The Observation

If you observe in a group with other people every observer has to observe independently from the others. Never try to combine data from different observers! Each observer must keep their own notes and fill in their own report forms.

General remarks

As already mentioned, meteor observing requires great concentration and quick reflexes. Your whole attention must be paid to your observation. Avoid talking or listening to music. As soon as you get tired take a break to walk around or to consume some food. In most cases this will fend off tiredness, and you will be able to continue the watch. If you do become too tired, you should stop observing and retire to bed, since the accuracy of your data will reduce as fatigue takes hold, meaning that you will miss many meteors. Thorough preparation before observing includes ensuring that you are sufficiently rested, as this is the one factor which may stop you watching that you can control, unlike, for instance, the weather.

How long should the watch last?

The answer to this question is very simple. As long as possible! The longer you observe, the more meteors you will see, and therefore the more certain your results will become. Furthermore, the part of the activity profile you cover becomes wider. Perhaps if you stop too early you will miss the best activity. Therefore, you should continue your observations as long as circumstances or fatigue permit. The minimum watch length which is useful is 1 hour.

Obstruction of the field of view

Your observations should be carried out with an unrestricted field of view. If any fraction of the field is covered by clouds you will miss a certain number of meteors. To calculate how many meteors you might have observed had your field been completely clear, we use a factor based on the number of meteors missed as being proportional to the field fraction obscured.

Although we always refer to an unrestricted field of view, due to the properties of the human eye, about 98% of all meteors are witnessed within an almost circular field of around 50° radius. We call this field the effective field of view. Whenever clouds cover your effective field record the time in your notes.

Clearly, it would take a very major effort to record every change in the percentage of cloud cover. Remember that you are outside first and foremost to observe meteors rather than to record cloud obscuration. Instead of recording every change, report the average cloud percentage during the past 10-15 minutes of your watch, until your field is cloudless again or you stop observing. Note the begin of the cloud cover and average the obstruction percentage unless it does not change severely.

At first glance this method seems to be useful for any value of cloud cover. But let us think one step further. Imagine a hole of about 40° radius in the clouds. Observing through this hole about 50% of the area of your effective field is covered. In order to obtain the number of meteors you would have observed in an unrestricted field you have to multiply the number you observed within the partially covered field by a factor of 2. But owing to the construction of the human eye, most meteors are seen in the center of your field of view. In our example you would miss only 10% of the meteors instead of 50%. This example may be an artificial one but the situation is similiar to many other real cases of cloud cover. Please therefore note that the cloud correction is an approximation only, which works primarily with small amounts of cloud cover. Thus, you should take a break as soon as cloud cover exceeds 20%, unless you are monitoring an unusual meteor storm.

What to record

It is important to record your observations correctly. This can be done by storing all the information on a tape recorder or by writing it onto scrap paper without taking your eyes off the sky. The notes taken must cover all the following details about the observation:

  • the times the watch began and ended at, and any breaks; give all times in UT only. Universal Time (UT) is the local time valid for 0° geographical longitude.
  • the limiting magnitude and any changes to it during your watch
  • details of any cloud cover present
  • time labels at least each half hour; it is not necessary to note time labels exactly at the half/full hour, but they should occur at about 15 minute intervals, for high activity even at about 5 minute intervals or less.
  • details of all meteors seen (see the section “When a meteor appears” for further details)
  • the center of the field of view; report this in right ascension, declination with an accuracy of 10° or a constellation or star name that you can convert into right ascension, declination after the watch using a star atlas.

It is recommended that while observing, you should follow the motion of the sky, and thus you will become more familiar with certain regions. If the position of the field becomes unfavourable (e.g. elevation less than 50° ) you should choose another field, and then record the center of the new field in your notes.

When a meteor appears

Having read to this point you may have got the impression that meteor observing consists mainly of recording lots of odd data unconnected with meteors. But that is not the case. Now we reach our main subject: What do you have to do when a meteor appears? The most important thing is to remain calm so that you can record what you have just seen as objectively as possible. Keep looking at the region of sky where you saw the meteor in order to memorize the following data in this order:

Meteor’s path

The most important information is its direction rather than the exact length and start/end points. Memorize it with respect to the background stars.

