Airfoil shape for a compressor

Information

  • Patent Grant
  • 8556588
  • Patent Number
    8,556,588
  • Date Filed
    Friday, June 3, 2011
    13 years ago
  • Date Issued
    Tuesday, October 15, 2013
    11 years ago
Abstract
An article of manufacture is disclosed. The article may have a nominal profile generally in accordance with Cartesian coordinate values of X, Y and Z set forth in TABLE A. X and Y may correspond to distances in inches which, when connected by smooth continuing arcs, define airfoil profile sections at each distance Z in inches, the airfoil profile sections at the Z distances being joined smoothly with one another to form a complete airfoil shape.
Description
FIELD OF THE INVENTION

The present subject matter relates generally to the design of airfoils. In particular, the present subject matter relates to compressor airfoil profiles for various stages of a gas turbine compressor, such as for use as rotor blades and stator vanes at various stages of the compressor. More particularly, the present subject matter relates to compressor airfoil profiles for a “Stage Zero” rotor blade.


BACKGROUND OF THE INVENTION

In a gas turbine, many system requirements should be met at each stage of a gas turbine's flow path section to meet design goals. These design goals may include, but are not limited to, overall improved efficiency, airfoil loading capability and component reliability. For example, a rotor blade of a compressor rotor may be designed to achieve thermal and mechanical operating requirements for the particular compressor stage at which it is located. Similarly, for example, a stator vane of a compressor stator may be designed to achieve thermal and mechanical operating requirements for the particular stage at which it is located.


Accordingly, an airfoil profile configured to meet the above mentioned design goals would be welcomed in the technology.


BRIEF DESCRIPTION OF THE INVENTION

Aspects and advantages of the invention will be set forth in part in the following description, or may be obvious from the description, or may be learned through practice of the invention.


In one aspect, the present subject matter discloses an article of manufacture. The article may have a nominal profile generally in accordance with Cartesian coordinate values of X, Y and Z set forth in TABLE A. X and Y may correspond to distances in inches which, when connected by smooth continuing arcs, define airfoil profile sections at each distance Z in inches, the airfoil profile sections at the Z distances being joined smoothly with one another to form a complete airfoil shape.


In another aspect, the present subject matter discloses a rotor blade having an airfoil. The airfoil may have a nominal profile generally in accordance with Cartesian coordinate values of X, Y and Z set forth in TABLE A. X and Y may correspond to distances in inches which, when connected by smooth continuing arcs, define airfoil profile sections at each distance Z in inches, the airfoil profile sections at the Z distances being joined smoothly with one another to form a complete airfoil shape.


In a further aspect, the present subject matter discloses a compressor having a rotor wheel and a plurality of rotor blades mounted to the rotor wheel. Each rotor blade includes an airfoil. The airfoil may have a nominal profile generally in accordance with Cartesian coordinate values of X, Y and Z set forth in TABLE A. X and Y may be distances in inches which, when connected by smooth continuing arcs, define airfoil profile sections at each distance Z in inches, the airfoil profile sections at the Z distances being joined smoothly with one another to form a complete airfoil shape.


These and other features, aspects and advantages of the present invention will become better understood with reference to the following description and appended claims. The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and, together with the description, serve to explain the principles of the invention.





BRIEF DESCRIPTION OF THE DRAWINGS

A full and enabling disclosure of the present invention, including the best mode thereof, directed to one of ordinary skill in the art, is set forth in the specification, which makes reference to the appended figures, in which:



FIG. 1 illustrates a schematic depiction of one embodiment of a gas turbine;



FIG. 2 illustrates a cross-sectional view of one embodiment of a flow path through multiple stages of a gas turbine compressor;



FIGS. 3 and 4 illustrate respective perspective views of one embodiment of a compressor rotor blade in accordance with aspects of the present subject matter, particularly illustrating the blade airfoil together with its corresponding platform and dovetail root;



FIGS. 5 and 6 illustrate side elevational views of the rotor blade shown in FIG. 3 as viewed in a generally circumferential direction from the pressure and suction sides of the blade airfoil, respectively;



FIG. 7 illustrates a cross-sectional view of the blade airfoil taken generally about line 7-7 of FIG. 6;



FIG. 8 illustrates differing views of the rotor blade shown in FIG. 3, particularly illustrating the rotor blade with the X, Y and Z axes of the Cartesian Coordinate System superimposed thereon; and



FIG. 9 illustrates differing views of one embodiment of a compressor stator vane in accordance with aspects of the present subject matter, particularly illustrating the stator vane with the X, Y and Z axes of the Cartesian Coordinate System superimposed thereon.





DETAILED DESCRIPTION OF THE INVENTION

Reference now will be made in detail to embodiments of the invention, one or more examples of which are illustrated in the drawings. Each example is provided by way of explanation of the invention, not limitation of the invention. In fact, it will be apparent to those skilled in the art that various modifications and variations can be made in the present invention without departing from the scope or spirit of the invention. For instance, features illustrated or described as part of one embodiment can be used with another embodiment to yield a still further embodiment. Thus, it is intended that the present invention covers such modifications and variations as come within the scope of the appended claims and their equivalents.


In general, the present subject matter discloses an article of manufacture having a nominal profile generally in accordance with the Cartesian coordinate values of X, Y and Z set forth in TABLE A below. In several embodiments, the article of manufacture may comprise an airfoil suitable for use within one of the stages of a gas turbine compressor. In such embodiments, the X and Y values may generally correspond to distances (measured in inches) which, when connected by smooth continuing arcs, define airfoil profile sections at each distance Z (measured in inches), with the airfoil profile sections at the Z distances being joined smoothly with one another to form a complete airfoil shape. Thus, in one embodiment, the X, Y and Z coordinate values may define a nominal airfoil profile for a rotor blade of the gas turbine compressor. For example, the airfoil profile disclosed herein may be used to form rotor blades comprising the first rotating stage (“Stage Zero” or “R0”) of the compressor. Alternatively, the X, Y and Z coordinate values may define a nominal airfoil profile for a stator vane of the gas turbine compressor.


The nominal airfoil profile defined by the coordinate values in TABLE A may generally provide numerous advantages as compared to other similar airfoil profiles having like applications. In particular, the inventors of the present subject matter have found that the disclosed airfoil profile may enhance rotor and/or stator stage airflow efficiency, improve aeromechanics, enhance the interaction between compressor stages to provide a smooth laminar flow from stage to stage, reduce thermal and mechanical stresses acting on the airfoil and enhance root airfoil root and tip stability, as well as provide numerous other advantages to the overall performance of a compressor and/or a gas turbine.


Moreover, it should be appreciated that an airfoil heats up during use. Thus, the airfoil profile will change as a result of mechanical loading and temperature. Accordingly, the cold or room temperature profile, for manufacturing purposes, is given by the X, Y and Z coordinates of TABLE A. A distance of plus or minus about 0.160 inches (+/−0.160″) from the nominal profile in a direction normal to any surface location along the nominal profile and which includes any coating, defines a profile envelope for the airfoil, as a manufactured airfoil profile may be different from the nominal airfoil profile provided in TABLE A.


Referring now to the drawings, FIG. 1 illustrates a schematic depiction of a gas turbine 10. The gas turbine 10 includes a compressor 12, a combustion section 14 having a plurality of combustors, and a turbine section 16. The compressor 12 and turbine section 16 may be coupled by a drive shaft 18. The drive shaft 18 may be a single shaft or a plurality of shaft segments coupled together to form the drive shaft 18. During operation of the gas turbine 10, the compressor 12 supplies compressed air to the combustion section 14. The compressed air is mixed with fuel and burned within each combustor and hot gases of combustion flow from the combustion section 14 to the turbine section 16, wherein energy is extracted from the hot gases to produce work.


Referring now to FIG. 2, one embodiment of an axial flow path 20 of a gas turbine compressor 12 is illustrated. As shown, the compressor 12 generally includes an inlet guide vane 22 disposed at the inlet of the compressor 12 and a plurality of compressor stages disposed downstream of the inlet guide vane 22 along the axial flow path 20 (the direction of the airflow within the flow path 20 being indicated by the arrow 24). Each compressor stage may generally include a rotor stage having a plurality of rotor blades 26 mounted onto a rotor wheel 28 of the compressor 12 and a stator stage following each rotor stage having a plurality of stator vanes 30 attached to a static casing 32 of the compressor 12. For example, the initial compressor stage 34 disposed within the flow path 20 of the compressor 12 may correspond to “Stage Zero” of the compressor 12, with subsequent compressor stages being sequentially numbered in the downstream direction of the compressor 12 (e.g., “Stage One,” “Stage Two,” etc.). As such, the rotor blades 26 disposed within the initial compressor stage 34 may correspond to “Stage Zero” or “R0” rotor blades 26 and the stator vanes 30 disposed within the initial compressor stage 34 may correspond to “Stage Zero” or “S0” stator vanes 30.


In general, the alternating rows of rotor blades 26 and stator vanes 30 may be designed to bring about a desired pressure rise in the air flowing through the compressor 12. For example, the rotor blades 26 may be configured to impart kinetic energy to the airflow and the stator vanes 30 may be configured to convert the increased rotational kinetic energy within the airflow into increased static pressure through diffusion. Thus, it should be appreciated that the particular configuration of the airfoil included in each rotor blade 26 and/or stator vane 30 (along with its interaction with the surrounding airfoils of adjacent rotor blades 26 and/or stator vanes 30) may generally provide for stage airflow efficiency, enhanced aeromechanics, smooth laminar flow from stage to stage, reduced thermal stresses, enhanced interrelation of the stages to effectively pass the airflow from stage to stage, and reduced mechanical stresses.


