Airfoil Shape for a Turbine Rotor Blade

Information

  • Patent Application
  • 20180320527
  • Publication Number
    20180320527
  • Date Filed
    May 02, 2017
    7 years ago
  • Date Published
    November 08, 2018
    5 years ago
Abstract
A turbine rotor blade is provided including an airfoil having an airfoil shape. The airfoil shape having a nominal profile substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in Table I wherein the Cartesian coordinate values of X, Y and Z are non-dimensional values from 0% to 100% convertible to dimensional distances in inches by multiplying the Cartesian coordinate values of X, Y and Z by a height of the airfoil in inches, and wherein X and Y are distances in inches which, when connected by smooth continuing arcs, define airfoil profile sections at each distance Z, the airfoil profile sections at Z distances being joined smoothly with one another to form a complete airfoil shape.
Description
FIELD

The present invention relates to an airfoil for a turbine rotor blade of a stage of a turbine and particularly relates to a shape defining a profile for an airfoil of a turbine rotor blade.


BACKGROUND

Some aircraft and/or power plant systems, for example certain jet aircraft, nuclear, simple cycle and combined cycle power plant systems, employ turbines (also referred to as turbomachines) in their design and operation. Some of these turbines employ airfoils (e.g., stator vanes or nozzles and rotor blades.) which during operation are exposed to fluid flows. These airfoils are configured to aerodynamically interact with the fluid flows and generate energy (e.g., creating thrust, turning kinetic energy to mechanical energy, thermal energy to mechanical energy, etc.) from these fluid flows as part of power generation. As a result of this interaction and conversion, the aerodynamic characteristics and losses of these airfoils have an impact on system and turbine operation, performance, thrust, efficiency, and power.


BRIEF DESCRIPTION

Aspects and advantages are set forth below in the following description, or may be obvious from the description, or may be learned through practice.


An aspect of the present invention may be embodied by a turbine rotor blade including an airfoil having an airfoil shape, the airfoil having a nominal profile substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in Table I wherein the Cartesian coordinate values of X, Y and Z are non-dimensional values from 0% to 100% convertible to dimensional distances in inches by multiplying the Cartesian coordinate values of X, Y and Z by a height of the airfoil in inches, and wherein X and Y are distances in inches which, when connected by smooth continuing arcs, define airfoil profile sections at each distance Z, the airfoil profile sections at Z distances being joined smoothly with one another to form a complete airfoil shape.


An aspect of the present invention may be embodied in a turbine rotor blade including an airfoil having a suction-side uncoated nominal airfoil profile substantially in accordance with suction-side Cartesian coordinate values of X, Y and Z set forth in Table I wherein the Cartesian coordinate values of X, Y and Z are non-dimensional values from 0% to 100% convertible to dimensional distances in inches by multiplying the Cartesian coordinate values of X, Y and Z by a height of the airfoil in inches, and wherein X and Y are distances in inches which, when connected by smooth continuing arcs, define airfoil profile sections at each Z distance, the airfoil profile sections at the Z distances being joined smoothly with one another to form a complete suction-side airfoil shape, the X, Y and Z distances being scalable as a function of the same constant or number to provide a scaled-up or scaled-down airfoil.


An aspect of the present invention may be embodied in a turbine comprising a turbine wheel having a plurality of turbine rotor blades, each of the turbine rotor blades including an airfoil having a suction-side airfoil shape, the airfoil having a nominal profile substantially in accordance with suction-side Cartesian coordinate values of X, Y and Z set forth in Table I wherein the Cartesian coordinate values of X, Y and Z are non-dimensional values from 0% to 100% convertible to dimensional distances by multiplying the Cartesian coordinate values of X, Y and Z by a height of the airfoil, and wherein X and Y are distances which, when connected by smooth continuing arcs, define airfoil profile sections at each Z distance, the airfoil profile sections at the Z distances being joined smoothly with one another to form a complete suction-side airfoil shape.


Those of ordinary skill in the art will better appreciate the features and aspects of such embodiments, and others, upon review of the specification.





BRIEF DESCRIPTION OF THE DRAWINGS

A full and enabling disclosure of various embodiments, including the best mode thereof to one skilled in the art, is set forth more particularly in the remainder of the specification, including reference to the accompanying figures, in which:



FIG. 1 is a schematic representation of an exemplary turbine having multiple stages with each stage including alternating rows of turbine rotor blades and stationary vanes or nozzles according to at least one embodiment of the present disclosure; and



FIG. 2 is a perspective view of a turbine rotor blade according to at least one embodiment of the present disclosure.





DETAILED DESCRIPTION

Referring now to the drawings, particularly to FIG. 1, there is illustrated an exemplary turbine 10 of a gas turbine 12 including a plurality of turbine stages arranged in serial flow order. Each stage of the turbine includes a row of turbine nozzles or vanes disposed axially adjacent to a corresponding row of turbine rotor blades. Four stages are illustrated in FIG. 1. The exact number of stages of the turbine 10 is a choice of engineering design, and may be more or less than the four stages illustrated in FIG. 1. The four stages are merely exemplary of one turbine design, and are not intended to limit the presently claimed turbine rotor blade in any manner.


The first stage comprises a plurality of turbine nozzles or vanes 100 and a plurality of turbine rotor blades 150. The turbine nozzles 100 are annularly arranged about an axis of a turbine rotor 14. The turbine rotor blades 150 are annularly arranged about and coupled to the turbine rotor 14. A second stage of the turbine 12 includes a plurality of turbine nozzles 200 annularly arranged about the axis of the turbine rotor 14 and a plurality of turbine rotor blades 250 annularly arranged about and coupled to the turbine rotor 14. The turbine nozzles 200 may be coupled to a casing 16 of the turbine 12.


As shown in FIG. 1, a third stage of the turbine 12 includes a plurality of turbine nozzles 300 annularly arranged about the axis of the turbine rotor 14 and a plurality of turbine rotor blades 350 annularly arranged about and coupled to the turbine rotor 14. The turbine nozzles 300 may be coupled to the casing 16 of the turbine 12. In particular embodiments, the turbine 12 includes a fourth stage which includes plurality of turbine nozzles 400 annularly arranged about the axis of the turbine rotor 14 and a plurality of turbine rotor blades 450 annularly arranged about and coupled to the turbine rotor 14. The fourth stage turbine nozzles 400 may be coupled to the casing 16 of the turbine 12.


It will be appreciated that the turbine nozzles 100, 200, 300 and 400 and turbine rotor blades 150, 250, 350 and 450 are disposed or at least partially disposed within a hot gas path 18 of the turbine 12. The various stages of the turbine 10 at least partially define the hot gas path 18 through which combustion gases, as indicated by arrows 20, flow during operation of the gas turbine 12.



FIG. 2 provides a perspective view of an exemplary turbine rotor blade 50 as may be incorporated in any stage of the turbine 12. For example, in one embodiment the turbine rotor blade 50 as presented in Table I below is representative of a turbine rotor blade 250 of the plurality of turbine rotor blades 250 of the second stage. As shown in FIG. 2, the turbine rotor blade 50 includes an airfoil 52 having a pressure-side wall 54 and an opposing suction-side wall 56. The pressure-side wall 54 and the suction-side wall 56 meet or intersect at a leading edge 58 and a trailing edge 60 of the airfoil 52. A chord line 62 extends between the leading edge 58 and the trailing edge 60 such that pressure and suction-side walls 54, 56 can be said to extend in chord or chordwise between the leading edge 58 and the trailing edge 60.


The airfoil 52 includes a root or first end 64 which intersects with and extends radially outwardly from a base or platform 66 of the turbine rotor blade 50. The airfoil 52 terminates radially at a second end or radial tip 68 of the airfoil 52. The pressure and suction-side walls 54, 56 can be said to extend in span or in a span-wise direction 70 between the root 64 and/or the platform 66 and the radial tip 68 of the airfoil 52. In other words, each turbine rotor blade 50 includes an airfoil 52 having opposing pressure and suction-side walls 54, 56 that extend in chord or chordwise 62 between opposing leading and trailing edges 58, 60 and that extend in span or span-wise 70 between the root 64 and the radial tip 68 of the airfoil 52.


In particular configurations, the airfoil 52 may include a fillet 72 formed between the platform 66 and the airfoil 52 proximate to the root 64. The fillet 72 can include a weld or braze fillet, which can be formed via conventional MIG welding, TIG welding, brazing, etc., and can include a profile that can reduce fluid dynamic losses as a result of the presence of fillet 72. In particular embodiments, the platform 66, airfoil 52 and the fillet 72 can be formed as a single component, such as by casting and/or machining and/or 3D printing and/or any other suitable technique now known or later developed and/or discovered. In particular configurations, the turbine rotor blade 50 includes a mounting portion 74 which is formed to connect and/or to secure the turbine rotor blade 50 to the rotor shaft 14.


The airfoil 52 of the turbine rotor blade 50 has a profile at any cross-section taken between the platform 66 or the root 64 and the radial tip 68. The X, Y, and Z values are given in Table I as percentage values of the airfoil length or height/span. As one example only, the height or radial span of the airfoil 52 of turbine rotor blade 50 may be from about 10 inches to about 40 inches. However, it is to be understood that heights below or above this range may also be employed as desired in the specific application.


A gas turbine hot gas path requires airfoils that meet system requirements of aerodynamic and mechanical blade loading and efficiency. To define the airfoil shape of each turbine rotor blade airfoil, there is a unique set or loci of points in space that meet the stage requirements and that can be manufactured. This unique loci of points meets the requirements for stage efficiency and are arrived at by iteration between aerodynamic and mechanical loadings enabling the turbine to run in an efficient, safe and smooth manner. These points are unique and specific to the system and are not obvious to those skilled in the art.


The loci which defines the airfoil profile of turbine rotor blade 50 comprises a set of about 2,200 points with X, Y and Z dimensions relative to a reference origin coordinate system. The Cartesian coordinate system of X, Y and Z values given in Table I below defines the airfoil profile of the turbine rotor blade 50 at various locations along its length and height or radial span. Table I lists data for a non-coated airfoil, and the envelope/tolerance for the coordinates is about +/− 5% in a direction normal to any airfoil surface location. A point data origin 76 is defined at or proximate to the root 64 at the leading edge 58. In one embodiment as presented in Table I below, the point data origin 76 is defined at or proximate to (above or below) a transition or intersection line 78 defined between the fillet 72 and the airfoil 52. The point data origin 76 corresponds to the non-dimensional Z value of Table I (presented below) at Z equals 0.


The coordinate values for the X, Y and Z coordinates are set forth in non-dimensionalized units by the airfoil height in Table I although other units of dimensions may be used when the values are appropriately converted. The X, Y, and Z values set forth in Table I are also expressed in non-dimensional form (X, Y, and Z) from 0% to 100% of the airfoil 52 height or radial span 70. To convert the Z value to a Z coordinate value, e.g., in inches, the non-dimensional Z value given in Table I is multiplied by the Z length of the airfoil in inches. As described above, the Cartesian coordinate system has orthogonally-related X, Y and Z axes and the X axis lies generally parallel to a centerline of the rotor shaft 14, i.e., the rotary axis and a positive X coordinate value is axial toward an aft, i.e., exhaust end of the turbine 10. The positive Y coordinate value extends tangentially in the direction of rotation of the rotor and the positive Z coordinate value is radially outwardly toward the radial tip 68. All the values in Table I are given at room temperature and do not include the fillet 72.


By defining X and Y coordinate values at selected locations in a Z direction normal to the X, Y plane, the profile section or airfoil shape of the airfoil 52 of the turbine rotor blade 50, at each Z distance along the length of the airfoil 52 can be ascertained. By connecting the X and Y values with smooth continuing arcs, each profile section at each distance Z is fixed. The airfoil profiles of the various surface locations between the distances Z are determined by smoothly connecting the adjacent profile sections to one another to form the airfoil profile.


The Table I values are generated and shown to four decimal places for determining the profile of the airfoil 52. As the turbine rotor blade 50 heats up during operation of the gas turbine 12, surface stress and temperature will cause a change in the X, Y and Z's. Accordingly, the values for the profile given in Table I represent ambient, non-operating or non-hot conditions (e.g., room temperature) and are for an uncoated airfoil.


There are typical manufacturing tolerances as well as coatings which must be accounted for in the actual profile of the airfoil 52. Each cross-section is joined smoothly with the other cross-sections to form the complete airfoil shape. It will therefore be appreciated that +/− typical manufacturing tolerances, i.e., +/− values, including any coating thicknesses, are additive to the X and Y values given in Table I below. Accordingly, a distance of +/− 5% in a direction normal to any surface location along the airfoil profile defines an airfoil profile envelope for this particular turbine rotor blade 50 airfoil design and turbine 12, i.e., a range of variation between measured points on the actual airfoil surface at nominal cold or room temperature and the ideal position of those points as given in Table I below at the same temperature. The data provided in Table I is scalable and the geometry pertains to all aerodynamic scales, at, above and/or below a 3000-3600 RPM range. The design of the airfoil 52 for turbine rotor blade 50 is robust to this range of variation without impairment of mechanical and aerodynamic functions.