Shower association

Members of a given meteor shower seem to originate from one small area of sky; the radiant. Since you memorized the radiant’s position in the sky before the start of the watch you can trace back the meteor’s path as an imaginary straight line, to see whether it intersects with the radiant. Now it becomes clear why it is best to look not too far from the radiant. Tracing back the meteor’s path over a large distance is difficult and brings in greater uncertainties. If the path can be traced back to the radiant, the meteor was a shower meteor, otherwise it was a sporadic. Please note additionally two general rules:

  • Shower meteors appear faster the larger their distance from the radiant (up to 90° ) and the higher their elevation above the horizon. Near the radiant or near the horizon shower meteors generally seem slower.
  • The apparent path length shows a similar behavior to the angular velocity. Near the radiant or near the horizon meteor paths are generally short, while they are longer with increasing distance from the radiant and nearer to the zenith.

This means that even if the trail came from the radiant, a meteor in the vicinity of the shower radiant does not belong to the shower if it was very fast and/or very long. A detailed explanation of the reasons for this can be found in Section 6.

Maximum magnitude

Estimate this by comparing the meteor with the brightness of nearby stars you memorized prior to the start of the watch. If you are very certain of the sighting, i.e. if it occured in the center of your viewing field, estimate it to the nearest 0.5mag, e.g. 3.5mag or 1.0mag; otherwise estimate it to the nearest whole magnitude, e.g. 3mag or 1mag.

Persistent train

If you observed a train that persisted after the meteor had disappeared give its duration in seconds. If you detected a train persisting only for a few tenth of a second you may note a “+” as an indication of a so-called wake.

Color

Note that it should theoretically be impossible to detect colors for meteors fainter than magnitude +2. This information is of least value of all the data and can be omitted during your first watches.

Other data

Unless you are going to photograph meteors or a fireball appears, the time of individual meteors is of little interest, since you set time labels for each ~30 minutes into your notes.

The duration of a meteor is usually less than one second. This requires exceptional concentration and quick reactions on the part of the observer. This is also the reason why the observer sees only a fraction of the meteors that actually appear.

After storing all the data in your memory you can transfer them to your record. If you are using a tape recorder you start the device and report the data in a format like this: “Perseid, magnitude +0.5, train 3 seconds, white”. Then stop recording until the next meteor appears or you want to record limiting magnitudes, etc.

In both recording techniques, you must take care that you do not interrupt your observation by looking at what you are doing. You have to use the tape or the paper ‘blind’. The tape should provide no problems but writing blind onto paper requires a little experience.

Determination of the limiting magnitude

The darker and more transparent the sky and the more sensitive your eyes, the more meteors you can see. To use your observations for scientific analyses a quantitative characterization of these factors has to be established. The limiting magnitude (which is defined as being the magnitude of the faintest star near the zenith that the observer can detect using the slightly averted naked eye) defines both the condition of the sky’s clarity and the quality of the observer’s eyes. Please note, the limiting magnitude is an observer specific quantity. Do not be surprised if other observers at the same site obtain different limiting magnitudes to you. This is the rule, rather than the exception. Only record your own values! There are several methods for determining the limiting magnitude. We describe one which is favoured by many meteor observers.

In Table 1 a number of star fields are shown. The stars visible within these areas, including the corner stars, have to be counted. After the observation the number of stars can be converted into the limiting magnitude by using Table 2. Do not increase your attention artificially when obtaining the limiting magnitude since it should characterize your average eye-state during your observation. Determine the limiting magnitude at the start of the watch, and then every 30-45 minutes, even if there is no considerable change. In this way you will reduce the random errors in the procedure.

You should preferentially use fields in your observing direction, and use at least two, or better three, fields for each determination. Again, doing this will help to reduce random errors. The fields should have an elevation of more than 40° . Remember to note the time, field number, and the number of stars counted.