As indicated above, each rotor stage may generally include a plurality of circumferentially spaced rotor blades 26 mounted onto one of the rotor wheels 28 about a centerline 36 of the compressor 12. The rotor wheels 28 may, in turn, be attached to the drive shaft 18 of the gas turbine 10 (FIG. 1) for rotation therewith. The drive shaft 18 may then be coupled to the turbine section 16 of the gas turbine 10 (FIG. 1) such that the energy extracted within the turbine section 16 may be used to drive the compressor 12.


Referring now to FIGS. 3-8, each rotor blade 26 of the compressor 12 may generally include a platform 38, a root 40 extending radially inwardly from the platform 38 and an airfoil 42 extending radially outwardly from the platform 38. The root 40 may generally be configured to provide a means for attaching each rotor blade 26 to one of the rotor wheels 28. For example, the root 40 may be configured as a substantially or near axial entry dovetail for connection with a complementary-shaped mating dovetail (not shown) of the rotor wheel 28. The airfoil 42 of each rotor blade 26 may generally extend radially between an airfoil base 44 disposed at the platform 38 and an airfoil tip 46 disposed opposite the airfoil base 44. Additionally, the airfoil 42 may generally define an aerodynamic shape. For instance, as shown in FIG. 7, the airfoil 42 of each of rotor blade 26 may generally have a profile section 48 at any cross-section from the airfoil base 44 to the airfoil tip 46.


Referring now to FIG. 9, similar to the rotor blades 26, each stator vane 30 of the compressor 12 may generally include a platform 50, a root 52 extending radially outwardly from the platform 50 and an airfoil 54 extending radially inwardly from the platform 50. The root 52 may generally be configured to provide a means for attaching each stator vane 30 to a portion of the static casing 32 of the compressor 12. Additionally, the airfoil 54 of each stator vane 30 may generally extend radially between an airfoil base 56 disposed at the platform 50 and an airfoil tip 58 disposed opposite the airfoil base 56. The airfoil 54 may also define an aerodynamic shape and, thus, may have a profile section the same as or similar to the profile section 48 shown in FIG. 7.


To define the airfoil profile of a rotor blade 26 and/or stator vane 30 of a compressor 12, a unique set or loci of points (identified by the X, Y and Z Cartesian Coordinates of TABLE A below) are provided to achieve the necessary efficiency, operability, durability and cost requirements for improved compressor performance. In particular, this unique loci of points has been developed through source codes, iterative modeling and/or other design practices such that the airfoil profile defined by the points generally meets the stage requirements for a “Stage Zero” or “R0” rotor blade 26 such that R0 rotor blades 26 may be manufactured and meet the desired requirements for stage efficiency and reduced thermal and mechanical stresses.


It should be appreciated that the Cartesian coordinate system of X, Y and Z values provided in TABLE A define an airfoil profile at various locations along the airfoil's length. The coordinate values for the X, Y and Z coordinates are set forth in inches, although other units of dimensions may be used when the values are appropriately converted. These values exclude fillet regions of the platform. Additionally, the X, Y, and Z coordinates may be joined smoothly at each Z location to form a smooth continuous airfoil cross-section. Moreover, each defined airfoil section in the X, Y plane is joined smoothly with adjacent airfoil sections in the Z direction to form the complete airfoil shape.


Additionally, the Cartesian coordinate system used herein has orthogonally-related X, Y and Z axes. For reference purposes only, there is established a Point-0 passing through the intersection of the airfoil and the platform along the stacking axis of the disclosed airfoil profile, as illustrated in FIG. 6. Thus, in the embodiments disclosed herein, the Point-0 may be defined as the reference profile section where the Z coordinate of TABLE A is at 0.000 inches, which may be set a predetermined distance from the compressor centerline 36. Additionally, as shown in FIGS. 8 and 9, the X axis may be defined parallel to the dovetail axis of the rotor blade 26 and/or the stator vane 30, which may be parallel or at an angle to the compressor centerline 36. A positive X coordinate value may, for example, be axial toward the aft, exhaust end of the compressor 12. A positive Y coordinate value may be directed normal to the dovetail axis. A positive Z coordinate value may be directed radially toward the tip 46, 58 of the airfoil 42, 54, which may be radially outward towards the static casing 32 of the compressor 12 for rotor blades 26 and radially inward towards the centerline 36 of the compressor 12 for stator vanes 30.


By defining X and Y coordinate values at selected locations in a Z direction normal to the X, Y plane, the profile section of the airfoil, such as, but not limited to, the profile section 48 shown in FIG. 7, at each Z distance along the length of the airfoil can be ascertained. By connecting the X and Y values with smooth continuing arcs, each profile section 48 at each distance Z can be fixed. The airfoil profiles of the various surface locations between the distances Z are determined by smoothly connecting the adjacent profile sections 48 to one another, thus forming the airfoil profile. It should be appreciated that, as indicated above, the values provided in TABLE A represent the airfoil profiles at ambient, non-operating or non-hot conditions and are for an uncoated airfoil.


The TABLE A coordinate values have been generated and are shown to three decimal places for determining the profile of the airfoil. There are typical manufacturing tolerances as well as coatings which should be accounted for in the actual profile of the airfoil. Accordingly, the values for the profile given are for a nominal airfoil. It will therefore be appreciated that +/− typical manufacturing tolerances, such as +/− values including coating thicknesses, are additive to the X and Y values. Therefore, a distance of about +/−0.160″ in a direction normal to any surface location along the airfoil profile defines an airfoil profile envelope for the disclosed airfoil design. In other words, a distance of about +/−0.160″ in a direction normal to any surface location along the airfoil profile defines 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, at the same temperature, as embodied by the invention.


The coordinate values given in TABLE A below provide the nominal profile envelope for an exemplary embodiment of a “Stage Zero” or “R0” rotor blade 26. However, as indicated above, it should be appreciated that, in alternative embodiments, the disclosed coordinate values may be utilized to manufacture airfoil profiles for rotor blades 26 of differing compressor stages and/or stator vanes 30 for any of the various stages of the compressor 12.