TABLE I







Suction-side

Pressure-side













X (%)
Y (%)
Z (%)
N
X (%)
Y (%)
Z (%)
















0.0000
0.0000
0.0000
1
0.0000
0.0000
0.0000


−0.3895
0.7151
0.0000
2
0.4741
−0.3831
0.0000


−0.5020
1.5243
0.0000
3
1.0407
−0.6129
0.0000


−0.4142
2.3392
0.0000
4
1.6441
−0.7127
0.0000


−0.2003
3.1309
0.0000
5
2.2562
−0.7119
0.0000


0.0974
3.8947
0.0000
6
2.8643
−0.6393
0.0000


0.4597
4.6305
0.0000
7
3.4637
−0.5132
0.0000


0.8699
5.3408
0.0000
8
4.0519
−0.3448
0.0000


1.3192
6.0271
0.0000
9
4.6305
−0.1437
0.0000


1.8005
6.6903
0.0000
10
5.2027
0.0758
0.0000


2.3113
7.3328
0.0000
11
5.7733
0.2977
0.0000


2.8460
7.9545
0.0000
12
6.3464
0.5156
0.0000


3.4022
8.5571
0.0000
13
6.9226
0.7247
0.0000


3.9777
9.1421
0.0000
14
7.5012
0.9250
0.0000


4.5682
9.7111
0.0000
15
8.0830
1.1173
0.0000


5.1748
10.2642
0.0000
16
8.6672
1.3017
0.0000


5.7965
10.7989
0.0000
17
9.2538
1.4781
0.0000


6.4342
11.3152
0.0000
18
9.8428
1.6449
0.0000


7.0870
11.8117
0.0000
19
10.4350
1.8037
0.0000


7.7550
12.2873
0.0000
20
11.0287
1.9529
0.0000


8.4389
12.7406
0.0000
21
11.6249
2.0934
0.0000


9.1381
13.1700
0.0000
22
12.2235
2.2235
0.0000


9.8508
13.5754
0.0000
23
12.8244
2.3440
0.0000


10.5778
13.9545
0.0000
24
13.4270
2.4541
0.0000


11.3192
14.3073
0.0000
25
14.0311
2.5547
0.0000


12.0726
14.6305
0.0000
26
14.6377
2.6433
0.0000


12.8380
14.9250
0.0000
27
15.2450
2.7215
0.0000


13.6153
15.1891
0.0000
28
15.8540
2.7885
0.0000


14.4014
15.4206
0.0000
29
16.4645
2.8428
0.0000


15.1979
15.6185
0.0000
30
17.0750
2.8859
0.0000


16.0016
15.7837
0.0000
31
17.6872
2.9170
0.0000


16.8109
15.9138
0.0000
32
18.2993
2.9354
0.0000


17.6257
16.0088
0.0000
33
18.9122
2.9409
0.0000


18.4437
16.0678
0.0000
34
19.5243
2.9338
0.0000


19.2642
16.0910
0.0000
35
20.1365
2.9138
0.0000


20.0838
16.0782
0.0000
36
20.7486
2.8803
0.0000


20.9026
16.0287
0.0000
37
21.3591
2.8340
0.0000


21.7191
15.9441
0.0000
38
21.9689
2.7733
0.0000


22.5299
15.8236
0.0000
39
22.5770
2.6983
0.0000


23.3352
15.6680
0.0000
40
23.1828
2.6105
0.0000


24.1333
15.4781
0.0000
41
23.7869
2.5084
0.0000


24.9226
15.2546
0.0000
42
24.3887
2.3919
0.0000


25.7023
14.9992
0.0000
43
24.9872
2.2618
0.0000


26.4701
14.7111
0.0000
44
25.5826
2.1173
0.0000


27.2259
14.3919
0.0000
45
26.1740
1.9593
0.0000


27.9681
14.0431
0.0000
46
26.7622
1.7869
0.0000


28.6967
13.6656
0.0000
47
27.3464
1.6018
0.0000


29.4102
13.2610
0.0000
48
27.9258
1.4022
0.0000


30.1077
12.8300
0.0000
49
28.4996
1.1891
0.0000


30.7901
12.3743
0.0000
50
29.0694
0.9633
0.0000


31.4557
11.8955
0.0000
51
29.6337
0.7247
0.0000


32.1038
11.3927
0.0000
52
30.1915
0.4733
0.0000


32.7342
10.8683
0.0000
53
30.7446
0.2083
0.0000


33.3472
10.3224
0.0000
54
31.2913
−0.0678
0.0000


33.9417
9.7574
0.0000
55
31.8316
−0.3567
0.0000


34.5188
9.1740
0.0000
56
32.3655
−0.6576
0.0000


35.0774
8.5738
0.0000
57
32.8923
−0.9697
0.0000


35.6193
7.9577
0.0000
58
33.4126
−1.2929
0.0000


36.1445
7.3272
0.0000
59
33.9258
−1.6265
0.0000


36.6528
6.6840
0.0000
60
34.4326
−1.9713
0.0000


37.1468
6.0295
0.0000
61
34.9322
−2.3264
0.0000


37.6273
5.3639
0.0000
62
35.4246
−2.6911
0.0000


38.0950
4.6903
0.0000
63
35.9090
−3.0646
0.0000


38.5515
4.0088
0.0000
64
36.3871
−3.4485
0.0000


38.9960
3.3192
0.0000
65
36.8579
−3.8412
0.0000


39.4302
2.6233
0.0000
66
37.3208
−4.2418
0.0000


39.8547
1.9210
0.0000
67
37.7765
−4.6512
0.0000


40.2690
1.2131
0.0000
68
38.2251
−5.0686
0.0000


40.6744
0.5004
0.0000
69
38.6656
−5.4940
0.0000


41.0710
−0.2179
0.0000
70
39.0998
−5.9266
0.0000


41.4597
−0.9401
0.0000
71
39.5259
−6.3663
0.0000


41.8420
−1.6664
0.0000
72
39.9449
−6.8125
0.0000


42.2163
−2.3958
0.0000
73
40.3575
−7.2658
0.0000


42.5842
−3.1285
0.0000
74
40.7622
−7.7255
0.0000


42.9465
−3.8651
0.0000
75
41.1604
−8.1915
0.0000


43.3017
−4.6042
0.0000
76
41.5515
−8.6632
0.0000


43.6512
−5.3464
0.0000
77
41.9362
−9.1397
0.0000


43.9952
−6.0910
0.0000
78
42.3136
−9.6225
0.0000


44.3336
−6.8388
0.0000
79
42.6840
−10.1101
0.0000


44.6680
−7.5874
0.0000
80
43.0487
−10.6026
0.0000


44.9968
−8.3392
0.0000
81
43.4062
−11.0998
0.0000


45.3208
−9.0926
0.0000
82
43.7574
−11.6018
0.0000


45.6409
−9.8484
0.0000
83
44.1022
−12.1085
0.0000


45.9569
−10.6049
0.0000
84
44.4413
−12.6185
0.0000


46.2682
−11.3639
0.0000
85
44.7741
−13.1333
0.0000


46.4046
−11.6999
0.0000
86
44.9186
−13.3615
0.0000


46.4916
−11.9162
0.0000
87
45.0120
−13.5092
0.0000


46.5786
−12.1325
0.0000
88
45.1038
−13.6568
0.0000


46.6656
−12.3488
0.0000
89
45.1955
−13.8045
0.0000


46.7518
−12.5658
0.0000
90
45.2873
−13.9529
0.0000


46.8380
−12.7821
0.0000
91
45.3775
−14.1014
0.0000


46.9242
−12.9992
0.0000
92
45.4685
−14.2498
0.0000


47.0096
−13.2155
0.0000
93
45.5666
−14.3935
0.0000


47.0950
−13.4326
0.0000
94
45.6903
−14.5156
0.0000


47.1612
−13.6560
0.0000
95
45.8348
−14.6129
0.0000


47.1716
−13.8883
0.0000
96
45.9944
−14.6816
0.0000


47.1229
−14.1157
0.0000
97
46.1636
−14.7191
0.0000


47.0176
−14.3232
0.0000
98
46.3376
−14.7223
0.0000


46.8627
−14.4964
0.0000
99
46.5084
−14.6903
0.0000


46.6704
−14.6265
0.0000
100
46.6704
−14.6265
0.0000


−0.0152
0.9234
10.0000
1
−0.0152
0.9234
10.0000


−0.3935
1.6449
10.0000
2
0.4613
0.5275
10.0000


−0.4852
2.4581
10.0000
3
1.0359
0.2953
10.0000


−0.3783
3.2721
10.0000
4
1.6488
0.1971
10.0000


−0.1468
4.0599
10.0000
5
2.2698
0.1971
10.0000


0.1708
4.8172
10.0000
6
2.8867
0.2721
10.0000


0.5507
5.5451
10.0000
7
3.4948
0.4014
10.0000


0.9785
6.2466
10.0000
8
4.0918
0.5762
10.0000


1.4453
6.9226
10.0000
9
4.6784
0.7813
10.0000


1.9449
7.5746
10.0000
10
5.2618
0.9976
10.0000


2.4733
8.2043
10.0000
11
5.8460
1.2091
10.0000


3.0255
8.8125
10.0000
12
6.4334
1.4126
10.0000


3.5986
9.4014
10.0000
13
7.0231
1.6089
10.0000


4.1891
9.9729
10.0000
14
7.6161
1.7965
10.0000


4.7949
10.5267
10.0000
15
8.2115
1.9761
10.0000


5.4174
11.0630
10.0000
16
8.8093
2.1468
10.0000


6.0567
11.5802
10.0000
17
9.4094
2.3081
10.0000


6.7111
12.0766
10.0000
18
10.0128
2.4605
10.0000


7.3815
12.5507
10.0000
19
10.6177
2.6026
10.0000


8.0678
13.0024
10.0000
20
11.2251
2.7350
10.0000


8.7702
13.4294
10.0000
21
11.8348
2.8563
10.0000


9.4876
13.8300
10.0000
22
12.4469
2.9681
10.0000


10.2195
14.2027
10.0000
23
13.0599
3.0678
10.0000


10.9657
14.5459
10.0000
24
13.6760
3.1564
10.0000


11.7263
14.8579
10.0000
25
14.2929
3.2338
10.0000


12.4988
15.1381
10.0000
26
14.9106
3.2985
10.0000


13.2825
15.3847
10.0000
27
15.5307
3.3512
10.0000


14.0758
15.5954
10.0000
28
16.1508
3.3903
10.0000


14.8787
15.7709
10.0000
29
16.7717
3.4166
10.0000


15.6887
15.9098
10.0000
30
17.3935
3.4302
10.0000


16.5036
16.0104
10.0000
31
18.0152
3.4294
10.0000


17.3232
16.0726
10.0000
32
18.6369
3.4150
10.0000


18.1445
16.0966
10.0000
33
19.2578
3.3863
10.0000


18.9657
16.0822
10.0000
34
19.8779
3.3432
10.0000


19.7853
16.0295
10.0000
35
20.4972
3.2865
10.0000


20.6026
15.9393
10.0000
36
21.1149
3.2139
10.0000


21.4142
15.8132
10.0000
37
21.7302
3.1269
10.0000


22.2195
15.6504
10.0000
38
22.3440
3.0239
10.0000


23.0168
15.4517
10.0000
39
22.9545
2.9066
10.0000


23.8045
15.2195
10.0000
40
23.5619
2.7749
10.0000


24.5818
14.9545
10.0000
41
24.1660
2.6273
10.0000


25.3480
14.6576
10.0000
42
24.7662
2.4645
10.0000


26.1022
14.3304
10.0000
43
25.3615
2.2873
10.0000


26.8420
13.9745
10.0000
44
25.9529
2.0950
10.0000


27.5690
13.5914
10.0000
45
26.5395
1.8883
10.0000


28.2809
13.1812
10.0000
46
27.1205
1.6672
10.0000


28.9785
12.7470
10.0000
47
27.6959
1.4326
10.0000


29.6608
12.2889
10.0000
48
28.2666
1.1844
10.0000


30.3272
11.8085
10.0000
49
28.8300
0.9226
10.0000


30.9777
11.3065
10.0000
50
29.3879
0.6480
10.0000


31.6121
10.7853
10.0000
51
29.9393
0.3607
10.0000


32.2306
10.2442
10.0000
52
30.4836
0.0607
10.0000


32.8332
9.6856
10.0000
53
31.0215
−0.2514
10.0000


33.4198
9.1101
10.0000
54
31.5523
−0.5754
10.0000


33.9904
8.5196
10.0000
55
32.0766
−0.9098
10.0000


34.5451
7.9130
10.0000
56
32.5930
−1.2554
10.0000


35.0854
7.2937
10.0000
57
33.1022
−1.6121
10.0000


35.6097
6.6616
10.0000
58
33.6049
−1.9785
10.0000


36.1197
6.0176
10.0000
59
34.0998
−2.3543
10.0000


36.6161
5.3631
10.0000
60
34.5874
−2.7398
10.0000


37.0998
4.6983
10.0000
61
35.0686
−3.1341
10.0000


37.5706
4.0247
10.0000
62
35.5419
−3.5371
10.0000


38.0303
3.3440
10.0000
63
36.0088
−3.9481
10.0000


38.4789
2.6552
10.0000
64
36.4685
−4.3671
10.0000


38.9170
1.9609
10.0000
65
36.9202
−4.7933
10.0000


39.3448
1.2594
10.0000
66
37.3663
−5.2267
10.0000


39.7638
0.5523
10.0000
67
37.8045
−5.6680
10.0000


40.1740
−0.1596
10.0000
68
38.2362
−6.1149
10.0000


40.5746
−0.8763
10.0000
69
38.6608
−6.5690
10.0000


40.9681
−1.5978
10.0000
70
39.0790
−7.0287
10.0000


41.3543
−2.3232
10.0000
71
39.4908
−7.4948
10.0000


41.7326
−3.0527
10.0000
72
39.8962
−7.9665
10.0000


42.1053
−3.7853
10.0000
73
40.2953
−8.4429
10.0000


42.4709
−4.5211
10.0000
74
40.6879
−8.9250
10.0000


42.8300
−5.2594
10.0000
75
41.0750
−9.4118
10.0000


43.1836
−6.0016
10.0000
76
41.4557
−9.9034
10.0000


43.5315
−6.7454
10.0000
77
41.8308
−10.3998
10.0000


43.8739
−7.4924
10.0000
78
42.2003
−10.8994
10.0000


44.2115
−8.2418
10.0000
79
42.5634
−11.4038
10.0000


44.5443
−8.9928
10.0000
80
42.9218
−11.9122
10.0000


44.8723
−9.7462
10.0000
81
43.2745
−12.4238
10.0000


45.1963
−10.5012
10.0000
82
43.6217
−12.9393