Fields near the Milky Way like Field 14 may cause systematically lower limiting magnitudes since the stars could not be resolved by your eyes. This effect was found for limiting magnitudes higher than 6.0 mag.

Download as PDF the Atlas Brno 2000.0 with and without all the star fields.


Table 1. Corner stars of the fields for the determination of the limiting magnitude.

Field Corner stars Field in the Atlas Brno
1 chi Dra — zeta Dra — delta Dra — xi Dra Chart 3
2 beta Per — delta Per — zeta Per Chart 1
3 23 UMa — theta UMa — beta UMa Chart 2
4 alpha Gem — epsilon Gem — beta Gem Chart 4
5 zeta Aql — gamma Aql — delta Aql Chart 9
6 alpha And — gamma Peg — alpha Peg Chart 6
7 alpha Cep — beta Cep — delta Cep Chart 1
8 alpha Tau — beta Tau — zeta Tau Chart 4
9 alpha Leo — beta Leo — gamma Leo — delta Leo Chart 8
10 alpha Vir — zeta Vir — gamma Vir Chart 5
11 alpha CrB — gamma Boo — alpha Boo Chart 5
12 alpha Ser — beta Lib — delta Oph Chart 5
13 beta Lyr — zeta Lyr — theta Her — nu Her Chart 3
14 epsilon Cyg — eta Cyg — gamma Cyg Chart 3
15 beta Dra — tau Her — pi Her Chart 3
16 alpha CVn — epsilon UMa — eta UMa Chart 2
17 epsilon Aur — theta Aur — delta Aur Chart 1
18 mu And — gamma And — phi And Chart 1
19 kappa Dra — alpha Dra — beta UMi Chart 2
20 42 Cam — beta Cam — gamma Cam Chart 1
21 alpha PsA — 98 Aqr — delta Aqr Chart 6
22 beta Lep — beta Ori — 53 Eri Chart 4
23 delta Crv — gamma Crv — epsilon Crv — beta Crv Chart 5
24 beta Lib — gamma Lib — sigma Lib — alpha Lib Chart 5
25 alpha Sco — epsilon Sco — chi Lup Chart 9
26 gamma TrA — alpha TrA — eta Ara — alpha Cen Chart 11
27 beta Cen — alpha Cru — gamma Cru Chart 11
28 beta Car — epsilon Car — iota Car Chart 10
29 gamma Hyd — alpha Hyd — beta Hyd Chart 10
30 alpha Tuc — alpha Pav — epsilon Pav Chart 12

Table 2. Conversion table for all 30 limiting-magnitude areas.

The number of stars (N) seen in one of the star fields (given in Table 1) including the corner stars correspond to a limiting magnitude (Lm) listed below. If you encounter gaps of more than 0.3 mag between two rows, use this magnitude value only if you do not have another estimate for the same period. Magnitude gaps of about 0.3 or more occurring for magnitudes fainter than +5.5 are marked by italic numbers. (The constellations given may help as a reminder, they do not define the actual count area.)