TABLE A





X
Y
Z

















−3.5642
0.5154
−0.4000


−3.5636
0.5167
−0.4000


−3.5624
0.5193
−0.4000


−3.5599
0.5244
−0.4000


−3.5540
0.5341
−0.4000


−3.5430
0.5480
−0.4000


−3.5187
0.5686
−0.4000


−3.4807
0.5877
−0.4000


−3.4255
0.5997
−0.4000


−3.3551
0.5989
−0.4000


−3.2642
0.5842
−0.4000


−3.1598
0.5645
−0.4000


−3.0482
0.5446
−0.4000


−2.9224
0.5236
−0.4000


−2.7825
0.5013
−0.4000


−2.6283
0.4793
−0.4000


−2.4669
0.4579
−0.4000


−2.2982
0.4381
−0.4000


−2.1220
0.4210
−0.4000


−1.9385
0.4064
−0.4000


−1.7476
0.3951
−0.4000


−1.5494
0.3875
−0.4000


−1.3442
0.3837
−0.4000


−1.1319
0.3843
−0.4000


−0.9195
0.3883
−0.4000


−0.7071
0.3944
−0.4000


−0.4947
0.4023
−0.4000


−0.2825
0.4117
−0.4000


−0.0703
0.4234
−0.4000


0.1416
0.4377
−0.4000


0.3535
0.4529
−0.4000


0.5654
0.4688
−0.4000


0.7772
0.4849
−0.4000


0.9891
0.5001
−0.4000


1.2010
0.5153
−0.4000


1.4058
0.5308
−0.4000


1.6035
0.5458
−0.4000


1.7943
0.5584
−0.4000


1.9781
0.5696
−0.4000


2.1546
0.5825
−0.4000


2.3241
0.5960
−0.4000


2.4865
0.6075
−0.4000


2.6349
0.6178
−0.4000


2.7692
0.6270
−0.4000


2.8894
0.6324
−0.4000


2.9955
0.6366
−0.4000


3.0874
0.6418
−0.4000


3.1652
0.6471
−0.4000


3.2315
0.6504
−0.4000


3.2853
0.6384
−0.4000


3.3245
0.6160
−0.4000


3.3509
0.5912
−0.4000


3.3674
0.5689
−0.4000


3.3775
0.5505
−0.4000


3.3842
0.5346
−0.4000


3.3886
0.5214
−0.4000


3.3912
0.5112
−0.4000


3.3934
0.5000
−0.4000


3.3953
0.4849
−0.4000


3.3960
0.4660
−0.4000


3.3944
0.4431
−0.4000


3.3879
0.4135
−0.4000


3.3723
0.3771
−0.4000


3.3423
0.3381
−0.4000


3.2931
0.3047
−0.4000


3.2275
0.2760
−0.4000


3.1503
0.2434
−0.4000


3.0594
0.2039
−0.4000


2.9551
0.1570
−0.4000


2.8358
0.1066
−0.4000


2.7013
0.0531
−0.4000


2.5523
−0.0054
−0.4000


2.3882
−0.0669
−0.4000


2.2162
−0.1288
−0.4000


2.0372
−0.1937
−0.4000


1.8504
−0.2596
−0.4000


1.6546
−0.3228
−0.4000


1.4503
−0.3839
−0.4000


1.2375
−0.4431
−0.4000


1.0162
−0.4996
−0.4000


0.7931
−0.5495
−0.4000


0.5686
−0.5926
−0.4000


0.3433
−0.6293
−0.4000


0.1168
−0.6584
−0.4000


−0.1109
−0.6798
−0.4000


−0.3385
−0.6929
−0.4000


−0.5652
−0.6954
−0.4000


−0.7909
−0.6864
−0.4000


−1.0155
−0.6655
−0.4000


−1.2391
−0.6323
−0.4000


−1.4617
−0.5871
−0.4000


−1.6759
−0.5326
−0.4000


−1.8802
−0.4703
−0.4000


−2.0743
−0.4019
−0.4000


−2.2588
−0.3291
−0.4000


−2.4344
−0.2542
−0.4000


−2.6007
−0.1775
−0.4000


−2.7581
−0.0996
−0.4000


−2.9075
−0.0228
−0.4000


−3.0417
0.0500
−0.4000


−3.1615
0.1175
−0.4000


−3.2669
0.1793
−0.4000


−3.3631
0.2415
−0.4000


−3.4420
0.3016
−0.4000


−3.4974
0.3538
−0.4000


−3.5360
0.4012
−0.4000


−3.5585
0.4411
−0.4000


−3.5684
0.4739
−0.4000


−3.5694
0.4930
−0.4000


−3.5676
0.5052
−0.4000


−3.5659
0.5111
−0.4000


−3.5648
0.5140
−0.4000


−3.5191
0.5682
0.0000


−3.5185
0.5695
0.0000


−3.5173
0.5721
0.0000


−3.5148
0.5771
0.0000


−3.5090
0.5867
0.0000


−3.4979
0.6003
0.0000


−3.4734
0.6203
0.0000


−3.4352
0.6380
0.0000


−3.3801
0.6482
0.0000


−3.3103
0.6454
0.0000


−3.2204
0.6300
0.0000


−3.1168
0.6109
0.0000


−3.0061
0.5914
0.0000


−2.8815
0.5703
0.0000


−2.7429
0.5477
0.0000


−2.5902
0.5246
0.0000


−2.4303
0.5017
0.0000


−2.2633
0.4796
0.0000


−2.0890
0.4590
0.0000


−1.9074
0.4402
0.0000


−1.7186
0.4237
0.0000


−1.5226
0.4101
0.0000


−1.3194
0.3997
0.0000


−1.1089
0.3931
0.0000


−0.8982
0.3901
0.0000


−0.6876
0.3898
0.0000


−0.4769
0.3916
0.0000


−0.2662
0.3947
0.0000


−0.0556
0.3997
0.0000


0.1549
0.4074
0.0000


0.3654
0.4165
0.0000


0.5758
0.4264
0.0000


0.7863
0.4364
0.0000


0.9967
0.4457
0.0000


1.2072
0.4551
0.0000


1.4107
0.4644
0.0000


1.6071
0.4731
0.0000


1.7966
0.4804
0.0000


1.9790
0.4870
0.0000


2.1545
0.4945
0.0000


2.3228
0.5025
0.0000


2.4842
0.5094
0.0000


2.6315
0.5153
0.0000


2.7649
0.5203
0.0000


2.8842
0.5231
0.0000


2.9895
0.5250
0.0000


3.0808
0.5275
0.0000


3.1580
0.5300
0.0000


3.2240
0.5316
0.0000


3.2781
0.5227
0.0000


3.3183
0.5023
0.0000


3.3455
0.4786
0.0000


3.3625
0.4567
0.0000


3.3727
0.4385
0.0000


3.3794
0.4226
0.0000


3.3836
0.4094
0.0000


3.3860
0.3992
0.0000


3.3879
0.3881
0.0000


3.3892
0.3732
0.0000


3.3890
0.3546
0.0000


3.3859
0.3322
0.0000


3.3773
0.3037
0.0000


3.3586
0.2695
0.0000


3.3250
0.2345
0.0000


3.2728
0.2071
0.0000


3.2069
0.1816
0.0000


3.1298
0.1519
0.0000


3.0389
0.1164
0.0000


2.9340
0.0751
0.0000


2.8145
0.0301
0.0000


2.6802
−0.0183
0.0000


2.5313
−0.0706
0.0000


2.3676
−0.1258
0.0000


2.1961
−0.1816
0.0000


2.0174
−0.2392
0.0000


1.8309
−0.2972
0.0000


1.6360
−0.3535
0.0000


1.4327
−0.4076
0.0000


1.2210
−0.4593
0.0000


1.0010
−0.5080
0.0000


0.7798
−0.5505
0.0000


0.5572
−0.5863
0.0000


0.3336
−0.6153
0.0000


0.1095
−0.6369
0.0000


−0.1152
−0.6510
0.0000


−0.3404
−0.6568
0.0000


−0.5658
−0.6520
0.0000


−0.7892
−0.6359
0.0000


−1.0106
−0.6086
0.0000


−1.2299
−0.5699
0.0000


−1.4473
−0.5203
0.0000


−1.6557
−0.4625
0.0000


−1.8552
−0.3979
0.0000


−2.0456
−0.3279
0.0000


−2.2264
−0.2545
0.0000


−2.3986
−0.1796
0.0000


−2.5621
−0.1036
0.0000


−2.7169
−0.0270
0.0000


−2.8640
0.0481
0.0000


−2.9965
0.1188
0.0000


−3.1149
0.1841
0.0000


−3.2192
0.2439
0.0000


−3.3148
0.3035
0.0000


−3.3936
0.3611
0.0000


−3.4494
0.4112
0.0000


−3.4884
0.4567
0.0000


−3.5117
0.4954
0.0000


−3.5224
0.5273
0.0000


−3.5238
0.5461
0.0000


−3.5223
0.5581
0.0000


−3.5207
0.5639
0.0000


−3.5196
0.5668
0.0000


−3.4507
0.6509
0.6200


−3.4502
0.6522
0.6200


−3.4490
0.6547
0.6200


−3.4466
0.6597
0.6200


−3.4407
0.6691
0.6200


−3.4293
0.6823
0.6200


−3.4043
0.7009
0.6200


−3.3656
0.7160
0.6200


−3.3106
0.7226
0.6200


−3.2418
0.7166
0.6200


−3.1530
0.7006
0.6200


−3.0506
0.6822
0.6200


−2.9412
0.6632
0.6200


−2.8181
0.6421
0.6200


−2.6813
0.6192
0.6200


−2.5306
0.5950
0.6200


−2.3730
0.5701
0.6200


−2.2085
0.5447
0.6200


−2.0370
0.5191
0.6200


−1.8585
0.4938
0.6200


−1.6729
0.4693
0.6200


−1.4800
0.4462
0.6200


−1.2799
0.4252
0.6200


−1.0724
0.4073
0.6200


−0.8646
0.3931
0.6200


−0.6566
0.3826
0.6200


−0.4485
0.3752
0.6200


−0.2403
0.3690
0.6200


−0.0321
0.3637
0.6200


0.1762
0.3611