10.0000


45.5156
−11.2578
10.0000
83
43.9641
−13.4589
10.0000


45.8308
−12.0168
10.0000
84
44.3017
−13.9808
10.0000


46.1421
−12.7773
10.0000
85
44.6337
−14.5068
10.0000


46.2793
−13.1141
10.0000
86
44.7789
−14.7398
10.0000


46.3663
−13.3304
10.0000
87
44.8723
−14.8899
10.0000


46.4533
−13.5467
10.0000
88
44.9649
−15.0407
10.0000


46.5403
−13.7638
10.0000
89
45.0575
−15.1915
10.0000


46.6265
−13.9808
10.0000
90
45.1492
−15.3424
10.0000


46.7135
−14.1979
10.0000
91
45.2402
−15.4932
10.0000


46.7997
−14.4150
10.0000
92
45.3312
−15.6449
10.0000


46.8851
−14.6321
10.0000
93
45.4286
−15.7925
10.0000


46.9721
−14.8484
10.0000
94
45.5515
−15.9186
10.0000


47.0375
−15.0726
10.0000
95
45.6959
−16.0200
10.0000


47.0471
−15.3049
10.0000
96
45.8571
−16.0918
10.0000


46.9984
−15.5331
10.0000
97
46.0287
−16.1325
10.0000


46.8923
−15.7398
10.0000
98
46.2051
−16.1381
10.0000


46.7366
−15.9130
10.0000
99
46.3791
−16.1077
10.0000


46.5427
−16.0431
10.0000
100
46.5427
−16.0431
10.0000


0.1061
2.1852
20.0000
1
0.1061
2.1852
20.0000


−0.2538
2.9130
20.0000
2
0.5802
1.7757
20.0000


−0.3272
3.7255
20.0000
3
1.1572
1.5291
20.0000


−0.2043
4.5331
20.0000
4
1.7757
1.4206
20.0000


0.0455
5.3121
20.0000
5
2.4046
1.4126
20.0000


0.3823
6.0575
20.0000
6
3.0295
1.4781
20.0000


0.7797
6.7733
20.0000
7
3.6464
1.6026
20.0000


1.2259
7.4589
20.0000
8
4.2522
1.7725
20.0000


1.7111
8.1181
20.0000
9
4.8492
1.9705
20.0000


2.2291
8.7518
20.0000
10
5.4429
2.1788
20.0000


2.7757
9.3607
20.0000
11
6.0391
2.3791
20.0000


3.3464
9.9473
20.0000
12
6.6393
2.5690
20.0000


3.9377
10.5132
20.0000
13
7.2418
2.7502
20.0000


4.5467
11.0599
20.0000
14
7.8468
2.9218
20.0000


5.1732
11.5866
20.0000
15
8.4549
3.0846
20.0000


5.8164
12.0918
20.0000
16
9.0654
3.2370
20.0000


6.4773
12.5754
20.0000
17
9.6784
3.3799
20.0000


7.1548
13.0343
20.0000
18
10.2937
3.5116
20.0000


7.8484
13.4693
20.0000
19
10.9106
3.6329
20.0000


8.5579
13.8763
20.0000
20
11.5307
3.7422
20.0000


9.2833
14.2554
20.0000
21
12.1516
3.8404
20.0000


10.0231
14.6049
20.0000
22
12.7749
3.9266
20.0000


10.7781
14.9218
20.0000
23
13.3998
4.0000
20.0000


11.5459
15.2051
20.0000
24
14.0263
4.0599
20.0000


12.3256
15.4533
20.0000
25
14.6536
4.1069
20.0000


13.1157
15.6672
20.0000
26
15.2817
4.1405
20.0000


13.9146
15.8436
20.0000
27
15.9106
4.1596
20.0000


14.7215
15.9824
20.0000
28
16.5403
4.1644
20.0000


15.5331
16.0822
20.0000
29
17.1692
4.1540
20.0000


16.3496
16.1437
20.0000
30
17.7981
4.1293
20.0000


17.1676
16.1660
20.0000
31
18.4262
4.0894
20.0000


17.9856
16.1484
20.0000
32
19.0527
4.0343
20.0000


18.8021
16.0926
20.0000
33
19.6776
3.9633
20.0000


19.6153
15.9976
20.0000
34
20.3009
3.8763
20.0000


20.4222
15.8651
20.0000
35
20.9218
3.7733
20.0000


21.2235
15.6967
20.0000
36
21.5395
3.6552
20.0000


22.0160
15.4932
20.0000
37
22.1540
3.5204
20.0000


22.7989
15.2546
20.0000
38
22.7646
3.3695
20.0000


23.5714
14.9832
20.0000
39
23.3719
3.2027
20.0000


24.3312
14.6808
20.0000
40
23.9737
3.0200
20.0000


25.0790
14.3480
20.0000
41
24.5714
2.8228
20.0000


25.8140
13.9872
20.0000
42
25.1636
2.6105
20.0000


26.5347
13.6002
20.0000
43
25.7502
2.3823
20.0000


27.2418
13.1875
20.0000
44
26.3304
2.1397
20.0000


27.9338
12.7510
20.0000
45
26.9050
1.8835
20.0000


28.6113
12.2921
20.0000
46
27.4725
1.6121
20.0000


29.2745
11.8117
20.0000
47
28.0343
1.3280
20.0000


29.9218
11.3113
20.0000
48
28.5882
1.0303
20.0000


30.5539
10.7917
20.0000
49
29.1357
0.7199
20.0000


31.1708
10.2538
20.0000
50
29.6760
0.3974
20.0000


31.7733
9.6999
20.0000
51
30.2091
0.0630
20.0000


32.3615
9.1309
20.0000
52
30.7342
−0.2825
20.0000


32.9354
8.5475
20.0000
53
31.2530
−0.6393
20.0000


33.4948
7.9497
20.0000
54
31.7638
−1.0064
20.0000


34.0407
7.3400
20.0000
55
32.2674
−1.3839
20.0000


34.5722
6.7175
20.0000
56
32.7638
−1.7702
20.0000


35.0910
6.0846
20.0000
57
33.2530
−2.1668
20.0000


35.5962
5.4405
20.0000
58
33.7342
−2.5714
20.0000


36.0894
4.7877
20.0000
59
34.2083
−2.9848
20.0000


36.5706
4.1253
20.0000
60
34.6760
−3.4062
20.0000


37.0399
3.4549
20.0000
61
35.1357
−3.8356
20.0000


37.4980
2.7765
20.0000
62
35.5898
−4.2713
20.0000


37.9465
2.0918
20.0000
63
36.0359
−4.7143
20.0000


38.3839
1.4006
20.0000
64
36.4765
−5.1644
20.0000


38.8125
0.7031
20.0000
65
36.9106
−5.6201
20.0000


39.2322
0.0000
20.0000
66
37.3376
−6.0814
20.0000


39.6425
−0.7079
20.0000
67
37.7590
−6.5491
20.0000


40.0447
−1.4206
20.0000
68
38.1740
−7.0215
20.0000


40.4389
−2.1381
20.0000
69
38.5834
−7.4996
20.0000


40.8252
−2.8595
20.0000
70
38.9864
−7.9824
20.0000


41.2051
−3.5842
20.0000
71
39.3839
−8.4709
20.0000


41.5778
−4.3128
20.0000
72
39.7757
−8.9625
20.0000


41.9449
−5.0447
20.0000
73
40.1620
−9.4597
20.0000


42.3049
−5.7797
20.0000
74
40.5427
−9.9609
20.0000


42.6600
−6.5172
20.0000
75
40.9178
−10.4653
20.0000


43.0088
−7.2578
20.0000
76
41.2881
−10.9745
20.0000


43.3520
−8.0000
20.0000
77
41.6536
−11.4868
20.0000


43.6911
−8.7454
20.0000
78
42.0136
−12.0024
20.0000


44.0247
−9.4924
20.0000
79
42.3695
−12.5211
20.0000


44.3536
−10.2418
20.0000
80
42.7207
−13.0431
20.0000


44.6792
−10.9936
20.0000
81
43.0670
−13.5682
20.0000


45.0000
−11.7462
20.0000
82
43.4094
−14.0966
20.0000


45.3160
−12.5012
20.0000
83
43.7478
−14.6273
20.0000


45.6289
−13.2570
20.0000
84
44.0822
−15.1596
20.0000


45.9377
−14.0152
20.0000
85
44.4126
−15.6951
20.0000


46.0734
−14.3504
20.0000
86
44.5579
−15.9330
20.0000


46.1604
−14.5666
20.0000
87
44.6504
−16.0854
20.0000


46.2466
−14.7821
20.0000
88
44.7430
−16.2386
20.0000


46.3328
−14.9984
20.0000
89
44.8348
−16.3919
20.0000


46.4190
−15.2147
20.0000
90
44.9266
−16.5451
20.0000


46.5052
−15.4310
20.0000
91
45.0184
−16.6991
20.0000


46.5906
−15.6472
20.0000
92
45.1101
−16.8524
20.0000


46.6760
−15.8635
20.0000
93
45.2059
−17.0032
20.0000


46.7622
−16.0798
20.0000
94
45.3280
−17.1333
20.0000


46.8260
−16.3025
20.0000
95
45.4733
−17.2378
20.0000


46.8340
−16.5347
20.0000
96
45.6353
−17.3128
20.0000


46.7845
−16.7614
20.0000
97
45.8085
−17.3559
20.0000


46.6776
−16.9673
20.0000
98
45.9864
−17.3631
20.0000


46.5219
−17.1389
20.0000
99
46.1628
−17.3328
20.0000


46.3288
−17.2682
20.0000
100
46.3288
−17.2682
20.0000


0.3711
3.7893
30.0000
1
0.3711
3.7893
30.0000


0.0327
4.5219
30.0000
2
0.8364
3.3567
30.0000


−0.0239
5.3304
30.0000
3
1.4118
3.0854
30.0000


0.1149
6.1309
30.0000
4
2.0351
2.9545
30.0000


0.3839
6.8978
30.0000
5
2.6728
2.9290
30.0000


0.7382
7.6297
30.0000
6
3.3081
2.9785
30.0000


1.1556
8.3280
30.0000
7
3.9370
3.0886
30.0000


1.6217
8.9944
30.0000
8
4.5547
3.2466
30.0000


2.1277
9.6321
30.0000
9
5.1652
3.4334
30.0000


2.6664
10.2410
30.0000
10
5.7741
3.6225
30.0000


3.2346
10.8236
30.0000
11
6.3855
3.8061
30.0000


3.8268
11.3807
30.0000
12
7.0000
3.9785
30.0000


4.4413
11.9138
30.0000
13
7.6169
4.1405
30.0000


5.0742
12.4254
30.0000
14
8.2370
4.2929
30.0000


5.7263
12.9114
30.0000
15
8.8587
4.4350
30.0000


6.3966
13.3727
30.0000
16
9.4836
4.5666
30.0000


7.0854
13.8053
30.0000
17
10.1101
4.6864
30.0000


7.7917
14.2083
30.0000
18
10.7390
4.7949
30.0000


8.5156
14.5794
30.0000
19
11.3703
4.8907
30.0000


9.2554
14.9178
30.0000
20
12.0024
4.9729
30.0000


10.0104
15.2211
30.0000
21
12.6369
5.0423
30.0000


10.7789
15.4884
30.0000
22
13.2729
5.0982
30.0000


11.5587
15.7191
30.0000
23
13.9098
5.1389
30.0000


12.3488
15.9114
30.0000
24
14.5475
5.1644
30.0000


13.1476
16.0654
30.0000
25
15.1852
5.1740
30.0000


13.9529
16.1804
30.0000
26
15.8236
5.1684
30.0000


14.7630
16.2570
30.0000
27
16.4613
5.1460
30.0000


15.5754
16.2929
30.0000
28
17.0982
5.1069
30.0000


16.3895
16.2897
30.0000
29
17.7334
5.0511
30.0000


17.2019
16.2482
30.0000
30
18.3679
4.9785
30.0000


18.0112
16.1692
30.0000
31
18.9992
4.8883
30.0000


18.8164
16.0527
30.0000
32
19.6289
4.7813
30.0000


19.6153
15.8994
30.0000
33
20.2546
4.6568
30.0000


20.4070
15.7119
30.0000
34
20.8763
4.5148
30.0000


21.1891
15.4900
30.0000
35
21.4948
4.3551
30.0000


21.9617
15.2354
30.0000
36
22.1077
4.1788
30.0000


22.7239
14.9497
30.0000
37
22.7159
3.9856
30.0000


23.4733
14.6345
30.0000
38
23.3184
3.7765
30.0000


24.2107
14.2905
30.0000
39
23.9154
3.5499
30.0000


24.9354
13.9210
30.0000
40
24.5060
3.3089
30.0000


25.6464
13.5259
30.0000
41
25.0902
3.0511
30.0000


26.3440
13.1069
30.0000
42
25.6672
2.7797
30.0000


27.0279
12.6664
30.0000
43
26.2378
2.4932
30.0000


27.6975
12.2043
30.0000
44
26.8005
2.1931
30.0000


28.3528
11.7231
30.0000
45
27.3559
1.8795
30.0000


28.9944
11.2227
30.0000
46
27.9042
1.5523
30.0000


29.6217
10.7047
30.0000
47
28.4453
1.2139
30.0000


30.2362
10.1708
30.0000
48
28.9785
0.8627
30.0000


30.8356
9.6217
30.0000
49
29.5036
0.5004
30.0000


31.4222
9.0575
30.0000
50
30.0208
0.1269
30.0000


31.9960
8.4804
30.0000
51
30.5307
−0.2562
30.0000


32.5563
7.8907
30.0000
52
31.0335
−0.6496
30.0000


33.1030
7.2889
30.0000
53
31.5283
−1.0527
30.0000


33.6385
6.6760
30.0000
54
32.0160
−1.4645
30.0000


34.1604
6.0519
30.0000
55
32.4956
−1.8851
30.0000


34.6704
5.4182
30.0000
56
32.9689
−2.3136
30.0000


35.1692
4.7757
30.0000
57
33.4342
−2.7494
30.0000


35.6560
4.1237
30.0000
58
33.8931
−3.1931
30.0000


36.1317
3.4637
30.0000
59
34.3448
−3.6441
30.0000


36.5970
2.7965
30.0000
60
34.7901
−4.1006
30.0000


37.0511
2.1213
30.0000
61
35.2291
−4.5642
30.0000


37.4964