1 2 3 4 5 6 7 8 9 10
Dra Per UMa Gem Aql Peg Cep Tau Leo Vir
N Lm N Lm N Lm N Lm N Lm N Lm N Lm N Lm N Lm N Lm
1 3.08 1 2.11 1 2.35 1 1.22 1 2.71 1 2.06 1 2.47 1 0.99 1 1.41 1 1.06
2 3.18 2 2.88 2 3.18 2 2.02 2 2.99 2 2.49 2 3.23 2 1.68 2 2.13 2 2.74
3 3.57 3 3.02 3 3.65 3 3.01 3 3.37 3 2.84 3 4.07 3 3.00 3 2.23 3 3.38
4 3.74 4 3.78 4 3.78 4 3.79 4 4.45 4 4.66 4 4.23 4 4.62 4 2.56 4 4.39
5 4.23 5 4.95 5 4.48 5 5.01 5 5.16 5 5.08 5 4.79 5 4.88 5 3.33 5 5.77
6 4.78 6 5.15 6 4.56 6 5.07 6 5.30 6 5.49 6 5.12 6 4.95 6 4.41 6 5.80
7 4.83 7 5.55 7 4.83 7 5.34 7 5.53 7 5.56 7 5.17 7 5.09 7 4.78 7 5.86
8 5.00 8 5.60 8 5.13 8 5.75 8 5.98 8 5.80 8 5.26 8 5.29 8 5.42 8 5.92
9 5.08 9 5.79 9 5.16 9 5.76 9 6.02 9 6.13 9 5.29 9 5.43 9 5.44 9 5.97
10 5.25 10 5.80 10 5.49 10 5.78 10 6.31 10 6.14 10 5.36 10 5.51 10 5.48 10 5.99
11 5.96 11 5.98 11 5.66 11 6.20 11 6.36 11 6.17 11 5.42 11 5.73 11 5.50 11 6.12
12 6.06 12 6.01 12 5.72 12 6.37 12 6.71 12 6.25 12 5.73 12 5.84 12 5.58 12 6.41
13 6.28 13 6.07 13 5.79 13 6.47 13 6.72 13 6.25 13 5.95 13 6.10 13 5.73 13 6.44
14 6.42 14 6.40 14 5.97 14 6.54 14 6.77 14 6.26 14 5.96 14 6.19 14 5.92 14 6.63
15 6.50 15 6.41 15 6.19 15 6.67 15 6.80 15 6.29 15 6.00 15 6.27 15 6.14 15 6.64
16 6.60 16 6.45 16 6.30 16 6.76 16 6.90 16 6.44 16 6.14 16 6.29 16 6.17 16 6.65
17 6.63 17 6.50 17 6.35 17 6.80 17 6.91 17 6.47 17 6.19 17 6.36 17 6.27 17 6.69
18 6.65 18 6.51 18 6.41 18 6.99 18 6.96 18 6.50 18 6.23 18 6.50 18 6.27 18 6.83
19 6.66 19 6.54 19 6.49 19 7.00 19 7.00 19 6.50 19 6.44 19 6.55 19 6.31 19 6.90
20 6.68 20 6.60 20 6.49 20 7.02 20 7.05 20 6.57 20 6.47 20 6.71 20 6.40 20 7.04
21 6.68 21 6.61 21 6.54 21 7.10 21 7.06 21 6.59 21 6.48 21 6.76 21 6.43 21 7.06
22 6.70 22 6.66 22 6.59 22 7.12 22 7.07 22 6.59 22 6.63 22 6.77 22 6.52 22 7.08
23 6.79 23 6.72 23 6.72 23 7.17 23 7.09 23 6.60 23 6.69 23 6.87 23 6.61 23 7.16
24 6.86 24 6.73 24 6.77 24 7.22 24 7.10 24 6.60 24 6.70 24 6.88 24 6.64 24 7.19
25 6.86 25 6.75 25 6.83 25 7.43 25 7.11 25 6.67 25 6.71 25 6.95 25 6.78 25 7.20
26 6.86 26 6.78 26 6.85 26 7.45 26 7.27 26 6.68 26 6.72 26 7.15 26 6.81 26 7.24
27 6.86 27 6.85 27 6.99 27 7.46 27 7.28 27 6.68 27 6.84 27 7.17 27 6.84 27 7.25