0.6200


0.3844
0.3610
0.6200


0.5927
0.3620
0.6200


0.8010
0.3625
0.6200


1.0093
0.3631
0.6200


1.2176
0.3639
0.6200


1.4190
0.3640
0.6200


1.6134
0.3626
0.6200


1.8009
0.3615
0.6200


1.9814
0.3616
0.6200


2.1550
0.3610
0.6200


2.3216
0.3599
0.6200


2.4813
0.3593
0.6200


2.6271
0.3583
0.6200


2.7590
0.3560
0.6200


2.8771
0.3546
0.6200


2.9812
0.3537
0.6200


3.0715
0.3520
0.6200


3.1478
0.3499
0.6200


3.2130
0.3474
0.6200


3.2676
0.3434
0.6200


3.3092
0.3271
0.6200


3.3374
0.3052
0.6200


3.3548
0.2840
0.6200


3.3651
0.2660
0.6200


3.3715
0.2501
0.6200


3.3753
0.2368
0.6200


3.3773
0.2267
0.6200


3.3786
0.2157
0.6200


3.3790
0.2011
0.6200


3.3773
0.1828
0.6200


3.3722
0.1614
0.6200


3.3605
0.1346
0.6200


3.3373
0.1044
0.6200


3.2983
0.0774
0.6200


3.2435
0.0578
0.6200


3.1779
0.0357
0.6200


3.1010
0.0101
0.6200


3.0098
−0.0191
0.6200


2.9040
−0.0512
0.6200


2.7844
−0.0881
0.6200


2.6504
−0.1288
0.6200


2.5017
−0.1714
0.6200


2.3386
−0.2171
0.6200


2.1680
−0.2636
0.6200


1.9896
−0.3094
0.6200


1.8035
−0.3548
0.6200


1.6100
−0.4006
0.6200


1.4084
−0.4443
0.6200


1.1986
−0.4845
0.6200


0.9808
−0.5215
0.6200


0.7622
−0.5533
0.6200


0.5426
−0.5783
0.6200


0.3224
−0.5956
0.6200


0.1019
−0.6061
0.6200


−0.1190
−0.6097
0.6200


−0.3395
−0.6048
0.6200


−0.5581
−0.5889
0.6200


−0.7749
−0.5622
0.6200


−0.9898
−0.5253
0.6200


−1.2030
−0.4782
0.6200


−1.4145
−0.4212
0.6200


−1.6174
−0.3576
0.6200


−1.8115
−0.2888
0.6200


−1.9962
−0.2164
0.6200


−2.1722
−0.1419
0.6200


−2.3400
−0.0668
0.6200


−2.4997
0.0082
0.6200


−2.6516
0.0828
0.6200


−2.7961
0.1555
0.6200


−2.9266
0.2233
0.6200


−3.0434
0.2856
0.6200


−3.1465
0.3424
0.6200


−3.2414
0.3985
0.6200


−3.3203
0.4526
0.6200


−3.3766
0.4999
0.6200


−3.4165
0.5430
0.6200


−3.4408
0.5799
0.6200


−3.4526
0.6108
0.6200


−3.4548
0.6291
0.6200


−3.4537
0.6409
0.6200


−3.4522
0.6466
0.6200


−3.4512
0.6495
0.6200


−3.3957
0.7329
1.2236


−3.3952
0.7342
1.2236


−3.3941
0.7368
1.2236


−3.3916
0.7417
1.2236


−3.3856
0.7509
1.2236


−3.3737
0.7636
1.2236


−3.3477
0.7805
1.2236


−3.3083
0.7927
1.2236


−3.2534
0.7955
1.2236


−3.1851
0.7866
1.2236


−3.0969
0.7702
1.2236


−2.9951
0.7516
1.2236


−2.8864
0.7324
1.2236


−2.7640
0.7110
1.2236


−2.6280
0.6876
1.2236


−2.4784
0.6622
1.2236


−2.3219
0.6355
1.2236


−2.1587
0.6074
1.2236


−1.9887
0.5781
1.2236


−1.8119
0.5478
1.2236


−1.6282
0.5168
1.2236


−1.4375
0.4858
1.2236


−1.2397
0.4556
1.2236


−1.0346
0.4272
1.2236


−0.8290
0.4022
1.2236


−0.6231
0.3809
1.2236


−0.4168
0.3633
1.2236


−0.2104
0.3473
1.2236


−0.0039
0.3323
1.2236


0.2028
0.3199
1.2236


0.4096
0.3109
1.2236


0.6165
0.3031
1.2236


0.8234
0.2948
1.2236


1.0303
0.2867
1.2236


1.2372
0.2788
1.2236


1.4372
0.2703
1.2236


1.6302
0.2601
1.2236


1.8164
0.2508
1.2236


1.9957
0.2434
1.2236


2.1680
0.2351
1.2236


2.3334
0.2257
1.2236


2.4920
0.2177
1.2236


2.6368
0.2100
1.2236


2.7676
0.2013
1.2236


2.8847
0.1943
1.2236


2.9881
0.1892
1.2236


3.0777
0.1831
1.2236


3.1534
0.1769
1.2236


3.2180
0.1713
1.2236


3.2724
0.1670
1.2236


3.3158
0.1577
1.2236


3.3460
0.1391
1.2236


3.3647
0.1190
1.2236


3.3753
0.1015
1.2236


3.3818
0.0856
1.2236


3.3852
0.0724
1.2236


3.3867
0.0622
1.2236


3.3874
0.0514
1.2236


3.3867
0.0370
1.2236


3.3834
0.0193
1.2236


3.3759
−0.0009
1.2236


3.3601
−0.0250
1.2236


3.3317
−0.0492
1.2236


3.2878
−0.0655
1.2236


3.2327
−0.0811
1.2236


3.1672
−0.0999
1.2236


3.0904
−0.1214
1.2236


2.9992
−0.1450
1.2236


2.8935
−0.1705
1.2236


2.7741
−0.2007
1.2236


2.6406
−0.2341
1.2236


2.4923
−0.2684
1.2236


2.3298
−0.3055
1.2236


2.1601
−0.3435
1.2236


1.9826
−0.3795
1.2236


1.7976
−0.4148
1.2236


1.6054
−0.4510
1.2236


1.4053
−0.4850
1.2236


1.1972
−0.5152
1.2236


0.9815
−0.5420
1.2236


0.7653
−0.5638
1.2236


0.5486
−0.5790
1.2236


0.3311
−0.5862
1.2236


0.1135
−0.5867
1.2236


−0.1038
−0.5806
1.2236


−0.3205
−0.5658
1.2236


−0.5368
−0.5400
1.2236


−0.7515
−0.5033
1.2236


−0.9639
−0.4569
1.2236


−1.1741
−0.4011
1.2236


−1.3821
−0.3365
1.2236


−1.5809
−0.2667
1.2236


−1.7705
−0.1936
1.2236


−1.9515
−0.1184
1.2236


−2.1243
−0.0420
1.2236


−2.2893
0.0340
1.2236


−2.4467
0.1089
1.2236


−2.5968
0.1825
1.2236


−2.7399
0.2538
1.2236


−2.8693
0.3200
1.2236


−2.9851
0.3807
1.2236


−3.0876
0.4357
1.2236


−3.1824
0.4895
1.2236


−3.2615
0.5411
1.2236


−3.3183
0.5863
1.2236


−3.3588
0.6277
1.2236


−3.3840
0.6633
1.2236


−3.3967
0.6934
1.2236


−3.3994
0.7114
1.2236


−3.3985
0.7230
1.2236


−3.3972
0.7287
1.2236


−3.3962
0.7315
1.2236


−3.3433
0.8786
2.3440


−3.3428
0.8799
2.3440


−3.3416
0.8824
2.3440


−3.3388
0.8873
2.3440


−3.3319
0.8961
2.3440


−3.3185
0.9073
2.3440


−3.2900
0.9202
2.3440


−3.2487
0.9259
2.3440


−3.1933
0.9209
2.3440


−3.1251
0.9069
2.3440


−3.0365
0.8884
2.3440


−2.9342
0.8681
2.3440


−2.8248
0.8471
2.3440


−2.7017
0.8241
2.3440


−2.5647
0.7991
2.3440


−2.4141
0.7718
2.3440


−2.2567
0.7430
2.3440


−2.0925
0.7124
2.3440


−1.9216
0.6799
2.3440


−1.7440
0.6450
2.3440


−1.5600
0.6071
2.3440


−1.3695
0.5665
2.3440


−1.1722
0.5237
2.3440


−0.9682
0.4795
2.3440


−0.7641
0.4360
2.3440


−0.5596
0.3941
2.3440


−0.3546
0.3547
2.3440


−0.1491
0.3184
2.3440


0.0569
0.2855
2.3440


0.2635
0.2563
2.3440


0.4705
0.2306
2.3440


0.6778
0.2073
2.3440


0.8853
0.1848
2.3440


1.0926
0.1612
2.3440


1.2999
0.1371
2.3440


1.5003
0.1140
2.3440


1.6937
0.0910
2.3440


1.8801
0.0678
2.3440


2.0594
0.0446
2.3440


2.2318
0.0218
2.3440


2.3973
−0.0004
2.3440


2.5557
−0.0223
2.3440


2.7004
−0.0426
2.3440


2.8313
−0.0609
2.3440


2.9482
−0.0787
2.3440


3.0510
−0.0967
2.3440


3.1401
−0.1118
2.3440


3.2157
−0.1236
2.3440


3.2804
−0.1332
2.3440


3.3348
−0.1414
2.3440


3.3795
−0.1483
2.3440


3.4150
−0.1545
2.3440


3.4397
−0.1674
2.3440


3.4541
−0.1829
2.3440


3.4623
−0.1985
2.3440


3.4660
−0.2120
2.3440


3.4670
−0.2226
2.3440


3.4665
−0.2334
2.3440


3.4632
−0.2474
2.3440


3.4553
−0.2634
2.3440


3.4408
−0.2793
2.3440


3.4152
−0.2922
2.3440


3.3781
−0.2991
2.3440


3.3317
−0.3070
2.3440


3.2752
−0.3165
2.3440


3.2080