1.4405
30.0000
62
35.6616
−5.0335
30.0000


37.9314
0.7534
30.0000
63
36.0878
−5.5084
30.0000


38.3575
0.0599
30.0000
64
36.5084
−5.9880
30.0000


38.7749
−0.6385
30.0000
65
36.9234
−6.4733
30.0000


39.1836
−1.3416
30.0000
66
37.3320
−6.9633
30.0000


39.5842
−2.0495
30.0000
67
37.7358
−7.4573
30.0000


39.9777
−2.7614
30.0000
68
38.1341
−7.9561
30.0000


40.3631
−3.4781
30.0000
69
38.5267
−8.4589
30.0000


40.7422
−4.1979
30.0000
70
38.9146
−8.9657
30.0000


41.1141
−4.9218
30.0000
71
39.2969
−9.4765
30.0000


41.4796
−5.6480
30.0000
72
39.6752
−9.9904
30.0000


41.8396
−6.3775
30.0000
73
40.0487
−10.5084
30.0000


42.1931
−7.1101
30.0000
74
40.4174
−11.0287
30.0000


42.5419
−7.8460
30.0000
75
40.7821
−11.5523
30.0000


42.8851
−8.5834
30.0000
76
41.1429
−12.0790
30.0000


43.2227
−9.3232
30.0000
77
41.4988
−12.6081
30.0000


43.5555
−10.0654
30.0000
78
41.8516
−13.1405
30.0000


43.8843
−10.8101
30.0000
79
42.2003
−13.6744
30.0000


44.2083
−11.5563
30.0000
80
42.5459
−14.2115
30.0000


44.5283
−12.3041
30.0000
81
42.8867
−14.7502
30.0000


44.8444
−13.0535
30.0000
82
43.2251
−15.2921
30.0000


45.1564
−13.8053
30.0000
83
43.5595
−15.8348
30.0000


45.4645
−14.5579
30.0000
84
43.8915
−16.3807
30.0000


45.7694
−15.3121
30.0000
85
44.2195
−16.9282
30.0000


45.9026
−15.6464
30.0000
86
44.3631
−17.1700
30.0000


45.9888
−15.8611
30.0000
87
44.4557
−17.3264
30.0000


46.0742
−16.0758
30.0000
88
44.5483
−17.4828
30.0000


46.1588
−16.2905
30.0000
89
44.6401
−17.6393
30.0000


46.2442
−16.5060
30.0000
90
44.7318
−17.7957
30.0000


46.3288
−16.7207
30.0000
91
44.8228
−17.9521
30.0000


46.4126
−16.9362
30.0000
92
44.9138
−18.1085
30.0000


46.4972
−17.1516
30.0000
93
45.0088
−18.2634
30.0000


46.5826
−17.3663
30.0000
94
45.1301
−18.3974
30.0000


46.6433
−17.5890
30.0000
95
45.2753
−18.5060
30.0000


46.6496
−17.8196
30.0000
96
45.4389
−18.5850
30.0000


46.5986
−18.0447
30.0000
97
45.6137
−18.6305
30.0000


46.4908
−18.2482
30.0000
98
45.7949
−18.6393
30.0000


46.3344
−18.4182
30.0000
99
45.9737
−18.6105
30.0000


46.1421
−18.5451
30.0000
100
46.1421
−18.5451
30.0000


0.7861
5.8994
40.0000
1
0.7861
5.8994
40.0000


0.4828
6.6361
40.0000
2
1.2338
5.4453
40.0000


0.4525
7.4342
40.0000
3
1.7973
5.1445
40.0000


0.6201
8.2163
40.0000
4
2.4150
4.9800
40.0000


0.9146
8.9617
40.0000
5
3.0527
4.9234
40.0000


1.2937
9.6680
40.0000
6
3.6927
4.9457
40.0000


1.7366
10.3352
40.0000
7
4.3280
5.0327
40.0000


2.2275
10.9689
40.0000
8
4.9545
5.1660
40.0000


2.7574
11.5698
40.0000
9
5.5746
5.3272
40.0000


3.3208
12.1405
40.0000
10
6.1939
5.4892
40.0000


3.9130
12.6808
40.0000
11
6.8172
5.6401
40.0000


4.5299
13.1931
40.0000
12
7.4421
5.7805
40.0000


5.1668
13.6792
40.0000
13
8.0694
5.9122
40.0000


5.8244
14.1381
40.0000
14
8.6983
6.0327
40.0000


6.5012
14.5674
40.0000
15
9.3296
6.1421
40.0000


7.1963
14.9665
40.0000
16
9.9633
6.2386
40.0000


7.9098
15.3312
40.0000
17
10.5986
6.3232
40.0000


8.6409
15.6608
40.0000
18
11.2354
6.3951
40.0000


9.3871
15.9529
40.0000
19
11.8731
6.4533
40.0000


10.1476
16.2067
40.0000
20
12.5124
6.4964
40.0000


10.9202
16.4206
40.0000
21
13.1524
6.5251
40.0000


11.7031
16.5938
40.0000
22
13.7933
6.5387
40.0000


12.4932
16.7263
40.0000
23
14.4342
6.5355
40.0000


13.2897
16.8164
40.0000
24
15.0742
6.5164
40.0000


14.0902
16.8667
40.0000
25
15.7143
6.4796
40.0000


14.8915
16.8763
40.0000
26
16.3528
6.4254
40.0000


15.6919
16.8460
40.0000
27
16.9888
6.3536
40.0000


16.4908
16.7765
40.0000
28
17.6233
6.2634
40.0000


17.2849
16.6688
40.0000
29
18.2546
6.1548
40.0000


18.0742
16.5251
40.0000
30
18.8827
6.0287
40.0000


18.8555
16.3472
40.0000
31
19.5068
5.8835
40.0000


19.6289
16.1357
40.0000
32
20.1269
5.7199
40.0000


20.3919
15.8915
40.0000
33
20.7414
5.5387
40.0000


21.1453
15.6169
40.0000
34
21.3504
5.3400
40.0000


21.8875
15.3136
40.0000
35
21.9529
5.1229
40.0000


22.6177
14.9832
40.0000
36
22.5499
4.8899
40.0000


23.3360
14.6265
40.0000
37
23.1397
4.6393
40.0000


24.0415
14.2458
40.0000
38
23.7223
4.3727
40.0000


24.7342
13.8428
40.0000
39
24.2977
4.0910
40.0000


25.4134
13.4182
40.0000
40
24.8651
3.7933
40.0000


26.0806
12.9729
40.0000
41
25.4246
3.4812
40.0000


26.7342
12.5084
40.0000
42
25.9769
3.1556
40.0000


27.3743
12.0263
40.0000
43
26.5211
2.8172
40.0000


28.0016
11.5275
40.0000
44
27.0567
2.4669
40.0000


28.6161
11.0128
40.0000
45
27.5850
2.1045
40.0000


29.2179
10.4828
40.0000
46
28.1053
1.7302
40.0000


29.8069
9.9393
40.0000
47
28.6177
1.3456
40.0000


30.3839
9.3823
40.0000
48
29.1229
0.9513
40.0000


30.9489
8.8132
40.0000
49
29.6193
0.5467
40.0000


31.5012
8.2322
40.0000
50
30.1085
0.1325
40.0000


32.0423
7.6409
40.0000
51
30.5906
−0.2897
40.0000


32.5714
7.0391
40.0000
52
31.0646
−0.7207
40.0000


33.0894
6.4278
40.0000
53
31.5323
−1.1588
40.0000


33.5970
5.8069
40.0000
54
31.9928
−1.6049
40.0000


34.0942
5.1780
40.0000
55
32.4461
−2.0575
40.0000


34.5802
4.5403
40.0000
56
32.8923
−2.5164
40.0000


35.0559
3.8947
40.0000
57
33.3328
−2.9824
40.0000


35.5211
3.2426
40.0000
58
33.7670
−3.4541
40.0000


35.9769
2.5826
40.0000
59
34.1947
−3.9306
40.0000


36.4230
1.9162
40.0000
60
34.6161
−4.4134
40.0000


36.8587
1.2442
40.0000
61
35.0327
−4.9002
40.0000


37.2865
0.5658
40.0000
62
35.4437
−5.3919
40.0000


37.7047
−0.1181
40.0000
63
35.8492
−5.8875
40.0000


38.1149
−0.8069
40.0000
64
36.2498
−6.3879
40.0000


38.5172
−1.5004
40.0000
65
36.6457
−6.8923
40.0000


38.9106
−2.1987
40.0000
66
37.0359
−7.3998
40.0000


39.2977
−2.9010
40.0000
67
37.4222
−7.9114
40.0000


39.6776
−3.6073
40.0000
68
37.8037
−8.4254
40.0000


40.0503
−4.3168
40.0000
69
38.1812
−8.9433
40.0000


40.4166
−5.0295
40.0000
70
38.5539
−9.4645
40.0000


40.7773
−5.7454
40.0000
71
38.9234
−9.9888
40.0000


41.1325
−6.4645
40.0000
72
39.2881
−10.5148
40.0000


41.4820
−7.1860
40.0000
73
39.6496
−11.0439
40.0000


41.8260
−7.9098
40.0000
74
40.0072
−11.5762
40.0000


42.1652
−8.6361
40.0000
75
40.3615
−12.1101
40.0000


42.4988
−9.3647
40.0000
76
40.7119
−12.6457
40.0000


42.8284
−10.0958
40.0000
77
41.0599
−13.1844
40.0000


43.1532
−10.8292
40.0000
78
41.4046
−13.7247
40.0000


43.4733
−11.5642
40.0000
79
41.7462
−14.2666
40.0000


43.7893
−12.3009
40.0000
80
42.0846
−14.8109
40.0000


44.1014
−13.0391
40.0000
81
42.4198
−15.3567
40.0000


44.4102
−13.7789
40.0000
82
42.7526
−15.9042
40.0000


44.7151
−14.5204
40.0000
83
43.0830
−16.4533
40.0000


45.0160
−15.2634
40.0000
84
43.4110
−17.0040
40.0000


45.3136
−16.0080
40.0000
85
43.7358
−17.5555
40.0000


45.4445
−16.3368
40.0000
86
43.8787
−17.8005
40.0000


45.5283
−16.5491
40.0000
87
43.9705
−17.9577
40.0000


45.6113
−16.7614
40.0000
88
44.0623
−18.1149
40.0000


45.6943
−16.9729
40.0000
89
44.1532
−18.2729
40.0000


45.7773
−17.1852
40.0000
90
44.2442
−18.4302
40.0000


45.8603
−17.3974
40.0000
91
44.3352
−18.5882
40.0000


45.9425
−17.6097
40.0000
92
44.4262
−18.7462
40.0000


46.0255
−17.8228
40.0000
93
44.5211
−18.9018
40.0000


46.1069
−18.0351
40.0000
94
44.6409
−19.0375
40.0000


46.1652
−18.2554
40.0000
95
44.7861
−19.1476
40.0000


46.1668
−18.4820
40.0000
96
44.9497
−19.2275
40.0000


46.1117
−18.7031
40.0000
97
45.1253
−19.2737
40.0000


46.0032
−18.9026
40.0000
98
45.3065
−19.2833
40.0000


45.8476
−19.0678
40.0000
99
45.4860
−19.2554
40.0000


45.6568
−19.1915
40.0000
100
45.6568
−19.1915
40.0000


1.3551
8.5403
50.0000
1
1.3551
8.5403
50.0000


1.1022
9.2753
50.0000
2
1.7678
8.0591
50.0000


1.1157
10.0559
50.0000
3
2.3065
7.7215
50.0000


1.3184
10.8109
50.0000
4
2.9082
7.5164
50.0000


1.6457
11.5219
50.0000
5
3.5371
7.4150
50.0000


2.0591
12.1868
50.0000
6
4.1732
7.3958
50.0000


2.5331
12.8101
50.0000
7
4.8085
7.4397
50.0000


3.0543
13.3943
50.0000
8
5.4389
7.5339
50.0000


3.6137
13.9425
50.0000
9
6.0638
7.6560
50.0000


4.2059
14.4549
50.0000
10
6.6887
7.7797
50.0000


4.8244
14.9354
50.0000
11
7.3168
7.8875
50.0000


5.4653
15.3855
50.0000
12
7.9465
7.9848
50.0000


6.1261
15.8053
50.0000
13
8.5778
8.0718
50.0000


6.8069
16.1931
50.0000
14
9.2099
8.1460
50.0000


7.5052
16.5467
50.0000
15
9.8444
8.2083
50.0000


8.2211
16.8643
50.0000
16
10.4796
8.2578
50.0000


8.9537
17.1421
50.0000
17
11.1157
8.2929
50.0000


9.6999
17.3799
50.0000
18
11.7518
8.3144
50.0000


10.4581
17.5762
50.0000
19
12.3895
8.3208
50.0000


11.2259
17.7310
50.0000
20
13.0263
8.3121
50.0000


12.0008
17.8428
50.0000
21
13.6632
8.2873
50.0000


12.7805
17.9106
50.0000
22
14.2985
8.2458
50.0000


13.5634
17.9354
50.0000
23
14.9330
8.1875
50.0000


14.3464
17.9186
50.0000
24
15.5658
8.1117
50.0000


15.1277
17.8611
50.0000
25
16.1955
8.0176
50.0000


15.9050
17.7638
50.0000
26
16.8228
7.9058
50.0000


16.6760
17.6281
50.0000
27
17.4461
7.7749
50.0000


17.4405
17.4573
50.0000
28
18.0654
7.6249
50.0000


18.1955
17.2514
50.0000
29
18.6800
7.4557
50.0000


18.9417
17.0128
50.0000
30
19.2889
7.2690
50.0000


19.6776
16.7438
50.0000
31
19.8923
7.0646
50.0000


20.4022
16.4469
50.0000
32
20.4892
6.8428
50.0000


21.1149
16.1229
50.0000
33
21.0798
6.6042
50.0000


21.8164
15.7733
50.0000
34
21.6640
6.3488
50.0000


22.5052
15.4006
50.0000
35
22.2402
6.0774
50.0000


23.1820
15.0064
50.0000
36
22.8085
5.7901
50.0000


23.8460
14.5914
50.0000
37
23.3687
5.4868
50.0000


24.4980
14.1572
50.0000
38
23.9210
5.1684
50.0000


25.1373
13.7047
50.0000
39
24.4637
4.8356
50.0000


25.7646
13.2362
50.0000