28 6.87 28 6.89 28 7.01 28 7.46 28 7.38 28 6.69 28 6.88 28 7.19 28 6.85 28 7.25
29 6.89 29 6.90 29 7.06 29 7.47 29 7.39 29 6.72 29 6.92 29 7.21 29 6.95 29 7.32
30 6.92 30 7.02 30 7.12 30 7.40 30 6.73 30 6.93 30 7.30 30 7.00 30 7.33
31 6.92 31 7.03 31 7.12 31 7.41 31 6.74 31 6.94 31 7.34 31 7.02 31 7.34
32 6.93 32 7.03 32 7.19 32 7.44 32 6.82 32 6.97 32 7.06 32 7.38
33 6.94 33 7.05 33 7.20 33 7.45 33 6.87 33 7.01 33 7.07 33 7.42
34 7.02 34 7.15 34 7.23 34 7.47 34 6.89 34 7.04 34 7.10
35 7.03 35 7.15 35 7.24 35 6.89 35 7.06 35 7.12
36 7.04 36 7.16 36 7.30 36 7.07 36 7.08 36 7.12
37 7.09 37 7.18 37 7.33 37 7.07 37 7.16 37 7.12
38 7.10 38 7.22 38 7.40 38 7.10 38 7.18 38 7.13
39 7.10 39 7.23 39 7.41 39 7.11 39 7.23 39 7.13
40 7.15 40 7.24 40 7.44 40 7.12 40 7.24 40 7.22
41 7.24 41 7.24 41 7.45 41 7.12 41 7.25 41 7.26
42 7.30 42 7.25 42 7.47 42 7.14 42 7.25 42 7.30
43 7.31 43 7.26 43 7.48 43 7.15 43 7.27 43 7.30
44 7.32 44 7.27 44 7.50 44 7.19 44 7.29 44 7.31
45 7.33 45 7.28 45 7.24 45 7.30 45 7.33
46 7.35 46 7.30 46 7.27 46 7.32 46 7.34
47 7.35 47 7.31 47 7.33 47 7.35 47 7.36
48 7.36 48 7.31 48 7.37 48 7.39 48 7.43
49 7.39 49 7.33 49 7.43 49 7.43 49 7.43
50 7.43 50 7.33 50 7.44 50 7.44 50 7.44
51 7.50 51 7.35 51 7.45 51 7.46 51 7.45
52 7.35 52 7.45 52 7.49 52 7.48
53 7.36 53 7.45 53 7.49
54 7.42 54 7.49
55 7.45 55 7.49
56 7.48 56 7.50
57 7.49
58 7.50
59 7.50
11 12 13 14 15 16 17 18 19 20
Boo Ser Lyr-Her Cyg Dra-Her UMa-CVn Aur And UMi-Dra Cam
N Lm N Lm N Lm N Lm N Lm N Lm N Lm N Lm N Lm N Lm
1 0.16 1 2.61 1 3.52 1 2.23 1 2.80 1 1.76 1 0.08 1 2.17 1 2.06 1 4.03
2 2.22 2 2.63 2 3.84 2 2.49 2 3.14 2 1.86 2 1.90 2 3.87 2 3.65 2 4.31
3 2.36 3 2.73 3 4.32 3 3.90 3 3.90 3 2.89 3 2.65 3 4.10 3 3.89 3 4.62
4 3.04 4 3.55 4 4.34 4 4.65 4 4.82 4 4.67 4 3.03 4 4.26 4 5.19 4 4.77
5 3.57 5 5.10 5 4.41 5 4.73 5 5.07 5 5.15 5 3.73 5 4.83 5 5.50 5 5.14
6 4.47 6 5.23 6 4.98 6 4.79 6 5.50 6 5.64 6 3.97 6 4.87 6 5.81 6 5.44
7 4.51 7 5.39 7 5.42 7 4.94 7 5.67 7 5.79 7 4.33 7 4.96 7 6.20 7 5.47
8 4.79 8 5.39 8 5.49 8 5.06 8 5.82 8 5.85 8 4.52 8 5.01 8 6.33 8 5.62
9 4.81 9 5.51 9 5.56 9 5.39 9 5.92 9 5.88 9 5.21 9 5.04 9 6.40 9 5.63
10 4.93 10 5.53 10 5.72 10 5.58 10 5.98 10 6.11 10 5.46 10 5.64 10 6.53 10 6.00