−0.3278
2.3440


3.1294
−0.3416
2.3440


3.0369
−0.3594
2.3440


2.9300
−0.3798
2.3440


2.8085
−0.4001
2.3440


2.6725
−0.4215
2.3440


2.5221
−0.4451
2.3440


2.3573
−0.4699
2.3440


2.1851
−0.4946
2.3440


2.0056
−0.5191
2.3440


1.8186
−0.5425
2.3440


1.6242
−0.5639
2.3440


1.4221
−0.5826
2.3440


1.2125
−0.5979
2.3440


0.9957
−0.6094
2.3440


0.7788
−0.6143
2.3440


0.5618
−0.6119
2.3440


0.3446
−0.6028
2.3440


0.1276
−0.5864
2.3440


−0.0884
−0.5616
2.3440


−0.3032
−0.5271
2.3440


−0.5160
−0.4828
2.3440


−0.7261
−0.4290
2.3440


−0.9337
−0.3661
2.3440


−1.1389
−0.2950
2.3440


−1.3419
−0.2169
2.3440


−1.5361
−0.1365
2.3440


−1.7221
−0.0554
2.3440


−1.9003
0.0255
2.3440


−2.0709
0.1058
2.3440


−2.2342
0.1845
2.3440


−2.3906
0.2608
2.3440


−2.5399
0.3350
2.3440


−2.6824
0.4067
2.3440


−2.8114
0.4730
2.3440


−2.9269
0.5337
2.3440


−3.0291
0.5886
2.3440


−3.1241
0.6415
2.3440


−3.2041
0.6913
2.3440


−3.2619
0.7350
2.3440


−3.3035
0.7751
2.3440


−3.3298
0.8098
2.3440


−3.3435
0.8393
2.3440


−3.3468
0.8572
2.3440


−3.3461
0.8688
2.3440


−3.3448
0.8745
2.3440


−3.3439
0.8772
2.3440


−3.3385
0.9138
2.6600


−3.3380
0.9151
2.6600


−3.3367
0.9176
2.6600


−3.3338
0.9224
2.6600


−3.3267
0.9311
2.6600


−3.3128
0.9418
2.6600


−3.2835
0.9531
2.6600


−3.2418
0.9567
2.6600


−3.1864
0.9494
2.6600


−3.1182
0.9342
2.6600


−3.0293
0.9151
2.6600


−2.9267
0.8940
2.6600


−2.8170
0.8723
2.6600


−2.6935
0.8485
2.6600


−2.5561
0.8228
2.6600


−2.4049
0.7949
2.6600


−2.2469
0.7654
2.6600


−2.0822
0.7340
2.6600


−1.9107
0.7005
2.6600


−1.7326
0.6645
2.6600


−1.5481
0.6253
2.6600


−1.3572
0.5829
2.6600


−1.1596
0.5377
2.6600


−0.9554
0.4903
2.6600


−0.7512
0.4431
2.6600


−0.5468
0.3967
2.6600


−0.3420
0.3523
2.6600


−0.1365
0.3109
2.6600


0.0697
0.2731
2.6600


0.2766
0.2392
2.6600


0.4841
0.2090
2.6600


0.6920
0.1817
2.6600


0.9001
0.1559
2.6600


1.1081
0.1291
2.6600


1.3159
0.1015
2.6600


1.5169
0.0748
2.6600


1.7107
0.0481
2.6600


1.8975
0.0212
2.6600


2.0773
−0.0055
2.6600


2.2500
−0.0316
2.6600


2.4158
−0.0573
2.6600


2.5744
−0.0832
2.6600


2.7192
−0.1073
2.6600


2.8504
−0.1278
2.6600


2.9676
−0.1478
2.6600


3.0703
−0.1689
2.6600


3.1596
−0.1862
2.6600


3.2355
−0.1989
2.6600


3.3004
−0.2091
2.6600


3.3550
−0.2180
2.6600


3.3998
−0.2260
2.6600


3.4355
−0.2329
2.6600


3.4616
−0.2430
2.6600


3.4772
−0.2576
2.6600


3.4861
−0.2730
2.6600


3.4899
−0.2867
2.6600


3.4908
−0.2974
2.6600


3.4899
−0.3082
2.6600


3.4859
−0.3221
2.6600


3.4766
−0.3375
2.6600


3.4603
−0.3516
2.6600


3.4330
−0.3606
2.6600


3.3956
−0.3666
2.6600


3.3489
−0.3734
2.6600


3.2919
−0.3810
2.6600


3.2241
−0.3897
2.6600


3.1449
−0.4009
2.6600


3.0518
−0.4169
2.6600


2.9443
−0.4354
2.6600


2.8219
−0.4522
2.6600


2.6850
−0.4702
2.6600


2.5338
−0.4912
2.6600


2.3681
−0.5131
2.6600


2.1949
−0.5341
2.6600


2.0145
−0.5548
2.6600


1.8267
−0.5746
2.6600


1.6314
−0.5925
2.6600


1.4287
−0.6075
2.6600


1.2183
−0.6190
2.6600


1.0004
−0.6265
2.6600


0.7822
−0.6273
2.6600


0.5643
−0.6207
2.6600


0.3467
−0.6076
2.6600


0.1295
−0.5869
2.6600


−0.0863
−0.5572
2.6600


−0.3005
−0.5177
2.6600


−0.5130
−0.4684
2.6600


−0.7226
−0.4100
2.6600


−0.9292
−0.3431
2.6600


−1.1333
−0.2688
2.6600


−1.3352
−0.1882
2.6600


−1.5289
−0.1059
2.6600


−1.7146
−0.0233
2.6600


−1.8927
0.0586
2.6600


−2.0632
0.1395
2.6600


−2.2265
0.2186
2.6600


−2.3830
0.2954
2.6600


−2.5324
0.3700
2.6600


−2.6749
0.4421
2.6600


−2.8039
0.5087
2.6600


−2.9195
0.5696
2.6600


−3.0217
0.6248
2.6600


−3.1168
0.6778
2.6600


−3.1971
0.7274
2.6600


−3.2554
0.7707
2.6600


−3.2976
0.8105
2.6600


−3.3243
0.8450
2.6600


−3.3384
0.8744
2.6600


−3.3420
0.8922
2.6600


−3.3414
0.9039
2.6600


−3.3400
0.9096
2.6600


−3.3391
0.9124
2.6600


−3.3159
1.0297
3.6230


−3.3152
1.0310
3.6230


−3.3139
1.0335
3.6230


−3.3107
1.0382
3.6230


−3.3026
1.0462
3.6230


−3.2872
1.0550
3.6230


−3.2561
1.0619
3.6230


−3.2139
1.0593
3.6230


−3.1589
1.0463
3.6230


−3.0906
1.0283
3.6230


−3.0014
1.0061
3.6230


−2.8983
0.9819
3.6230


−2.7881
0.9570
3.6230


−2.6639
0.9297
3.6230


−2.5257
0.9003
3.6230


−2.3736
0.8685
3.6230


−2.2146
0.8351
3.6230


−2.0488
0.7997
3.6230


−1.8764
0.7620
3.6230


−1.6973
0.7216
3.6230


−1.5118
0.6777
3.6230


−1.3200
0.6298
3.6230


−1.1219
0.5781
3.6230


−0.9175
0.5225
3.6230


−0.7136
0.4653
3.6230


−0.5099
0.4068
3.6230


−0.3061
0.3485
3.6230


−0.1019
0.2919
3.6230


0.1030
0.2385
3.6230


0.3090
0.1892
3.6230


0.5160
0.1441
3.6230


0.7239
0.1029
3.6230


0.9323
0.0647
3.6230


1.1408
0.0267
3.6230


1.3492
−0.0119
3.6230


1.5505
−0.0499
3.6230


1.7446
−0.0876
3.6230


1.9316
−0.1251
3.6230


2.1114
−0.1625
3.6230


2.2841
−0.1993
3.6230


2.4497
−0.2354
3.6230


2.6081
−0.2717
3.6230


2.7526
−0.3052
3.6230


2.8838
−0.3336
3.6230


3.0010
−0.3599
3.6230


3.1035
−0.3866
3.6230


3.1924
−0.4094
3.6230


3.2681
−0.4268
3.6230


3.3329
−0.4413
3.6230


3.3872
−0.4539
3.6230


3.4318
−0.4649
3.6230


3.4673
−0.4743
3.6230


3.4944
−0.4822
3.6230


3.5117
−0.4942
3.6230


3.5216
−0.5090
3.6230


3.5255
−0.5227
3.6230


3.5258
−0.5333
3.6230


3.5240
−0.5440
3.6230


3.5180
−0.5571
3.6230


3.5056
−0.5703
3.6230


3.4858
−0.5788
3.6230


3.4568
−0.5819
3.6230


3.4191
−0.5853
3.6230


3.3718
−0.5888
3.6230


3.3144
−0.5922
3.6230


3.2460
−0.5958
3.6230


3.1660
−0.6009
3.6230


3.0716
−0.6094
3.6230


2.9626
−0.6190
3.6230


2.8389
−0.6257
3.6230


2.7005
−0.6335
3.6230


2.5478
−0.6443
3.6230


2.3804
−0.6552
3.6230


2.2057
−0.6649
3.6230


2.0237
−0.6739
3.6230


1.8343
−0.6815
3.6230


1.6375
−0.6867
3.6230


1.4333
−0.6891
3.6230


1.2220
−0.6879
3.6230


1.0036
−0.6818
3.6230


0.7855
−0.6691
3.6230


0.5678
−0.6492
3.6230


0.3506
−0.6222
3.6230


0.1350
−0.5868
3.6230


−0.0786
−0.5418
3.6230


−0.2901
−0.4870
3.6230


−0.4995
−0.4231
3.6230


−0.7062
−0.3513
3.6230


−0.9104
−0.2732
3.6230


−1.1127
−0.1900
3.6230


−1.3135
−0.1029
3.6230


−1.5064
−0.0159
3.6230


−1.6916
0.0702
3.6230


−1.8694
0.1551
3.6230


−2.0397
0.2386
3.6230


−2.2029
0.3200
3.6230


−2.3592
0.3991
3.6230


−2.5082
0.4762
3.6230


−2.6504