40
24.9992
4.4900
50.0000


26.3799
12.7510
50.0000
41
25.5259
4.1317
50.0000


26.9832
12.2514
50.0000
42
26.0447
3.7614
50.0000


27.5746
11.7382
50.0000
43
26.5547
3.3799
50.0000


28.1548
11.2123
50.0000
44
27.0567
2.9880
50.0000


28.7239
10.6736
50.0000
45
27.5499
2.5850
50.0000


29.2809
10.1237
50.0000
46
28.0359
2.1732
50.0000


29.8276
9.5634
50.0000
47
28.5140
1.7518
50.0000


30.3639
8.9920
50.0000
48
28.9848
1.3224
50.0000


30.8891
8.4110
50.0000
49
29.4485
0.8859
50.0000


31.4046
7.8212
50.0000
50
29.9050
0.4413
50.0000


31.9098
7.2227
50.0000
51
30.3551
−0.0096
50.0000


32.4046
6.6161
50.0000
52
30.7989
−0.4669
50.0000


32.8899
6.0008
50.0000
53
31.2354
−0.9306
50.0000


33.3655
5.3783
50.0000
54
31.6672
−1.3998
50.0000


33.8316
4.7494
50.0000
55
32.0918
−1.8739
50.0000


34.2881
4.1125
50.0000
56
32.5116
−2.3536
50.0000


34.7358
3.4701
50.0000
57
32.9250
−2.8380
50.0000


35.1740
2.8212
50.0000
58
33.3336
−3.3264
50.0000


35.6042
2.1668
50.0000
59
33.7374
−3.8196
50.0000


36.0255
1.5060
50.0000
60
34.1357
−4.3168
50.0000


36.4389
0.8412
50.0000
61
34.5291
−4.8180
50.0000


36.8444
0.1708
50.0000
62
34.9186
−5.3216
50.0000


37.2426
−0.5036
50.0000
63
35.3041
−5.8292
50.0000


37.6337
−1.1820
50.0000
64
35.6856
−6.3400
50.0000


38.0168
−1.8651
50.0000
65
36.0623
−6.8532
50.0000


38.3943
−2.5515
50.0000
66
36.4366
−7.3687
50.0000


38.7646
−3.2418
50.0000
67
36.8061
−7.8875
50.0000


39.1285
−3.9354
50.0000
68
37.1732
−8.4086
50.0000


39.4860
−4.6321
50.0000
69
37.5363
−8.9322
50.0000


39.8380
−5.3320
50.0000
70
37.8955
−9.4581
50.0000


40.1852
−6.0343
50.0000
71
38.2522
−9.9864
50.0000


40.5259
−6.7390
50.0000
72
38.6057
−10.5164
50.0000


40.8619
−7.4461
50.0000
73
38.9553
−11.0487
50.0000


41.1939
−8.1564
50.0000
74
39.3033
−11.5826
50.0000


41.5204
−8.8683
50.0000
75
39.6472
−12.1189
50.0000


41.8420
−9.5818
50.0000
76
39.9888
−12.6568
50.0000


42.1596
−10.2985
50.0000
77
40.3272
−13.1963
50.0000


42.4733
−11.0160
50.0000
78
40.6640
−13.7374
50.0000


42.7821
−11.7358
50.0000
79
40.9976
−14.2801
50.0000


43.0878
−12.4565
50.0000
80
41.3288
−14.8236
50.0000


43.3903
−13.1796
50.0000
81
41.6584
−15.3695
50.0000


43.6887
−13.9034
50.0000
82
41.9856
−15.9162
50.0000


43.9832
−14.6289
50.0000
83
42.3105
−16.4637
50.0000


44.2753
−15.3559
50.0000
84
42.6337
−17.0128
50.0000


44.5634
−16.0838
50.0000
85
42.9545
−17.5634
50.0000


44.6903
−16.4062
50.0000
86
43.0966
−17.8069
50.0000


44.7709
−16.6137
50.0000
87
43.1868
−17.9633
50.0000


44.8516
−16.8212
50.0000
88
43.2777
−18.1205
50.0000


44.9322
−17.0287
50.0000
89
43.3679
−18.2769
50.0000


45.0128
−17.2362
50.0000
90
43.4589
−18.4342
50.0000


45.0934
−17.4437
50.0000
91
43.5491
−18.5906
50.0000


45.1732
−17.6520
50.0000
92
43.6393
−18.7478
50.0000


45.2530
−17.8595
50.0000
93
43.7334
−18.9026
50.0000


45.3312
−18.0678
50.0000
94
43.8540
−19.0367
50.0000


45.3815
−18.2841
50.0000
95
43.9984
−19.1453
50.0000


45.3767
−18.5060
50.0000
96
44.1612
−19.2243
50.0000


45.3176
−18.7199
50.0000
97
44.3360
−19.2706
50.0000


45.2067
−18.9130
50.0000
98
44.5164
−19.2809
50.0000


45.0519
−19.0718
50.0000
99
44.6951
−19.2530
50.0000


44.8643
−19.1907
50.0000
100
44.8643
−19.1907
50.0000


2.0806
11.8069
60.0000
1
2.0806
11.8069
60.0000


1.8986
12.5315
60.0000
2
2.4358
11.3017
60.0000


1.9713
13.2777
60.0000
3
2.9234
10.9218
60.0000


2.2251
13.9848
60.0000
4
3.4860
10.6640
60.0000


2.5994
14.6369
60.0000
5
4.0846
10.5068
60.0000


3.0495
15.2394
60.0000
6
4.6999
10.4270
60.0000


3.5563
15.7941
60.0000
7
5.3192
10.4142
60.0000


4.1101
16.3033
60.0000
8
5.9377
10.4493
60.0000


4.6999
16.7702
60.0000
9
6.5547
10.5132
60.0000


5.3176
17.1995
60.0000
10
7.1716
10.5722
60.0000


5.9561
17.5970
60.0000
11
7.7901
10.6201
60.0000


6.6145
17.9601
60.0000
12
8.4094
10.6552
60.0000


7.2913
18.2897
60.0000
13
9.0287
10.6776
60.0000


7.9840
18.5826
60.0000
14
9.6488
10.6872
60.0000


8.6911
18.8388
60.0000
15
10.2690
10.6832
60.0000


9.4110
19.0559
60.0000
16
10.8883
10.6656
60.0000


10.1429
19.2322
60.0000
17
11.5076
10.6329
60.0000


10.8827
19.3679
60.0000
18
12.1261
10.5858
60.0000


11.6289
19.4613
60.0000
19
12.7422
10.5227
60.0000


12.3791
19.5124
60.0000
20
13.3575
10.4445
60.0000


13.1317
19.5211
60.0000
21
13.9705
10.3512
60.0000


13.8827
19.4884
60.0000
22
14.5810
10.2410
60.0000


14.6313
19.4150
60.0000
23
15.1875
10.1149
60.0000


15.3751
19.3025
60.0000
24
15.7909
9.9721
60.0000


16.1125
19.1540
60.0000
25
16.3903
9.8125
60.0000


16.8420
18.9713
60.0000
26
16.9840
9.6353
60.0000


17.5626
18.7550
60.0000
27
17.5730
9.4413
60.0000


18.2737
18.5076
60.0000
28
18.1564
9.2306
60.0000


18.9729
18.2314
60.0000
29
18.7326
9.0024
60.0000


19.6608
17.9266
60.0000
30
19.3025
8.7582
60.0000


20.3368
17.5962
60.0000
31
19.8651
8.4980
60.0000


21.0000
17.2418
60.0000
32
20.4214
8.2235
60.0000


21.6512
16.8651
60.0000
33
20.9697
7.9338
60.0000


22.2897
16.4677
60.0000
34
21.5100
7.6305
60.0000


22.9162
16.0511
60.0000
35
22.0431
7.3144
60.0000


23.5299
15.6161
60.0000
36
22.5682
6.9848
60.0000


24.1325
15.1652
60.0000
37
23.0854
6.6425
60.0000


24.7231
14.6991
60.0000
38
23.5946
6.2881
60.0000


25.3017
14.2187
60.0000
39
24.0950
5.9226
60.0000


25.8683
13.7247
60.0000
40
24.5874
5.5451
60.0000


26.4254
13.2179
60.0000
41
25.0718
5.1588
60.0000


26.9705
12.6999
60.0000
42
25.5483
4.7622
60.0000


27.5060
12.1716
60.0000
43
26.0176
4.3575
60.0000


28.0311
11.6329
60.0000
44
26.4796
3.9433
60.0000


28.5459
11.0838
60.0000
45
26.9346
3.5219
60.0000


29.0503
10.5259
60.0000
46
27.3823
3.0934
60.0000


29.5451
9.9601
60.0000
47
27.8236
2.6576
60.0000


30.0311
9.3855
60.0000
48
28.2586
2.2163
60.0000


30.5076
8.8029
60.0000
49
28.6872
1.7678
60.0000


30.9753
8.2139
60.0000
50
29.1101
1.3144
60.0000


31.4350
7.6185
60.0000
51
29.5267
0.8555
60.0000


31.8859
7.0160
60.0000
52
29.9385
0.3919
60.0000


32.3288
6.4078
60.0000
53
30.3456
−0.0758
60.0000


32.7638
5.7941
60.0000
54
30.7478
−0.5475
60.0000


33.1899
5.1748
60.0000
55
31.1445
−1.0239
60.0000


33.6089
4.5491
60.0000
56
31.5371
−1.5036
60.0000


34.0200
3.9194
60.0000
57
31.9250
−1.9872
60.0000


34.4238
3.2849
60.0000
58
32.3089
−2.4741
60.0000


34.8196
2.6449
60.0000
59
32.6887
−2.9641
60.0000


35.2091
2.0016
60.0000
60
33.0646
−3.4573
60.0000


35.5914
1.3536
60.0000
61
33.4374
−3.9529
60.0000


35.9673
0.7015
60.0000
62
33.8061
−4.4517
60.0000


36.3360
0.0463
60.0000
63
34.1716
−4.9521
60.0000


36.6991
−0.6129
60.0000
64
34.5347
−5.4549
60.0000


37.0567
−1.2745
60.0000
65
34.8939
−5.9601
60.0000


37.4078
−1.9401
60.0000
66
35.2506
−6.4669
60.0000


37.7534
−2.6081
60.0000
67
35.6049
−6.9761
60.0000


38.0934
−3.2793
60.0000
68
35.9569
−7.4868
60.0000


38.4294
−3.9521
60.0000
69
36.3057
−7.9992
60.0000


38.7598
−4.6281
60.0000
70
36.6520
−8.5140
60.0000


39.0854
−5.3065
60.0000
71
36.9960
−9.0295
60.0000


39.4070
−5.9864
60.0000
72
37.3376
−9.5467
60.0000


39.7239
−6.6688
60.0000
73
37.6768
−10.0662
60.0000


40.0367
−7.3528
60.0000
74
38.0136
−10.5866
60.0000


40.3456
−8.0391
60.0000
75
38.3488
−11.1077
60.0000


40.6504
−8.7263
60.0000
76
38.6816
−11.6313
60.0000


40.9521
−9.4158
60.0000
77
39.0120
−12.1556
60.0000


41.2498
−10.1069
60.0000
78
39.3416
−12.6808
60.0000


41.5435
−10.7989
60.0000
79
39.6688
−13.2075
60.0000


41.8340
−11.4932
60.0000
80
39.9936
−13.7350
60.0000


42.1221
−12.1883
60.0000
81
40.3176
−14.2642
60.0000


42.4062
−12.8843
60.0000
82
40.6401
−14.7941
60.0000


42.6879
−13.5826
60.0000
83
40.9609
−15.3248
60.0000


42.9665
−14.2809
60.0000
84
41.2801
−15.8555
60.0000


43.2426
−14.9808
60.0000
85
41.5978
−16.3879
60.0000


43.3631
−15.2905
60.0000
86
41.7382
−16.6241
60.0000


43.4413
−15.4900
60.0000
87
41.8284
−16.7749
60.0000


43.5188
−15.6895
60.0000
88
41.9178
−16.9266
60.0000


43.5954
−15.8883
60.0000
89
42.0080
−17.0782
60.0000


43.6728
−16.0878
60.0000
90
42.0974
−17.2298
60.0000


43.7494
−16.2873
60.0000
91
42.1875
−17.3815
60.0000


43.8260
−16.4876
60.0000
92
42.2769
−17.5339
60.0000


43.9026
−16.6872
60.0000
93
42.3727
−17.6816
60.0000


43.9737
−16.8883
60.0000
94
42.4948
−17.8077
60.0000


44.0128
−17.0982
60.0000
95
42.6385
−17.9098
60.0000


43.9984
−17.3113
60.0000
96
42.7981
−17.9840
60.0000


43.9330
−17.5140
60.0000
97
42.9681
−18.0271
60.0000


43.8204
−17.6951
60.0000
98
43.1437
−18.0367
60.0000


43.6672
−17.8436
60.0000
99
43.3184
−18.0112
60.0000


43.4844
−17.9537
60.0000
100
43.4844
−17.9537
60.0000


2.9641
15.6528
70.0000
1
2.9641
15.6528
70.0000


2.8771
16.3551
70.0000
2
3.2354
15.1261
70.0000


3.0239
17.0487
70.0000
3
3.6457
14.6983
70.0000


3.3384
17.6856
70.0000
4
4.1429
14.3743
70.0000


3.7614
18.2578
70.0000
5
4.6887
14.1429
70.0000


4.2546
18.7702
70.0000
6
5.2618
13.9840
70.0000


4.7989
19.2275
70.0000
7
5.8484
13.8891
70.0000


5.3807
19.6377
70.0000
8
6.4405
13.8460
70.0000


5.9912
20.0032
70.0000
9
7.0351
13.8348
70.0000


6.6249
20.3264
70.0000
10
7.6289
13.8204
70.0000


7.2769
20.6121
70.0000
11
8.2227
13.7941
70.0000


7.9433
20.8619
70.0000
12
8.8156
13.7542
70.0000


8.6225
21.0750
70.0000
13
9.4078
13.7015
70.0000


9.3121
21.2514
70.0000
14
9.9984
13.6345
70.0000


10.0104
21.3887
70.0000
15
10.5866
13.5523
70.0000


10.7151
21.4876
70.0000
16
11.1732
13.4557
70.0000


11.4238
21.5475
70.0000
17
11.7574