11 5.28 11 5.57 11 5.99 11 5.64 11 6.06 11 6.42 11 5.64 11 5.67 11 6.70 11 6.04
12 5.51 12 5.87 12 6.01 12 5.87 12 6.11 12 6.48 12 5.91 12 5.94 12 7.00 12 6.17
13 5.67 13 6.25 13 6.03 13 5.91 13 6.16 13 6.55 13 5.99 13 5.98 13 7.17 13 6.17
14 5.79 14 6.34 14 6.05 14 6.04 14 6.17 14 6.70 14 6.09 14 6.13 14 7.22 14 6.20
15 5.81 15 6.51 15 6.10 15 6.25 15 6.29 15 6.79 15 6.11 15 6.13 15 7.25 15 6.21
16 5.88 16 6.52 16 6.17 16 6.29 16 6.34 16 6.80 16 6.23 16 6.39 16 7.30 16 6.24
17 5.90 17 6.54 17 6.47 17 6.31 17 6.36 17 6.81 17 6.30 17 6.42 17 7.33 17 6.25
18 6.00 18 6.71 18 6.59 18 6.34 18 6.36 18 6.84 18 6.30 18 6.52 18 7.41 18 6.35
19 6.01 19 6.85 19 6.62 19 6.38 19 6.45 19 6.96 19 6.41 19 6.55 19 7.45 19 6.36
20 6.04 20 6.87 20 6.67 20 6.47 20 6.46 20 6.98 20 6.44 20 6.58 20 7.49 20 6.38
21 6.06 21 6.88 21 6.70 21 6.48 21 6.58 21 6.98 21 6.47 21 6.60 21 6.43
22 6.13 22 6.95 22 6.89 22 6.60 22 6.66 22 7.05 22 6.48 22 6.64 22 6.49
23 6.13 23 6.96 23 6.93 23 6.73 23 6.66 23 7.06 23 6.51 23 6.65 23 6.61
24 6.22 24 6.97 24 7.00 24 6.74 24 6.74 24 7.23 24 6.54 24 6.68 24 6.62
25 6.27 25 7.04 25 7.01 25 6.82 25 6.78 25 7.26 25 6.56 25 6.68 25 6.63
26 6.32 26 7.13 26 7.02 26 6.87 26 6.82 26 7.28 26 6.57 26 6.77 26 6.64
27 6.38 27 7.16 27 7.02 27 6.90 27 6.85 27 7.33 27 6.58 27 6.77 27 6.64
28 6.38 28 7.16 28 7.03 28 6.96 28 6.87 28 7.38 28 6.58 28 6.84 28 6.66
29 6.40 29 7.19 29 7.04 29 7.00 29 6.87 29 7.47 29 6.59 29 6.90 29 6.69
30 6.40 30 7.21 30 7.06 30 7.02 30 7.00 30 7.48 30 6.60 30 6.95 30 6.71
31 6.56 31 7.23 31 7.08 31 7.02 31 7.02 31 6.63 31 7.07 31 6.74
32 6.68 32 7.25 32 7.19 32 7.08 32 7.04 32 6.66 32 7.14 32 6.81
33 6.70 33 7.26 33 7.23 33 7.09 33 7.12 33 6.69 33 7.19 33 6.82
34 6.71 34 7.27 34 7.27 34 7.10 34 7.17 34 6.75 34 7.21 34 6.85
35 6.76 35 7.27 35 7.29 35 7.12 35 7.23 35 6.77 35 7.23 35 6.86
36 6.77 36 7.28 36 7.31 36 7.13 36 7.24 36 6.80 36 7.23 36 6.88
37 6.79 37 7.32 37 7.33 37 7.23 37 7.35 37 6.81 37 7.25 37 6.89
38 6.83 38 7.34 38 7.34 38 7.27 38 7.37 38 6.82 38 7.26 38 6.89
39 6.84 39 7.35 39 7.37 39 7.29 39 7.38 39 6.84 39 7.26 39 6.92
40 6.87 40 7.36 40 7.37 40 7.30 40 7.39 40 6.86 40 7.27 40 6.95