0.5508
3.6230


−2.7791
0.6195
3.6230


−2.8944
0.6824
3.6230


−2.9963
0.7394
3.6230


−3.0911
0.7941
3.6230


−3.1717
0.8442
3.6230


−3.2305
0.8874
3.6230


−3.2732
0.9269
3.6230


−3.3006
0.9611
3.6230


−3.3154
0.9903
3.6230


−3.3193
1.0082
3.6230


−3.3189
1.0199
3.6230


−3.3175
1.0256
3.6230


−3.3164
1.0284
3.6230


−3.2843
1.2601
5.3470


−3.2836
1.2614
5.3470


−3.2820
1.2638
5.3470


−3.2780
1.2681
5.3470


−3.2682
1.2744
5.3470


−3.2507
1.2791
5.3470


−3.2182
1.2776
5.3470


−3.1764
1.2659
5.3470


−3.1218
1.2468
5.3470


−3.0533
1.2236
5.3470


−2.9640
1.1946
5.3470


−2.8604
1.1627
5.3470


−2.7495
1.1299
5.3470


−2.6245
1.0940
5.3470


−2.4854
1.0549
5.3470


−2.3323
1.0121
5.3470


−2.1722
0.9675
5.3470


−2.0051
0.9209
5.3470


−1.8312
0.8720
5.3470


−1.6507
0.8198
5.3470


−1.4639
0.7634
5.3470


−1.2709
0.7026
5.3470


−1.0717
0.6372
5.3470


−0.8667
0.5666
5.3470


−0.6628
0.4928
5.3470


−0.4601
0.4158
5.3470


−0.2583
0.3366
5.3470


−0.0568
0.2563
5.3470


0.1448
0.1766
5.3470


0.3471
0.0987
5.3470


0.5506
0.0239
5.3470


0.7555
−0.0473
5.3470


0.9616
−0.1149
5.3470


1.1687
−0.1795
5.3470


1.3763
−0.2426
5.3470


1.5771
−0.3032
5.3470


1.7710
−0.3614
5.3470


1.9578
−0.4183
5.3470


2.1371
−0.4748
5.3470


2.3092
−0.5302
5.3470


2.4742
−0.5837
5.3470


2.6323
−0.6357
5.3470


2.7764
−0.6835
5.3470


2.9067
−0.7270
5.3470


3.0232
−0.7661
5.3470


3.1259
−0.8010
5.3470


3.2148
−0.8316
5.3470


3.2900
−0.8576
5.3470


3.3542
−0.8800
5.3470


3.4081
−0.8989
5.3470


3.4524
−0.9144
5.3470


3.4879
−0.9269
5.3470


3.5152
−0.9364
5.3470


3.5347
−0.9456
5.3470


3.5457
−0.9596
5.3470


3.5495
−0.9733
5.3470


3.5491
−0.9841
5.3470


3.5456
−0.9945
5.3470


3.5368
−1.0061
5.3470


3.5207
−1.0145
5.3470


3.4987
−1.0149
5.3470


3.4692
−1.0129
5.3470


3.4309
−1.0104
5.3470


3.3830
−1.0073
5.3470


3.3248
−1.0036
5.3470


3.2555
−0.9991
5.3470


3.1745
−0.9939
5.3470


3.0787
−0.9874
5.3470


2.9682
−0.9797
5.3470


2.8430
−0.9707
5.3470


2.7031
−0.9606
5.3470


2.5485
−0.9493
5.3470


2.3792
−0.9364
5.3470


2.2025
−0.9223
5.3470


2.0186
−0.9071
5.3470


1.8274
−0.8894
5.3470


1.6292
−0.8682
5.3470


1.4240
−0.8437
5.3470


1.2120
−0.8149
5.3470


0.9938
−0.7795
5.3470


0.7767
−0.7372
5.3470


0.5610
−0.6870
5.3470


0.3471
−0.6283
5.3470


0.1360
−0.5617
5.3470


−0.0724
−0.4877
5.3470


−0.2783
−0.4071
5.3470


−0.4821
−0.3209
5.3470


−0.6842
−0.2302
5.3470


−0.8849
−0.1362
5.3470


−1.0844
−0.0399
5.3470


−1.2832
0.0580
5.3470


−1.4748
0.1537
5.3470


−1.6592
0.2472
5.3470


−1.8364
0.3388
5.3470


−2.0061
0.4287
5.3470


−2.1687
0.5163
5.3470


−2.3243
0.6012
5.3470


−2.4729
0.6836
5.3470


−2.6145
0.7632
5.3470


−2.7427
0.8367
5.3470


−2.8573
0.9041
5.3470


−2.9585
0.9651
5.3470


−3.0526
1.0236
5.3470


−3.1332
1.0758
5.3470


−3.1930
1.1191
5.3470


−3.2373
1.1581
5.3470


−3.2661
1.1917
5.3470


−3.2826
1.2206
5.3470


−3.2875
1.2384
5.3470


−3.2875
1.2502
5.3470


−3.2861
1.2559
5.3470


−3.2850
1.2587
5.3470


−3.2638
1.3320
5.9521


−3.2631
1.3333
5.9521


−3.2613
1.3357
5.9521


−3.2571
1.3398
5.9521


−3.2468
1.3452
5.9521


−3.2288
1.3483
5.9521


−3.1963
1.3440
5.9521


−3.1551
1.3298
5.9521


−3.1008
1.3090
5.9521


−3.0327
1.2838
5.9521


−2.9437
1.2522
5.9521


−2.8406
1.2172
5.9521


−2.7301
1.1812
5.9521


−2.6054
1.1419
5.9521


−2.4667
1.0989
5.9521


−2.3139
1.0520
5.9521


−2.1542
1.0031
5.9521


−1.9875
0.9521
5.9521


−1.8140
0.8985
5.9521


−1.6340
0.8416
5.9521


−1.4477
0.7804
5.9521


−1.2552
0.7148
5.9521


−1.0568
0.6444
5.9521


−0.8525
0.5690
5.9521


−0.6493
0.4902
5.9521


−0.4474
0.4083
5.9521


−0.2465
0.3238
5.9521


−0.0463
0.2377
5.9521


0.1537
0.1512
5.9521


0.3540
0.0654
5.9521


0.5552
−0.0184
5.9521


0.7576
−0.0992
5.9521


0.9614
−0.1766
5.9521


1.1664
−0.2507
5.9521


1.3722
−0.3225
5.9521


1.5715
−0.3908
5.9521


1.7640
−0.4565
5.9521


1.9496
−0.5202
5.9521


2.1280
−0.5822
5.9521


2.2993
−0.6425
5.9521


2.4636
−0.7011
5.9521


2.6207
−0.7578
5.9521


2.7641
−0.8101
5.9521


2.8937
−0.8577
5.9521


3.0095
−0.9005
5.9521


3.1117
−0.9385
5.9521


3.2002
−0.9714
5.9521


3.2750
−0.9994
5.9521


3.3390
−1.0234
5.9521


3.3927
−1.0435
5.9521


3.4370
−1.0601
5.9521


3.4723
−1.0734
5.9521


3.4995
−1.0837
5.9521


3.5193
−1.0925
5.9521


3.5307
−1.1062
5.9521


3.5345
−1.1201
5.9521


3.5337
−1.1308
5.9521


3.5297
−1.1410
5.9521


3.5200
−1.1520
5.9521


3.5032
−1.1587
5.9521


3.4811
−1.1571
5.9521


3.4517
−1.1537
5.9521


3.4136
−1.1492
5.9521


3.3659
−1.1437
5.9521


3.3079
−1.1369
5.9521


3.2389
−1.1290
5.9521


3.1581
−1.1196
5.9521


3.0627
−1.1086
5.9521


2.9525
−1.0959
5.9521


2.8278
−1.0814
5.9521


2.6883
−1.0650
5.9521


2.5342
−1.0465
5.9521


2.3655
−1.0257
5.9521


2.1896
−1.0031
5.9521


2.0066
−0.9785
5.9521


1.8165
−0.9514
5.9521


1.6194
−0.9212
5.9521


1.4154
−0.8868
5.9521


1.2048
−0.8470
5.9521


0.9879
−0.8001
5.9521


0.7728
−0.7465
5.9521


0.5598
−0.6852
5.9521


0.3490
−0.6161
5.9521


0.1407
−0.5398
5.9521


−0.0653
−0.4574
5.9521


−0.2691
−0.3699
5.9521


−0.4712
−0.2783
5.9521


−0.6718
−0.1835
5.9521


−0.8711
−0.0862
5.9521


−1.0695
0.0130
5.9521


−1.2672
0.1135
5.9521


−1.4578
0.2116
5.9521


−1.6415
0.3072
5.9521


−1.8179
0.4007
5.9521


−1.9870
0.4922
5.9521


−2.1490
0.5813
5.9521


−2.3041
0.6676
5.9521


−2.4521
0.7513
5.9521


−2.5932
0.8323
5.9521


−2.7209
0.9069
5.9521


−2.8350
0.9754
5.9521


−2.9358
1.0374
5.9521


−3.0294
1.0968
5.9521


−3.1097
1.1497
5.9521


−3.1699
1.1926
5.9521


−3.2148
1.2311
5.9521


−3.2442
1.2641
5.9521


−3.2614
1.2926
5.9521


−3.2668
1.3103
5.9521


−3.2670
1.3221
5.9521


−3.2656
1.3279
5.9521


−3.2645
1.3307
5.9521


−3.1584
1.5003
7.5877


−3.1576
1.5015
7.5877


−3.1556
1.5037
7.5877


−3.1508
1.5071
7.5877


−3.1395
1.5102
7.5877


−3.1212
1.5094
7.5877


−3.0900
1.4994
7.5877


−3.0505
1.4809
7.5877


−2.9980
1.4560
7.5877


−2.9321
1.4254
7.5877


−2.8458
1.3867
7.5877


−2.7457
1.3435
7.5877


−2.6384
1.2987
7.5877


−2.5172
1.2495
7.5877


−2.3820
1.1961
7.5877


−2.2329
1.1383
7.5877


−2.0769
1.0783
7.5877


−1.9140
1.0160
7.5877


−1.7443
0.9508
7.5877


−1.5682
0.8824