13.3440
70.0000


12.1349
21.5682
70.0000
18
12.3376
13.2171
70.0000


12.8468
21.5515
70.0000
19
12.9146
13.0750
70.0000


13.5563
21.4964
70.0000
20
13.4876
12.9178
70.0000


14.2618
21.4046
70.0000
21
14.0567
12.7446
70.0000


14.9617
21.2769
70.0000
22
14.6201
12.5563
70.0000


15.6552
21.1157
70.0000
23
15.1788
12.3536
70.0000


16.3400
20.9226
70.0000
24
15.7318
12.1349
70.0000


17.0160
20.6991
70.0000
25
16.2785
11.9026
70.0000


17.6808
20.4461
70.0000
26
16.8196
11.6568
70.0000


18.3352
20.1660
70.0000
27
17.3536
11.3958
70.0000


18.9785
19.8603
70.0000
28
17.8811
11.1221
70.0000


19.6089
19.5315
70.0000
29
18.4014
10.8356
70.0000


20.2283
19.1796
70.0000
30
18.9154
10.5363
70.0000


20.8348
18.8077
70.0000
31
19.4214
10.2251
70.0000


21.4294
18.4174
70.0000
32
19.9202
9.9018
70.0000


22.0120
18.0088
70.0000
33
20.4126
9.5682
70.0000


22.5834
17.5834
70.0000
34
20.8970
9.2243
70.0000


23.1421
17.1437
70.0000
35
21.3751
8.8707
70.0000


23.6895
16.6887
70.0000
36
21.8452
8.5076
70.0000


24.2259
16.2211
70.0000
37
22.3089
8.1357
70.0000


24.7510
15.7406
70.0000
38
22.7662
7.7558
70.0000


25.2650
15.2482
70.0000
39
23.2155
7.3671
70.0000


25.7686
14.7446
70.0000
40
23.6592
6.9721
70.0000


26.2610
14.2306
70.0000
41
24.0966
6.5690
70.0000


26.7438
13.7079
70.0000
42
24.5283
6.1604
70.0000


27.2163
13.1756
70.0000
43
24.9537
5.7454
70.0000


27.6800
12.6361
70.0000
44
25.3735
5.3248
70.0000


28.1341
12.0878
70.0000
45
25.7877
4.8986
70.0000


28.5802
11.5331
70.0000
46
26.1963
4.4677
70.0000


29.0168
10.9713
70.0000
47
26.6002
4.0311
70.0000


29.4461
10.4030
70.0000
48
27.0000
3.5914
70.0000


29.8667
9.8292
70.0000
49
27.3943
3.1468
70.0000


30.2801
9.2498
70.0000
50
27.7845
2.6983
70.0000


30.6864
8.6656
70.0000
51
28.1708
2.2466
70.0000


31.0862
8.0766
70.0000
52
28.5531
1.7917
70.0000


31.4789
7.4828
70.0000
53
28.9322
1.3336
70.0000


31.8643
6.8851
70.0000
54
29.3073
0.8723
70.0000


32.2442
6.2833
70.0000
55
29.6784
0.4086
70.0000


32.6177
5.6768
70.0000
56
30.0471
−0.0575
70.0000


32.9848
5.0670
70.0000
57
30.4118
−0.5267
70.0000


33.3456
4.4541
70.0000
58
30.7741
−0.9976
70.0000


33.7015
3.8372
70.0000
59
31.1333
−1.4717
70.0000


34.0511
3.2179
70.0000
60
31.4900
−1.9473
70.0000


34.3951
2.5946
70.0000
61
31.8436
−2.4246
70.0000


34.7342
1.9689
70.0000
62
32.1947
−2.9042
70.0000


35.0686
1.3408
70.0000
63
32.5443
−3.3847
70.0000


35.3982
0.7095
70.0000
64
32.8907
−3.8675
70.0000


35.7223
0.0758
70.0000
65
33.2354
−4.3520
70.0000


36.0423
−0.5595
70.0000
66
33.5786
−4.8372
70.0000


36.3583
−1.1971
70.0000
67
33.9194
−5.3240
70.0000


36.6696
−1.8372
70.0000
68
34.2586
−5.8125
70.0000


36.9777
−2.4789
70.0000
69
34.5954
−6.3017
70.0000


37.2817
−3.1229
70.0000
70
34.9314
−6.7925
70.0000


37.5818
−3.7678
70.0000
71
35.2650
−7.2841
70.0000


37.8795
−4.4142
70.0000
72
35.5970
−7.7773
70.0000


38.1732
−5.0630
70.0000
73
35.9274
−8.2713
70.0000


38.4629
−5.7127
70.0000
74
36.2562
−8.7662
70.0000


38.7502
−6.3639
70.0000
75
36.5834
−9.2626
70.0000


39.0343
−7.0168
70.0000
76
36.9090
−9.7598
70.0000


39.3152
−7.6704
70.0000
77
37.2330
−10.2578
70.0000


39.5938
−8.3256
70.0000
78
37.5563
−10.7566
70.0000


39.8691
−8.9816
70.0000
79
37.8779
−11.2562
70.0000


40.1421
−9.6393
70.0000
80
38.1987
−11.7566
70.0000


40.4118
−10.2977
70.0000
81
38.5180
−12.2578
70.0000


40.6792
−10.9569
70.0000
82
38.8364
−12.7598
70.0000


40.9449
−11.6177
70.0000
83
39.1532
−13.2626
70.0000


41.2075
−12.2793
70.0000
84
39.4693
−13.7662
70.0000


41.4685
−12.9409
70.0000
85
39.7845
−14.2698
70.0000


41.5834
−13.2346
70.0000
86
39.7845
−14.2698
70.0000


41.6568
−13.4230
70.0000
87
39.8835
−14.4294
70.0000


41.7302
−13.6113
70.0000
88
39.9832
−14.5882
70.0000


41.8029
−13.7997
70.0000
89
40.0822
−14.7478
70.0000


41.8755
−13.9888
70.0000
90
40.1812
−14.9074
70.0000


41.9489
−14.1772
70.0000
91
40.2801
−15.0662
70.0000


42.0215
−14.3663
70.0000
92
40.3791
−15.2259
70.0000


42.0934
−14.5547
70.0000
93
40.4781
−15.3855
70.0000


42.1516
−14.7486
70.0000
94
40.5962
−15.5315
70.0000


42.1692
−14.9497
70.0000
95
40.7406
−15.6504
70.0000


42.1453
−15.1500
70.0000
96
40.9058
−15.7398
70.0000


42.0758
−15.3400
70.0000
97
41.0846
−15.7957
70.0000


41.9625
−15.5060
70.0000
98
41.2706
−15.8148
70.0000


41.8125
−15.6417
70.0000
99
41.4573
−15.7957
70.0000


41.6361
−15.7398
70.0000
100
41.6361
−15.7398
70.0000


4.0112
20.1133
80.0000
1
4.0112
20.1133
80.0000


4.0287
20.7773
80.0000
2
4.1852
19.5794
80.0000


4.2506
21.4054
80.0000
3
4.4972
19.1109
80.0000


4.6177
21.9617
80.0000
4
4.9042
18.7223
80.0000


5.0798
22.4429
80.0000
5
5.3743
18.4118
80.0000


5.6049
22.8547
80.0000
6
5.8843
18.1724
80.0000


6.1708
23.2091
80.0000
7
6.4182
17.9904
80.0000


6.7662
23.5100
80.0000
8
6.9641
17.8492
80.0000


7.3839
23.7638
80.0000
9
7.5148
17.7287
80.0000


8.0176
23.9737
80.0000
10
8.0654
17.6073
80.0000


8.6640
24.1429
80.0000
11
8.6129
17.4717
80.0000


9.3192
24.2721
80.0000
12
9.1572
17.3232
80.0000


9.9800
24.3623
80.0000
13
9.6975
17.1612
80.0000


10.6457
24.4158
80.0000
14
10.2338
16.9864
80.0000


11.3136
24.4310
80.0000
15
10.7654
16.7981
80.0000


11.9808
24.4086
80.0000
16
11.2921
16.5970
80.0000


12.6457
24.3512
80.0000
17
11.8140
16.3831
80.0000


13.3073
24.2594
80.0000
18
12.3304
16.1564
80.0000


13.9633
24.1349
80.0000
19
12.8412
15.9170
80.0000


14.6121
23.9777
80.0000
20
13.3456
15.6656
80.0000


15.2530
23.7901
80.0000
21
13.8452
15.4030
80.0000


15.8851
23.5738
80.0000
22
14.3376
15.1293
80.0000


16.5068
23.3320
80.0000
23
14.8252
14.8444
80.0000


17.1189
23.0638
80.0000
24
15.3057
14.5499
80.0000


17.7199
22.7725
80.0000
25
15.7805
14.2450
80.0000


18.3089
22.4589
80.0000
26
16.2490
13.9306
80.0000


18.8867
22.1245
80.0000
27
16.7111
13.6081
80.0000


19.4533
21.7702
80.0000
28
17.1676
13.2761
80.0000


20.0080
21.3982
80.0000
29
17.6177
12.9370
80.0000


20.5507
21.0104
80.0000
30
18.0623
12.5898
80.0000


21.0822
20.6057
80.0000
31
18.5004
12.2346
80.0000


21.6018
20.1860
80.0000
32
18.9338
11.8739
80.0000


22.1093
19.7518
80.0000
33
19.3615
11.5060
80.0000


22.6057
19.3057
80.0000
34
19.7837
11.1325
80.0000


23.0910
18.8468
80.0000
35
20.2011
10.7526
80.0000


23.5650
18.3767
80.0000
36
20.6129
10.3679
80.0000


24.0287
17.8962
80.0000
37
21.0208
9.9785
80.0000


24.4820
17.4054
80.0000
38
21.4238
9.5842
80.0000


24.9258
16.9066
80.0000
39
21.8228
9.1852
80.0000


25.3607
16.3998
80.0000
40
22.2179
8.7821
80.0000


25.7853
15.8851
80.0000
41
22.6089
8.3759
80.0000


26.2019
15.3631
80.0000
42
22.9960
7.9657
80.0000


26.6105
14.8340
80.0000
43
23.3791
7.5523
80.0000


27.0104
14.2993
80.0000
44
23.7590
7.1357
80.0000


27.4022
13.7590
80.0000
45
24.1357
6.7159
80.0000


27.7869
13.2131
80.0000
46
24.5092
6.2929
80.0000


28.1636
12.6616
80.0000
47
24.8795
5.8675
80.0000


28.5339
12.1061
80.0000
48
25.2466
5.4389
80.0000


28.8970
11.5459
80.0000
49
25.6105
5.0088
80.0000


29.2546
10.9816
80.0000
50
25.9729
4.5762
80.0000


29.6065
10.4142
80.0000
51
26.3320
4.1413
80.0000


29.9529
9.8436
80.0000
52
26.6887
3.7047
80.0000


30.2937
9.2690
80.0000
53
27.0431
3.2658
80.0000


30.6297
8.6919
80.0000
54
27.3958
2.8260
80.0000


30.9609
8.1117
80.0000
55
27.7462
2.3839
80.0000


31.2873
7.5291
80.0000
56
28.0950
1.9401
80.0000


31.6089
6.9441
80.0000
57
28.4413
1.4956
80.0000


31.9258
6.3567
80.0000
58
28.7861
1.0487
80.0000


32.2386
5.7662
80.0000
59
29.1285
0.6010
80.0000


32.5475
5.1740
80.0000
60
29.4693
0.1516
80.0000


32.8516
4.5802
80.0000
61
29.8093
−0.2985
80.0000


33.1524
3.9840
80.0000
62
30.1468
−0.7502
80.0000


33.4493
3.3855
80.0000
63
30.4828
−1.2027
80.0000


33.7430
2.7861
80.0000
64
30.8180
−1.6568
80.0000


34.0335
2.1844
80.0000
65
31.1516
−2.1117
80.0000


34.3200
1.5810
80.0000
66
31.4836
−2.5674
80.0000


34.6042
0.9769
80.0000
67
31.8148
−3.0239
80.0000


34.8851
0.3711
80.0000
68
32.1453
−3.4812
80.0000


35.1628
−0.2362
80.0000
69
32.4733
−3.9393
80.0000


35.4381
−0.8444
80.0000
70
32.8013
−4.3990
80.0000


35.7119
−1.4533
80.0000
71
33.1269
−4.8587
80.0000


35.9824
−2.0638
80.0000
72
33.4525
−5.3192
80.0000


36.2506
−2.6752
80.0000
73
33.7765
−5.7813
80.0000


36.5164
−3.2881
80.0000
74
34.0998
−6.2434
80.0000


36.7805
−3.9018
80.0000
75
34.4214
−6.7063
80.0000


37.0415
−4.5164
80.0000
76
34.7430
−7.1700
80.0000


37.3009
−5.1317
80.0000
77
35.0630
−7.6345
80.0000


37.5579
−5.7478
80.0000
78
35.3823
−8.0990
80.0000


37.8132
−6.3647
80.0000
79
35.7007
−8.5650
80.0000


38.0662
−6.9824
80.0000
80
36.0184
−9.0311
80.0000


38.3176
−7.6018
80.0000
81
36.3352
−9.4972
80.0000


38.5666
−8.2211
80.0000
82
36.6504
−9.9649
80.0000


38.8148
−8.8412
80.0000
83
36.9657
−10.4326
80.0000


39.0607
−9.4621
80.0000
84
37.2801
−10.9002
80.0000


39.3049
−10.0830
80.0000
85
37.5946
−11.3695
80.0000


39.4126
−10.3583
80.0000
86
37.7326
−11.5762
80.0000


39.4812
−10.5355
80.0000
87
37.8220
−11.7095
80.0000


39.5499
−10.7119
80.0000
88
37.9106
−11.8436
80.0000


39.6185
−10.8891
80.0000
89
37.9992
−11.9769
80.0000


39.6872
−11.0662
80.0000
90
38.0886
−12.1101
80.0000


39.7558
−11.2434
80.0000
91
38.1772
−12.2434
80.0000


39.8260
−11.4190
80.0000
92
38.2666
−12.3767
80.0000


39.8931
−11.5970
80.0000
93
38.3703
−12.4980
80.0000


39.9362
−11.7813
80.0000
94
38.4940
−12.6002
80.0000