41 6.89 41 7.41 41 7.38 41 7.32 41 7.47 41 6.86 41 7.27 41 6.97
42 6.94 42 7.42 42 7.41 42 7.33 42 7.48 42 6.89 42 7.30 42 6.98
43 6.95 43 7.43 43 7.43 43 7.34 43 7.49 43 6.93 43 7.33 43 6.99
44 6.96 44 7.44 44 7.44 44 7.42 44 7.49 44 6.95 44 7.43 44 7.01
45 6.96 45 7.47 45 7.45 45 7.42 45 7.50 45 6.95 45 7.44 45 7.03
46 7.01 46 7.48 46 7.45 46 7.43 46 7.50 46 6.98 46 7.46 46 7.05
47 7.03 47 7.48 47 7.46 47 7.44 47 6.98 47 7.47 47 7.08
48 7.04 48 7.50 48 7.46 48 7.44 48 7.01 48 7.48 48 7.12
49 7.12 49 7.50 49 7.49 49 7.44 49 7.16 49 7.50 49 7.12
50 7.14 50 7.47 50 7.19 50 7.14
51 7.15 51 7.47 51 7.20 51 7.17
52 7.17 52 7.21 52 7.27
53 7.21 53 7.24 53 7.28
54 7.22 54 7.24 54 7.30
56 7.25 60 7.27 56 7.32
63 7.30 61 7.31 57 7.37
66 7.38 67 7.37 59 7.40
67 7.43 68 7.40 61 7.43
70 7.45 71 7.46 64 7.45
73 7.49 76 7.50 65 7.47
21 22 23 24 25 26 27 28 29 30
Aqr Lep-Ori Crv Lib Sco TrA-Cen Cru Car Hyi Tuc-Pav
N Lm N Lm N Lm N Lm N Lm N Lm N Lm N Lm N Lm N Lm
1 1.23 1 0.28 1 2.59 1 2.61 1 1.07 1 -0.01 1 0.64 1 1.67 1 2.82 1 1.92
2 3.27 2 2.84 2 2.66 2 2.75 2 2.29 2 1.91 2 1.31 2 1.95 2 2.86 2 2.86
3 3.68 3 3.29 3 2.97 3 3.28 3 3.96 3 2.84 3 1.58 3 2.25 3 3.26 3 3.42
4 3.96 4 3.87 4 3.01 4 3.92 4 5.26 4 2.88 4 1.65 4 3.84 4 4.08 4 3.65
5 4.48 5 4.28 5 5.21 5 4.56 5 5.40 5 3.76 5 4.31 5 3.96 5 4.69 5 3.95
6 4.72 6 4.43 6 5.81 6 5.19 6 5.50 6 3.85 6 4.56 6 4.00 6 4.74 6 4.23
7 5.54 7 4.47 7 5.95 7 5.64 7 5.84 7 4.11 7 4.59 7 4.33 7 5.51 7 4.76
8 5.66 8 4.78 8 6.40 8 5.72 8 5.92 8 4.85 8 4.61 8 5.46 8 5.57 8 4.86
9 5.98 9 5.46 9 6.62 9 6.08 9 6.00 9 5.08 9 4.69 9 5.54 9 5.67 9 5.12
10 6.28 10 5.49 10 6.84 10 6.14 10 6.09 10 5.10 10 4.92 10 5.78 10 5.99 10 5.15
11 6.30 11 5.68 11 7.06 11 6.15 11 6.15 11 5.11 11 5.50 11 5.79 11 6.09 11 5.18
12 6.35 12 5.68 12 7.25 12 6.17 12 6.32 12 5.17 12 5.75 12 6.36 12 6.36 12 5.61
13 6.79 13 5.69 13 7.30 13 6.19 13 6.41 13 5.18 13 5.82 13 6.36 13 6.43 13 5.62
14 6.82 14 5.72 14 7.41 14 6.41 14 6.47 14 5.29 14 6.04 14 6.49 14 6.57 14 5.76
15 6.97 15 5.82 15 7.44 15 6.46 15 6.56 15 5.50 15 6.20 15 6.54 15 6.59 15 5.92
16 7.05 16 5.96 16 7.44 16 6.50 16 6.56 16 5.72 16 6.20 16 6.63 16 6.65 16 6.09