7.5877


−1.3858
0.8101
7.5877


−1.1973
0.7333
7.5877


−1.0031
0.6516
7.5877


−0.8034
0.5642
7.5877


−0.6050
0.4737
7.5877


−0.4081
0.3802
7.5877


−0.2125
0.2838
7.5877


−0.0182
0.1850
7.5877


0.1753
0.0844
7.5877


0.3682
−0.0174
7.5877


0.5609
−0.1196
7.5877


0.7537
−0.2216
7.5877


0.9470
−0.3225
7.5877


1.1412
−0.4218
7.5877


1.3365
−0.5188
7.5877


1.5265
−0.6099
7.5877


1.7111
−0.6956
7.5877


1.8899
−0.7766
7.5877


2.0626
−0.8537
7.5877


2.2289
−0.9272
7.5877


2.3886
−0.9977
7.5877


2.5417
−1.0652
7.5877


2.6813
−1.1271
7.5877


2.8076
−1.1831
7.5877


2.9206
−1.2335
7.5877


3.0201
−1.2781
7.5877


3.1063
−1.3170
7.5877


3.1792
−1.3500
7.5877


3.2415
−1.3782
7.5877


3.2939
−1.4018
7.5877


3.3370
−1.4212
7.5877


3.3716
−1.4366
7.5877


3.3982
−1.4483
7.5877


3.4181
−1.4572
7.5877


3.4314
−1.4693
7.5877


3.4356
−1.4833
7.5877


3.4342
−1.4942
7.5877


3.4291
−1.5038
7.5877


3.4175
−1.5125
7.5877


3.3995
−1.5139
7.5877


3.3781
−1.5086
7.5877


3.3497
−1.5015
7.5877


3.3126
−1.4924
7.5877


3.2663
−1.4812
7.5877


3.2100
−1.4677
7.5877


3.1429
−1.4519
7.5877


3.0644
−1.4334
7.5877


2.9716
−1.4116
7.5877


2.8645
−1.3862
7.5877


2.7433
−1.3573
7.5877


2.6078
−1.3247
7.5877


2.4581
−1.2884
7.5877


2.2945
−1.2479
7.5877


2.1241
−1.2045
7.5877


1.9473
−1.1576
7.5877


1.7641
−1.1063
7.5877


1.5751
−1.0499
7.5877


1.3805
−0.9871
7.5877


1.1807
−0.9168
7.5877


0.9760
−0.8383
7.5877


0.7731
−0.7542
7.5877


0.5720
−0.6651
7.5877


0.3723
−0.5719
7.5877


0.1739
−0.4753
7.5877


−0.0233
−0.3762
7.5877


−0.2196
−0.2752
7.5877


−0.4150
−0.1727
7.5877


−0.6099
−0.0689
7.5877


−0.8042
0.0357
7.5877


−0.9981
0.1411
7.5877


−1.1918
0.2470
7.5877


−1.3787
0.3499
7.5877


−1.5588
0.4498
7.5877


−1.7321
0.5470
7.5877


−1.8983
0.6416
7.5877


−2.0576
0.7337
7.5877


−2.2098
0.8232
7.5877


−2.3550
0.9101
7.5877


−2.4931
0.9944
7.5877


−2.6180
1.0723
7.5877


−2.7296
1.1436
7.5877


−2.8281
1.2081
7.5877


−2.9197
1.2696
7.5877


−2.9985
1.3239
7.5877


−3.0585
1.3663
7.5877


−3.1046
1.4029
7.5877


−3.1355
1.4342
7.5877


−3.1542
1.4616
7.5877


−3.1606
1.4787
7.5877


−3.1615
1.4905
7.5877


−3.1603
1.4963
7.5877


−3.1591
1.4990
7.5877


−3.1537
1.6836
9.0620


−3.1528
1.6848
9.0620


−3.1505
1.6868
9.0620


−3.1449
1.6892
9.0620


−3.1329
1.6898
9.0620


−3.1146
1.6851
9.0620


−3.0843
1.6702
9.0620


−3.0448
1.6486
9.0620


−2.9920
1.6200
9.0620


−2.9257
1.5848
9.0620


−2.8389
1.5403
9.0620


−2.7380
1.4903
9.0620


−2.6299
1.4381
9.0620


−2.5077
1.3805
9.0620


−2.3714
1.3177
9.0620


−2.2209
1.2500
9.0620


−2.0630
1.1804
9.0620


−1.8981
1.1080
9.0620


−1.7264
1.0324
9.0620


−1.5484
0.9527
9.0620


−1.3640
0.8686
9.0620


−1.1737
0.7796
9.0620


−0.9777
0.6852
9.0620


−0.7762
0.5849
9.0620


−0.5761
0.4818
9.0620


−0.3775
0.3759
9.0620


−0.1804
0.2671
9.0620


0.0152
0.1558
9.0620


0.2094
0.0423
9.0620


0.4025
−0.0732
9.0620


0.5946
−0.1903
9.0620


0.7859
−0.3087
9.0620


0.9768
−0.4278
9.0620


1.1676
−0.5471
9.0620


1.3587
−0.6657
9.0620


1.5443
−0.7792
9.0620


1.7244
−0.8871
9.0620


1.8991
−0.9892
9.0620


2.0685
−1.0857
9.0620


2.2324
−1.1767
9.0620


2.3904
−1.2629
9.0620


2.5424
−1.3445
9.0620


2.6814
−1.4185
9.0620


2.8074
−1.4851
9.0620


2.9203
−1.5445
9.0620


3.0198
−1.5969
9.0620


3.1061
−1.6423
9.0620


3.1791
−1.6807
9.0620


3.2416
−1.7133
9.0620


3.2943
−1.7404
9.0620


3.3377
−1.7626
9.0620


3.3725
−1.7802
9.0620


3.3993
−1.7937
9.0620


3.4195
−1.8038
9.0620


3.4347
−1.8142
9.0620


3.4399
−1.8278
9.0620


3.4383
−1.8388
9.0620


3.4320
−1.8481
9.0620


3.4184
−1.8542
9.0620


3.4000
−1.8503
9.0620


3.3786
−1.8432
9.0620


3.3500
−1.8337
9.0620


3.3127
−1.8214
9.0620


3.2662
−1.8062
9.0620


3.2095
−1.7877
9.0620


3.1421
−1.7659
9.0620


3.0632
−1.7404
9.0620


2.9700
−1.7099
9.0620


2.8627
−1.6742
9.0620


2.7413
−1.6332
9.0620


2.6059
−1.5867
9.0620


2.4566
−1.5343
9.0620


2.2937
−1.4755
9.0620


2.1245
−1.4119
9.0620


1.9495
−1.3428
9.0620


1.7689
−1.2675
9.0620


1.5830
−1.1852
9.0620


1.3919
−1.0956
9.0620


1.1957
−0.9988
9.0620


0.9945
−0.8949
9.0620


0.7949
−0.7880
9.0620


0.5967
−0.6788
9.0620


0.3993
−0.5680
9.0620


0.2025
−0.4561
9.0620


0.0061
−0.3435
9.0620


−0.1900
−0.2304
9.0620


−0.3857
−0.1167
9.0620


−0.5812
−0.0024
9.0620


−0.7763
0.1123
9.0620


−0.9712
0.2275
9.0620


−1.1659
0.3431
9.0620


−1.3538
0.4552
9.0620


−1.5349
0.5640
9.0620


−1.7092
0.6695
9.0620


−1.8767
0.7718
9.0620


−2.0372
0.8708
9.0620


−2.1907
0.9670
9.0620


−2.3370
1.0604
9.0620


−2.4758
1.1514
9.0620


−2.6011
1.2355
9.0620


−2.7131
1.3124
9.0620


−2.8120
1.3817
9.0620


−2.9039
1.4477
9.0620


−2.9830
1.5057
9.0620


−3.0434
1.5510
9.0620


−3.0912
1.5879
9.0620


−3.1247
1.6183
9.0620


−3.1459
1.6447
9.0620


−3.1542
1.6616
9.0620


−3.1565
1.6734
9.0620


−3.1557
1.6794
9.0620


−3.1545
1.6822
9.0620


−3.1672
1.8795
10.6014


−3.1661
1.8807
10.6014


−3.1634
1.8823
10.6014


−3.1572
1.8835
10.6014


−3.1449
1.8814
10.6014


−3.1273
1.8732
10.6014


−3.0976
1.8549
10.6014


−3.0580
1.8304
10.6014


−3.0049
1.7984
10.6014


−2.9381
1.7591
10.6014


−2.8506
1.7090
10.6014


−2.7490
1.6525
10.6014


−2.6400
1.5933
10.6014


−2.5169
1.5276
10.6014


−2.3796
1.4557
10.6014


−2.2280
1.3776
10.6014


−2.0693
1.2965
10.6014


−1.9036
1.2119
10.6014


−1.7312
1.1235
10.6014


−1.5522
1.0308
10.6014


−1.3672
0.9332
10.6014


−1.1762
0.8301
10.6014


−0.9797
0.7212
10.6014


−0.7777
0.6061
10.6014


−0.5770
0.4884
10.6014


−0.3778
0.3683
10.6014


−0.1801
0.2458
10.6014


0.0161
0.1210
10.6014


0.2108
−0.0059
10.6014


0.4043
−0.1348
10.6014


0.5965
−0.2656
10.6014


0.7877
−0.3980
10.6014


0.9781
−0.5316
10.6014


1.1681
−0.6657
10.6014


1.3581
−0.7999
10.6014


1.5421
−0.9290
10.6014


1.7205
−1.0527
10.6014


1.8934
−1.1706
10.6014


2.0610
−1.2827
10.6014


2.2231
−1.3890
10.6014


2.3798
−1.4893
10.6014


2.5310
−1.5841
10.6014


2.6697
−1.6694
10.6014


2.7957
−1.7456
10.6014


2.9090
−1.8131
10.6014


3.0093
−1.8720
10.6014


3.0965
−1.9227
10.6014


3.1704
−1.9652
10.6014


3.2337
−2.0014
10.6014


3.2869
−2.0317
10.6014


3.3307
−2.0566