39.9401
−11.9705
80.0000
95
38.6321
−12.6808
80.0000


39.9034
−12.1564
80.0000
96
38.7821
−12.7382
80.0000


39.8292
−12.3304
80.0000
97
38.9385
−12.7702
80.0000


39.7175
−12.4844
80.0000
98
39.0990
−12.7741
80.0000


39.5746
−12.6081
80.0000
99
39.2570
−12.7502
80.0000


39.4094
−12.6999
80.0000
100
39.4094
−12.6999
80.0000


5.2658
25.1612
90.0000
1
5.2658
25.1612
90.0000


5.3615
25.7773
90.0000
2
5.3456
24.6265
90.0000


5.6425
26.3352
90.0000
3
5.5634
24.1325
90.0000


6.0495
26.8101
90.0000
4
5.8931
23.7031
90.0000


6.5371
27.2011
90.0000
5
6.2977
23.3432
90.0000


7.0782
27.5164
90.0000
6
6.7494
23.0447
90.0000


7.6536
27.7630
90.0000
7
7.2219
22.7789
90.0000


8.2522
27.9473
90.0000
8
7.6975
22.5188
90.0000


8.8651
28.0742
90.0000
9
8.1668
22.2474
90.0000


9.4876
28.1445
90.0000
10
8.6273
21.9617
90.0000


10.1141
28.1612
90.0000
11
9.0806
21.6656
90.0000


10.7390
28.1269
90.0000
12
9.5283
21.3599
90.0000


11.3599
28.0455
90.0000
13
9.9697
21.0447
90.0000


11.9737
27.9202
90.0000
14
10.4046
20.7223
90.0000


12.5778
27.7550
90.0000
15
10.8348
20.3919
90.0000


13.1716
27.5547
90.0000
16
11.2586
20.0543
90.0000


13.7534
27.3232
90.0000
17
11.6784
19.7111
90.0000


14.3232
27.0638
90.0000
18
12.0926
19.3623
90.0000


14.8811
26.7781
90.0000
19
12.5028
19.0080
90.0000


15.4270
26.4701
90.0000
20
12.9090
18.6480
90.0000


15.9609
26.1429
90.0000
21
13.3105
18.2841
90.0000


16.4836
25.7981
90.0000
22
13.7079
17.9154
90.0000


16.9968
25.4381
90.0000
23
14.1014
17.5435
90.0000


17.4988
25.0638
90.0000
24
14.4916
17.1668
90.0000


17.9912
24.6768
90.0000
25
14.8779
16.7869
90.0000


18.4757
24.2785
90.0000
26
15.2618
16.4046
90.0000


18.9505
23.8707
90.0000
27
15.6425
16.0184
90.0000


19.4166
23.4517
90.0000
28
16.0208
15.6305
90.0000


19.8739
23.0239
90.0000
29
16.3966
15.2394
90.0000


20.3240
22.5874
90.0000
30
16.7694
14.8460
90.0000


20.7654
22.1437
90.0000
31
17.1397
14.4509
90.0000


21.2003
21.6927
90.0000
32
17.5084
14.0535
90.0000


21.6273
21.2346
90.0000
33
17.8747
13.6536
90.0000


22.0487
20.7702
90.0000
34
18.2386
13.2522
90.0000


22.4621
20.3001
90.0000
35
18.6010
12.8492
90.0000


22.8691
19.8236
90.0000
36
18.9609
12.4445
90.0000


23.2690
19.3416
90.0000
37
19.3200
12.0383
90.0000


23.6624
18.8540
90.0000
38
19.6776
11.6305
90.0000


24.0487
18.3607
90.0000
39
20.0327
11.2211
90.0000


24.4286
17.8627
90.0000
40
20.3871
10.8117
90.0000


24.8021
17.3599
90.0000
41
20.7406
10.4006
90.0000


25.1692
16.8524
90.0000
42
21.0926
9.9888
90.0000


25.5299
16.3400
90.0000
43
21.4437
9.5754
90.0000


25.8851
15.8244
90.0000
44
21.7941
9.1620
90.0000


26.2346
15.3041
90.0000
45
22.1429
8.7470
90.0000


26.5778
14.7805
90.0000
46
22.4908
8.3312
90.0000


26.9162
14.2530
90.0000
47
22.8372
7.9146
90.0000


27.2498
13.7223
90.0000
48
23.1828
7.4972
90.0000


27.5778
13.1891
90.0000
49
23.5275
7.0790
90.0000


27.9018
12.6528
90.0000
50
23.8715
6.6592
90.0000


28.2211
12.1133
90.0000
51
24.2139
6.2394
90.0000


28.5355
11.5714
90.0000
52
24.5555
5.8188
90.0000


28.8460
11.0271
90.0000
53
24.8962
5.3974
90.0000


29.1516
10.4812
90.0000
54
25.2362
4.9753
90.0000


29.4541
9.9322
90.0000
55
25.5746
4.5523
90.0000


29.7518
9.3807
90.0000
56
25.9130
4.1285
90.0000


30.0455
8.8276
90.0000
57
26.2498
3.7039
90.0000


30.3360
8.2729
90.0000
58
26.5858
3.2785
90.0000


30.6225
7.7159
90.0000
59
26.9218
2.8532
90.0000


30.9058
7.1564
90.0000
60
27.2562
2.4270
90.0000


31.1852
6.5962
90.0000
61
27.5898
2.0000
90.0000


31.4621
6.0343
90.0000
62
27.9226
1.5722
90.0000


31.7350
5.4701
90.0000
63
28.2554
1.1437
90.0000


32.0048
4.9050
90.0000
64
28.5866
0.7151
90.0000


32.2721
4.3384
90.0000
65
28.9170
0.2849
90.0000


32.5371
3.7702
90.0000
66
29.2466
−0.1453
90.0000


32.7981
3.2011
90.0000
67
29.5754
−0.5762
90.0000


33.0575
2.6305
90.0000
68
29.9034
−1.0072
90.0000


33.3144
2.0591
90.0000
69
30.2306
−1.4397
90.0000


33.5690
1.4868
90.0000
70
30.5563
−1.8723
90.0000


33.8212
0.9138
90.0000
71
30.8819
−2.3057
90.0000


34.0710
0.3392
90.0000
72
31.2067
−2.7398
90.0000


34.3192
−0.2362
90.0000
73
31.5315
−3.1740
90.0000


34.5650
−0.8125
90.0000
74
31.8547
−3.6089
90.0000


34.8085
−1.3895
90.0000
75
32.1780
−4.0439
90.0000


35.0503
−1.9673
90.0000
76
32.4996
−4.4796
90.0000


35.2905
−2.5459
90.0000
77
32.8212
−4.9162
90.0000


35.5283
−3.1253
90.0000
78
33.1429
−5.3528
90.0000


35.7646
−3.7063
90.0000
79
33.4629
−5.7901
90.0000


35.9984
−4.2873
90.0000
80
33.7829
−6.2275
90.0000


36.2306
−4.8691
90.0000
81
34.1022
−6.6648
90.0000


36.4613
−5.4509
90.0000
82
34.4214
−7.1030
90.0000


36.6911
−6.0343
90.0000
83
34.7406
−7.5419
90.0000


36.9186
−6.6177
90.0000
84
35.0583
−7.9808
90.0000


37.1445
−7.2019
90.0000
85
35.3759
−8.4198
90.0000


37.2442
−7.4605
90.0000
86
35.5164
−8.6137
90.0000


37.3081
−7.6265
90.0000
87
35.6065
−8.7382
90.0000


37.3719
−7.7933
90.0000
88
35.6967
−8.8635
90.0000


37.4350
−7.9593
90.0000
89
35.7869
−8.9880
90.0000


37.4988
−8.1261
90.0000
90
35.8771
−9.1133
90.0000


37.5619
−8.2921
90.0000
91
35.9673
−9.2378
90.0000


37.6249
−8.4589
90.0000
92
36.0583
−9.3623
90.0000


37.6808
−8.6273
90.0000
93
36.1636
−9.4749
90.0000


37.7087
−8.8029
90.0000
94
36.2857
−9.5682
90.0000


37.6983
−8.9800
90.0000
95
36.4214
−9.6417
90.0000


37.6528
−9.1524
90.0000
96
36.5666
−9.6919
90.0000


37.5738
−9.3113
90.0000
97
36.7183
−9.7183
90.0000


37.4637
−9.4509
90.0000
98
36.8723
−9.7199
90.0000


37.3272
−9.5642
90.0000
99
37.0239
−9.6959
90.0000


37.1700
−9.6480
90.0000
100
37.1700
−9.6480
90.0000


6.3121
30.9753
100.0000
1
6.3121
30.9753
100.0000


6.4693
31.6042
100.0000
2
6.2961
30.4445
100.0000


6.7646
32.1820
100.0000
3
6.3791
29.9202
100.0000


7.1692
32.6895
100.0000
4
6.5531
29.4182
100.0000


7.6544
33.1213
100.0000
5
6.8021
28.9497
100.0000


8.1971
33.4781
100.0000
6
7.1141
28.5196
100.0000


8.7797
33.7646
100.0000
7
7.4757
28.1301
100.0000


9.3903
33.9888
100.0000
8
7.8651
27.7686
100.0000


10.0184
34.1540
100.0000
9
8.2650
27.4190
100.0000


10.6592
34.2642
100.0000
10
8.6624
27.0654
100.0000


11.3049
34.3344
100.0000
11
9.0583
26.7103
100.0000


11.9529
34.3903
100.0000
12
9.4525
26.3536
100.0000


12.6010
34.4350
100.0000
13
9.8460
25.9960
100.0000


13.2506
34.4637
100.0000
14
10.2378
25.6377
100.0000


13.9010
34.4733
100.0000
15
10.6289
25.2769
100.0000


14.5507
34.4589
100.0000
16
11.0184
24.9154
100.0000


15.1987
34.4158
100.0000
17
11.4062
24.5523
100.0000


15.8444
34.3392
100.0000
18
11.7933
24.1875
100.0000


16.4844
34.2259
100.0000
19
12.1780
23.8212
100.0000


17.1157
34.0710
100.0000
20
12.5611
23.4525
100.0000


17.7342
33.8707
100.0000
21
12.9417
23.0822
100.0000


18.3344
33.6225
100.0000
22
13.3208
22.7095
100.0000


18.9130
33.3256
100.0000
23
13.6983
22.3344
100.0000


19.4661
32.9848
100.0000
24
14.0726
21.9569
100.0000


19.9936
32.6049
100.0000
25
14.4445
21.5778
100.0000


20.4948
32.1907
100.0000
26
14.8140
21.1955
100.0000


20.9681
31.7462
100.0000
27
15.1812
20.8109
100.0000


21.4174
31.2761
100.0000
28
15.5451
20.4238
100.0000


21.8436
30.7861
100.0000
29
15.9066
20.0335
100.0000


22.2498
30.2785
100.0000
30
16.2650
19.6409
100.0000


22.6385
29.7574
100.0000
31
16.6209
19.2458
100.0000


23.0112
29.2251
100.0000
32
16.9729
18.8484
100.0000


23.3711
28.6832
100.0000
33
17.3232
18.4477
100.0000


23.7191
28.1341
100.0000
34
17.6696
18.0447
100.0000


24.0551
27.5778
100.0000
35
18.0128
17.6393
100.0000


24.3799
27.0144
100.0000
36
18.3536
17.2306
100.0000


24.6943
26.4461
100.0000
37
18.6911
16.8204
100.0000


25.0000
25.8723
100.0000
38
19.0247
16.4070
100.0000


25.2969
25.2937
100.0000
39
19.3559
15.9912
100.0000


25.5858
24.7111
100.0000
40
19.6840
15.5730
100.0000


25.8675
24.1261
100.0000
41
20.0096
15.1524
100.0000


26.1437
23.5371
100.0000
42
20.3320
14.7302
100.0000


26.4134
22.9457
100.0000
43
20.6520
14.3057
100.0000


26.6776
22.3520
100.0000
44
20.9697
13.8787
100.0000


26.9362
21.7558
100.0000
45
21.2849
13.4509
100.0000


27.1891
21.1564
100.0000
46
21.5970
13.0208
100.0000


27.4381
20.5563
100.0000
47
21.9074
12.5898
100.0000


27.6816
19.9537
100.0000
48
22.2155
12.1564
100.0000


27.9202
19.3488
100.0000
49
22.5219
11.7215
100.0000


28.1556
18.7430
100.0000
50
22.8260
11.2857
100.0000


28.3871
18.1357
100.0000
51
23.1285
10.8484
100.0000


28.6145
17.5267
100.0000
52
23.4286
10.4102
100.0000


28.8388
16.9162
100.0000
53
23.7279
9.9705
100.0000


29.0599
16.3049
100.0000
54
24.0247
9.5299
100.0000


29.2777
15.6927
100.0000
55
24.3200
9.0878
100.0000


29.4924
15.0790
100.0000
56
24.6145
8.6449
100.0000


29.7039
14.4645
100.0000
57
24.9074
8.2019
100.0000


29.9130
13.8492
100.0000
58
25.1995
7.7574
100.0000


30.1189
13.2322
100.0000
59
25.4900
7.3121
100.0000


30.3224
12.6145
100.0000
60
25.7797
6.8667
100.0000


30.5227
11.9968
100.0000
61
26.0686
6.4206
100.0000


30.7207
11.3775
100.0000
62
26.3575
5.9737
100.0000


30.9162
10.7574
100.0000
63
26.6449
5.5267
100.0000


31.1093
10.1365
100.0000
64
26.9314
5.0790
100.0000


31.3001
9.5148
100.0000
65
27.2171
4.6313
100.0000


31.4884
8.8931
100.0000
66
27.5028
4.1828
100.0000


31.6744
8.2706
100.0000
67
27.7869
3.7334
100.0000


31.8587
7.6464
100.0000
68
28.0710
3.2841
100.0000


32.0415
7.0231
100.0000
69
28.3543
2.8340
100.0000


32.2211
6.3982
100.0000
70
28.6369
2.3839
100.0000


