 | 21 | 0.7652 |  | 16 | 11 | 315.33 | -0.47 | -167 | 2 | 1 | 5 | 0.2918
23 | 3 | 82.33 | -0.30 | -107 | 31 | 2 | 22 | 0.4364 |  | 20 | 9 | 259.33 | -0.36 | -129 | 40 | 2 | 32 | 0.6388
12 | 8 | 221.33 | 0.47 | 171 | 52 | 3 | 36 | 0.4339 |  | 23 | 3 | 82.33 | -0.34 | -121 | 48 | 3 | 35 | 0.4158
16 | 11 | 315.33 | 0.46 | 164 | 58 | 4 | 41 | 0.2911 |  | 12 | 8 | 221.33 | 0.36 | 129 | 62 | 4 | 48 | 0.3990
11 | 1 | 10.33 | 0.44 | 158 | 64 | 5 | 45 | 0.1788 |  | 26 | 1 | 25.33 | -0.26 | -95 | 74 | 5 | 55 | 0.3040
20 | 9 | 259.33 | -0.19 | -69 | 68 | 6 | 49 | 0.1060 |  | 11 | 1 | 10.33 | 0.23 | 83 | 108 | 6 | 75 | 0.3840
5 | 8 | 214.33 | 0.02 | 6 | 144 | 7 | 88 | 0.3715 |  | 5 | 8 | 214.33 | 0.12 | 44 | 147 | 7 | 94 | 0.4379

Shu:$~{}n_{G}=3$,$~{}N_{G}=177$,$~{}q_{B}=0.0169$
---
$P=2.85$, $\Theta_{R}=5$ |  |  $P=29.60$, $\Theta_{R}=-158$
No periodicity |  | No periodicity
D | M | $g_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$ |  | D | M | $g_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$
21 | 3 | 80.33 | 0.00 | 0 | 5 | 1 | 6 | 0.0975 |  | 21 | 3 | 80.33 | -0.40 | -146 | 13 | 1 | 7 | 0.1128
30 | 10 | 299.33 | -0.16 | -57 | 62 | 2 | 84 | 0.4176 |  | 16 | 5 | 135.33 | 0.45 | 163 | 39 | 2 | 25 | 0.0666
16 | 5 | 135.33 | 0.30 | 107 | 102 | 3 | 121 | 0.3372 |  | 30 | 10 | 299.33 | -0.01 | -2 | 156 | 3 | 151 | 0.4725
Shu:$~{}n_{S}=1$,$~{}N_{S}=105$,$~{}q_{B}=0.0095$
$P=2.85$, $\Theta_{R}=13$ |  |  $P=29.60$, $\Theta_{R}=-99$
No periodicity |  | No periodicity
D | M | $s_{i}$ | $\phi_{i}$ | $\Theta_{i}$ |  |  |  |  |  | D | M | $s_{i}$ | $\phi_{i}$ | $\Theta_{i}$ |  |  |  |
22 | 10 | 291.33 | 0.04 | 13 |  |  |  |  |  | 22 | 10 | 291.33 | -0.28 | -99 |  |  |  |

Sobek:$~{}n_{G}=1$,$~{}N_{G}=177$,$~{}q_{B}=0.0056$
---
$P=2.85$, $\Theta_{R}=25$ |  |  $P=29.60$, $\Theta_{R}=107$
No periodicity |  | No periodicity
D | M | $g_{i}$ | $\phi_{i}$ | $\Theta_{i}$ |  |  |  |  |  | D | M | $g_{i}$ | $\phi_{i}$ | $\Theta_{i}$ |  |  |  |
11 | 6 | 160.33 | 0.07 | 25 |  |  |  |  |  | 11 | 6 | 160.33 | 0.30 | 107 |  |  |  |
Sobek:$~{}n_{S}=3$,$~{}N_{S}=105$,$~{}q_{B}=0.0286$
$P=2.85$, $\Theta_{R}=161$ |  |  $P=29.60$, $\Theta_{R}=-89$
No periodicity |  | No periodicity
D | M | $s_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$ |  | D | M | $s_{i}$ | $\phi_{i}$ | $\Theta_{i}$ | $\Delta\Theta_{i}$ | $n_{1}$ | $n_{2}$ | $Q_{B}$
26 | 10 | 295.33 | 0.44 | 158 | 3 | 1 | 2 | 0.0563 |  | 25 | 8 | 234.33 | -0.20 | -73 | 17 | 1 | 13 | 0.3140
17 | 1 | 16.33 | -0.46 | -164 | 35 | 2 | 20 | 0.1105 |  | 26 | 10 | 295.33 | -0.14 | -51 | 38 | 2 | 24 | 0.1492
25 | 8 | 234.33 | 0.04 | 13 | 148 | 3 | 91 | 0.4838 |  | 17 | 1 | 16.33 | 0.43 | 156 | 115 | 3 | 67 | 0.2998