17 7.25 17 5.96 17 7.46 17 6.63 17 6.62 17 5.75 17 6.23 17 6.72 17 6.66 17 6.22
18 7.42 18 6.05 18 6.64 18 6.85 18 5.77 18 6.42 18 6.85 18 6.69 18 6.22
19 7.45 19 6.15 19 6.67 19 6.90 19 5.89 19 6.61 19 6.90 19 6.69 19 6.28
20 7.46 20 6.23 20 6.75 20 6.97 20 5.89 20 6.61 20 6.93 20 6.71 20 6.33
21 7.48 21 6.27 21 6.76 21 6.98 21 5.95 21 6.66 21 6.99 21 6.77 21 6.35
22 7.50 22 6.35 22 6.76 22 7.01 22 5.95 22 6.69 22 7.04 22 6.81 22 6.36
23 6.40 23 6.80 23 7.07 23 6.02 23 6.73 23 7.08 23 6.84 23 6.40
24 6.42 24 6.87 24 7.13 24 6.07 24 6.74 24 7.14 24 6.85 24 6.50
25 6.46 25 6.94 25 7.14 25 6.12 25 6.75 25 7.15 25 6.86 25 6.59
26 6.47 26 7.07 26 7.15 26 6.14 26 6.92 26 7.16 26 6.88 26 6.70
27 6.54 27 7.14 27 7.26 27 6.16 27 6.93 27 7.18 27 6.89 27 6.70
28 6.68 28 7.16 28 7.40 28 6.17 28 6.96 28 7.19 28 6.89 28 6.73
29 6.71 29 7.19 29 7.46 29 6.20 29 6.98 29 7.25 29 6.91 29 6.77
30 6.73 30 7.20 30 6.20 30 7.07 30 7.29 30 6.94 30 6.83
31 6.75 31 7.22 31 6.21 31 7.11 31 7.31 31 7.01 31 6.84
32 6.76 32 7.24 32 6.22 32 7.13 32 7.37 32 7.09 32 6.86
33 6.96 33 7.25 33 6.25 33 7.19 33 7.38 33 7.09 33 6.87
34 7.02 34 7.29 34 6.25 34 7.19 34 7.38 34 7.10 34 6.91
35 7.04 35 7.29 35 6.30 35 7.21 35 7.38 35 7.13 35 6.92
36 7.12 36 7.32 36 6.31 36 7.24 36 7.38 36 7.19 36 6.92
37 7.14 37 7.35 37 6.33 37 7.26 37 7.44 37 7.22 37 6.97
38 7.14 38 7.37 38 6.39 38 7.27 38 7.45 38 7.22 38 7.00
39 7.21 39 7.38 40 6.42 39 7.29 39 7.46 39 7.23 39 7.03
40 7.21 40 7.41 41 6.48 40 7.31 40 7.24 40 7.09
41 7.22 41 7.46 43 6.50 41 7.37 41 7.26 41 7.10
42 7.28 42 7.49 47 6.57 42 7.38 42 7.27 42 7.10
43 7.32 43 7.50 49 6.61 43 7.40 43 7.29 43 7.12
44 7.32 50 6.70 44 7.45 44 7.30 44 7.15
45 7.33 53 6.75 45 7.50 45 7.30 45 7.18
46 7.34 54 6.81 46 7.32 46 7.20
47 7.34 58 6.85 47 7.32 47 7.21
48 7.37 64 6.90 48 7.37 48 7.23
49 7.38 66 6.95 49 7.37 49 7.24
50 7.38 70 7.00 50 7.37 50 7.24
51 7.41 75 7.05 51 7.38 51 7.27
52 7.42 76 7.10 52 7.39 52 7.35
53 7.43 81 7.14 53 7.41 53 7.36
54 7.43 83 7.20 54 7.46 54 7.41
55 7.45 86 7.24 55 7.47 55 7.44
56 7.45 90 7.29 56 7.50 56 7.44
57 7.47 92 7.34 57 7.50 57 7.47
58 7.48 97 7.40 58 7.48
102 7.45 59 7.50
106 7.50 60 7.50

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