32.3998
5.7733
100.0000
71
28.9186
1.9330
100.0000


32.5762
5.1476
100.0000
72
29.2003
1.4820
100.0000


32.7510
4.5211
100.0000
73
29.4812
1.0311
100.0000


32.9226
3.8947
100.0000
74
29.7614
0.5794
100.0000


33.0918
3.2666
100.0000
75
30.0415
0.1277
100.0000


33.2586
2.6385
100.0000
76
30.3208
−0.3248
100.0000


33.4238
2.0096
100.0000
77
30.6002
−0.7765
100.0000


33.5858
1.3807
100.0000
78
30.8795
−1.2291
100.0000


33.7462
0.7502
100.0000
79
31.1588
−1.6816
100.0000


33.9042
0.1197
100.0000
80
31.4374
−2.1341
100.0000


34.0607
−0.5108
100.0000
81
31.7151
−2.5874
100.0000


34.2147
−1.1429
100.0000
82
31.9928
−3.0407
100.0000


34.3671
−1.7749
100.0000
83
32.2698
−3.4940
100.0000


34.5172
−2.4070
100.0000
84
32.5467
−3.9481
100.0000


34.6656
−3.0399
100.0000
85
32.8228
−4.4022
100.0000


34.7302
−3.3200
100.0000
86
32.9441
−4.6034
100.0000


34.7717
−3.4996
100.0000
87
33.0223
−4.7326
100.0000


34.8132
−3.6800
100.0000
88
33.1006
−4.8619
100.0000


34.8547
−3.8603
100.0000
89
33.1788
−4.9912
100.0000


34.8955
−4.0399
100.0000
90
33.2570
−5.1205
100.0000


34.9362
−4.2203
100.0000
91
33.3352
−5.2498
100.0000


34.9777
−4.4006
100.0000
92
33.4166
−5.3767
100.0000


35.0200
−4.5802
100.0000
93
33.5180
−5.4884
100.0000


35.0479
−4.7630
100.0000
94
33.6369
−5.5818
100.0000


35.0399
−4.9473
100.0000
95
33.7694
−5.6544
100.0000


34.9936
−5.1261
100.0000
96
33.9114
−5.7031
100.0000


34.9138
−5.2921
100.0000
97
34.0607
−5.7279
100.0000


34.8029
−5.4389
100.0000
98
34.2115
−5.7263
100.0000


34.6632
−5.5603
100.0000
99
34.3599
−5.6999
100.0000


34.5028
−5.6504
100.0000
100
34.5028
−5.6504
100.0000









It will also be appreciated that the airfoil 52 disclosed in the above Table I may be scaled up or down geometrically for use in other similar turbine designs. Consequently, the coordinate values set forth in Table I may be scaled upwardly or downwardly such that the airfoil profile shape remains unchanged. A scaled version of the coordinates in Table I would be represented by X, Y and Z coordinate values of Table I, with the X, Y and Z non-dimensional coordinate values converted to inches, multiplied or divided by a constant number.


An important term in this disclosure is “profile”. The profile is the range of the variation between measured points on an airfoil surface and the ideal position listed in Table I. The actual profile on a manufactured turbine rotor blade will be different than those in Table I and the design is robust to this variation meaning that mechanical and aerodynamic function are not impaired. As noted above, a + or − 5% profile tolerance is used herein. The X, Y and Z values are all non-dimensionalized relative to the airfoil height.


The disclosed airfoil shape optimizes and is specific to the machine conditions and specifications. It provides a unique profile to achieve 1) interaction between other stages in the turbine 10; 2) aerodynamic efficiency; and 3) normalized aerodynamic and mechanical blade loadings. The disclosed loci of points defined in Table I allow the gas turbine 12 or any other suitable turbine to run in an efficient, safe and smooth manner. As also noted, any scale of the disclosed airfoil 52 may be adopted as long as 1) interaction between other stages in the pressure turbine 10; 2) aerodynamic efficiency; and 3) normalized aerodynamic and mechanical blade loadings are maintained in the scaled turbine.


This written description uses examples to disclose the invention, including the best mode, and also to enable any person skilled in the art to practice the invention, including making and using any devices or systems and performing any incorporated methods. The patentable scope of the invention is defined by the claims, and may include other examples that occur to those skilled in the art. Such other examples are intended to be within the scope of the claims if they have structural elements that do not differ from the literal language of the claims, or if they include equivalent structural elements with insubstantial differences from the literal languages of the claims.

Claims
  • 1. A turbine rotor blade including an airfoil having an airfoil shape, the airfoil having a nominal profile substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in Table I, wherein the Cartesian coordinate values of X, Y and Z are non-dimensional values from 0% to 100% convertible to dimensional distances in inches by multiplying the Cartesian coordinate values of X, Y and Z by a height of the airfoil in inches, and wherein X and Y are distances in inches which, when connected by smooth continuing arcs, define airfoil profile sections at each distance Z, the airfoil profile sections at Z distances being joined smoothly with one another to form a complete airfoil shape.
  • 2. The turbine rotor blade as in claim 1, forming part of a stage of a turbine.
  • 3. The turbine rotor blade as in claim 1, wherein the turbine rotor blade forms a part of a second stage of turbine rotor blades of a turbine of a gas turbine.
  • 4. The turbine rotor blade as in claim 1, wherein the airfoil shape lies in an envelope within +/− 5% in a direction normal to any airfoil surface location.
  • 5. The turbine rotor blade as in claim 1, wherein a height of the turbine rotor blade is 10 inches to 40 inches.
  • 6. A turbine rotor blade including an airfoil having a suction-side uncoated nominal airfoil profile substantially in accordance with suction-side Cartesian coordinate values of X, Y and Z set forth in Table I, wherein the Cartesian coordinate values of X, Y and Z are non-dimensional values from 0% to 100% convertible to dimensional distances in inches by multiplying the Cartesian coordinate values of X, Y and Z by a height of the airfoil in inches, and wherein X and Y are distances in inches which, when connected by smooth continuing arcs, define airfoil profile sections at each Z distance, the airfoil profile sections at the Z distances being joined smoothly with one another to form a complete suction-side airfoil shape, the X, Y and Z distances being scalable as a function of the same constant or number to provide a scaled-up or scaled-down airfoil.
  • 7. The turbine rotor blade as in claim 6, forming part of a stage of a turbine.
  • 8. The turbine rotor blade as in claim 6, wherein the turbine rotor blade forms a part of a second stage of turbine rotor blades of a turbine of a gas turbine.
  • 9. The turbine rotor blade as in claim 6, wherein the suction-side airfoil shape lies in an envelope within +/− 5% in a direction normal to any suction-side airfoil surface location.
  • 10. The turbine rotor blade as in claim 6, wherein a height of the turbine rotor blade is about 10 inches to about 40 inches.
  • 11. A turbine comprising a turbine wheel having a plurality of turbine rotor blades, each of the turbine rotor blades including an airfoil having a suction-side airfoil shape, the airfoil having a nominal profile substantially in accordance with suction-side Cartesian coordinate values of X, Y and Z set forth in Table I wherein the Cartesian coordinate values of X, Y and Z are non-dimensional values from 0% to 100% convertible to dimensional distances by multiplying the Cartesian coordinate values of X, Y and Z by a height of the airfoil, and wherein X and Y are distances which, when connected by smooth continuing arcs, define airfoil profile sections at each Z distance, the airfoil profile sections at the Z distances being joined smoothly with one another to form a complete suction-side airfoil shape.
  • 12. The turbine as in claim 11, wherein the turbine wheel comprises a stage of the turbine.
  • 13. The turbine as in claim 11, wherein X represents a distance parallel to the turbine axis of rotation.
  • 14. The turbine as in claim 11, wherein the suction-side airfoil shape lies in an envelope within +/− 5% in a direction normal to any suction-side airfoil surface location.
  • 15. The turbine as in claim 11, wherein a height of the turbine rotor blade is about 10 inches to about 40 inches.
  • 16. The turbine as in claim 11, wherein each of the turbine rotor blades includes an airfoil having a pressure-side airfoil shape, the airfoil having a nominal profile substantially in accordance with pressure-side Cartesian coordinate values of X, Y and Z set forth in Table I wherein the pressure-side Cartesian coordinate values of X, Y and Z are non-dimensional values from 0% to 100% convertible to dimensional distances by multiplying the pressure-side Cartesian coordinate values of X, Y and Z by a height of the airfoil, and wherein X and Y are distances which, when connected by smooth continuing arcs, define airfoil profile sections at each Z distance, the airfoil profile sections at Z distances being joined smoothly with one another to form a complete airfoil shape.
  • 17. The turbine as in claim 16, wherein the turbine rotor blade is a second stage turbine rotor blade.
  • 18. The turbine as in claim 14, wherein X represents a distance parallel to the turbine axis of rotation.
  • 19. The turbine as in claim 16, wherein the airfoil shape lies in an envelope within +/− 5% in a direction normal to any airfoil surface location.
  • 20. The turbine as in claim 16, wherein a height of the turbine rotor blade is about 10 inches to about 40 inches.