10.6014


3.3658
−2.0766
10.6014


3.3927
−2.0919
10.6014


3.4129
−2.1034
10.6014


3.4295
−2.1134
10.6014


3.4365
−2.1269
10.6014


3.4348
−2.1384
10.6014


3.4273
−2.1472
10.6014


3.4124
−2.1503
10.6014


3.3941
−2.1436
10.6014


3.3724
−2.1351
10.6014


3.3434
−2.1237
10.6014


3.3058
−2.1088
10.6014


3.2588
−2.0900
10.6014


3.2018
−2.0670
10.6014


3.1342
−2.0393
10.6014


3.0551
−2.0065
10.6014


2.9619
−1.9673
10.6014


2.8545
−1.9216
10.6014


2.7333
−1.8690
10.6014


2.5984
−1.8088
10.6014


2.4502
−1.7406
10.6014


2.2890
−1.6636
10.6014


2.1221
−1.5806
10.6014


1.9496
−1.4914
10.6014


1.7717
−1.3956
10.6014


1.5886
−1.2929
10.6014


1.4002
−1.1835
10.6014


1.2068
−1.0675
10.6014


1.0081
−0.9451
10.6014


0.8107
−0.8209
10.6014


0.6139
−0.6955
10.6014


0.4176
−0.5694
10.6014


0.2215
−0.4431
10.6014


0.0253
−0.3168
10.6014


−0.1708
−0.1905
10.6014


−0.3669
−0.0640
10.6014


−0.5628
0.0626
10.6014


−0.7586
0.1895
10.6014


−0.9542
0.3167
10.6014


−1.1496
0.4441
10.6014


−1.3385
0.5674
10.6014


−1.5208
0.6865
10.6014


−1.6964
0.8016
10.6014


−1.8653
0.9128
10.6014


−2.0272
1.0204
10.6014


−2.1821
1.1246
10.6014


−2.3300
1.2251
10.6014


−2.4707
1.3225
10.6014


−2.5977
1.4122
10.6014


−2.7114
1.4939
10.6014


−2.8118
1.5674
10.6014


−2.9051
1.6373
10.6014


−2.9855
1.6987
10.6014


−3.0468
1.7466
10.6014


−3.0955
1.7853
10.6014


−3.1312
1.8153
10.6014


−3.1551
1.8407
10.6014


−3.1654
1.8572
10.6014


−3.1692
1.8690
10.6014


−3.1690
1.8752
10.6014


−3.1680
1.8782
10.6014


−3.0639
2.0638
12.7118


−3.0627
2.0648
12.7118


−3.0598
2.0660
12.7118


−3.0535
2.0658
12.7118


−3.0417
2.0615
12.7118


−3.0253
2.0510
12.7118


−2.9969
2.0304
12.7118


−2.9588
2.0032
12.7118


−2.9075
1.9677
12.7118


−2.8430
1.9239
12.7118


−2.7585
1.8679
12.7118


−2.6603
1.8045
12.7118


−2.5548
1.7379
12.7118


−2.4357
1.6638
12.7118


−2.3028
1.5822
12.7118


−2.1563
1.4931
12.7118


−2.0029
1.4002
12.7118


−1.8429
1.3032
12.7118


−1.6766
1.2016
12.7118


−1.5039
1.0954
12.7118


−1.3253
0.9841
12.7118


−1.1407
0.8675
12.7118


−0.9505
0.7454
12.7118


−0.7549
0.6172
12.7118


−0.5606
0.4872
12.7118


−0.3675
0.3551
12.7118


−0.1757
0.2212
12.7118


0.0147
0.0855
12.7118


0.2039
−0.0519
12.7118


0.3920
−0.1907
12.7118


0.5792
−0.3310
12.7118


0.7654
−0.4724
12.7118


0.9509
−0.6149
12.7118


1.1356
−0.7583
12.7118


1.3198
−0.9024
12.7118


1.4974
−1.0423
12.7118


1.6693
−1.1769
12.7118


1.8356
−1.3059
12.7118


1.9963
−1.4294
12.7118


2.1517
−1.5470
12.7118


2.3022
−1.6581
12.7118


2.4476
−1.7631
12.7118


2.5812
−1.8576
12.7118


2.7029
−1.9421
12.7118


2.8124
−2.0168
12.7118


2.9094
−2.0820
12.7118


2.9938
−2.1382
12.7118


3.0654
−2.1855
12.7118


3.1266
−2.2257
12.7118


3.1781
−2.2595
12.7118


3.2205
−2.2872
12.7118


3.2545
−2.3094
12.7118


3.2806
−2.3265
12.7118


3.3001
−2.3393
12.7118


3.3164
−2.3499
12.7118


3.3253
−2.3623
12.7118


3.3236
−2.3738
12.7118


3.3150
−2.3817
12.7118


3.2998
−2.3806
12.7118


3.2821
−2.3723
12.7118


3.2608
−2.3623
12.7118


3.2325
−2.3489
12.7118


3.1958
−2.3314
12.7118


3.1499
−2.3093
12.7118


3.0943
−2.2823
12.7118


3.0283
−2.2498
12.7118


2.9514
−2.2111
12.7118


2.8608
−2.1648
12.7118


2.7567
−2.1107
12.7118


2.6393
−2.0480
12.7118


2.5092
−1.9764
12.7118


2.3667
−1.8951
12.7118


2.2123
−1.8035
12.7118


2.0528
−1.7053
12.7118


1.8882
−1.6007
12.7118


1.7185
−1.4894
12.7118


1.5440
−1.3712
12.7118


1.3642
−1.2468
12.7118


1.1787
−1.1168
12.7118


0.9874
−0.9813
12.7118


0.7967
−0.8451
12.7118


0.6062
−0.7086
12.7118


0.4158
−0.5718
12.7118


0.2257
−0.4347
12.7118


0.0358
−0.2973
12.7118


−0.1540
−0.1598
12.7118


−0.3437
−0.0221
12.7118


−0.5332
0.1157
12.7118


−0.7227
0.2537
12.7118


−0.9122
0.3917
12.7118


−1.1015
0.5299
12.7118


−1.2845
0.6635
12.7118


−1.4609
0.7928
12.7118


−1.6308
0.9178
12.7118


−1.7942
1.0386
12.7118


−1.9509
1.1551
12.7118


−2.1011
1.2675
12.7118


−2.2446
1.3755
12.7118


−2.3813
1.4797
12.7118


−2.5049
1.5754
12.7118


−2.6156
1.6621
12.7118


−2.7134
1.7399
12.7118


−2.8044
1.8138
12.7118


−2.8825
1.8787
12.7118


−2.9420
1.9293
12.7118


−2.9893
1.9702
12.7118


−3.0246
2.0010
12.7118


−3.0495
2.0258
12.7118


−3.0608
2.0417
12.7118


−3.0654
2.0533
12.7118


−3.0657
2.0595
12.7118


−3.0648
2.0625
12.7118


−3.0158
2.1443
13.4430


−3.0146
2.1453
13.4430


−3.0116
2.1463
13.4430


−3.0053
2.1459
13.4430


−2.9936
2.1412
13.4430


−2.9774
2.1302
13.4430


−2.9493
2.1090
13.4430


−2.9116
2.0809
13.4430


−2.8610
2.0441
13.4430


−2.7972
1.9986
13.4430


−2.7138
1.9404
13.4430


−2.6169
1.8741
13.4430


−2.5129
1.8043
13.4430


−2.3956
1.7263
13.4430


−2.2649
1.6401
13.4430


−2.1208
1.5459
13.4430


−1.9700
1.4475
13.4430


−1.8127
1.3447
13.4430


−1.6492
1.2373
13.4430


−1.4795
1.1249
13.4430


−1.3038
1.0074
13.4430


−1.1221
0.8848
13.4430


−0.9347
0.7568
13.4430


−0.7415
0.6233
13.4430


−0.5491
0.4887
13.4430


−0.3576
0.3528
13.4430


−0.1671
0.2155
13.4430


0.0222
0.0767
13.4430


0.2104
−0.0636
13.4430


0.3975
−0.2055
13.4430


0.5836
−0.3486
13.4430


0.7688
−0.4930
13.4430


0.9531
−0.6384
13.4430


1.1367
−0.7848
13.4430


1.3196
−0.9321
13.4430


1.4958
−1.0752
13.4430


1.6659
−1.2134
13.4430


1.8302
−1.3464
13.4430


1.9884
−1.4743
13.4430


2.1410
−1.5968
13.4430


2.2884
−1.7133
13.4430


2.4306
−1.8236
13.4430


2.5615
−1.9231
13.4430


2.6808
−2.0120
13.4430


2.7881
−2.0906
13.4430


2.8832
−2.1594
13.4430


2.9660
−2.2187
13.4430


3.0361
−2.2687
13.4430


3.0962
−2.3112
13.4430


3.1467
−2.3468
13.4430


3.1884
−2.3760
13.4430


3.2217
−2.3994
13.4430


3.2474
−2.4173
13.4430


3.2666
−2.4308
13.4430


3.2827
−2.4420
13.4430


3.2921
−2.4540
13.4430


3.2905
−2.4655
13.4430


3.2815
−2.4730
13.4430


3.2664
−2.4702
13.4430


3.2488
−2.4615
13.4430


3.2277
−2.4510
13.4430


3.1996
−2.4369
13.4430


3.1631
−2.4185
13.4430


3.1176
−2.3953
13.4430


3.0624
−2.3670
13.4430


2.9969
−2.3328
13.4430


2.9207
−2.2922
13.4430


2.8309
−2.2434
13.4430


2.7280
−2.1861
13.4430


2.6123
−2.1196
13.4430


2.4843
−2.0434
13.4430


2.3444
−1.9567
13.4430


2.1928
−1.8592
13.4430


2.0363
−1.7549
13.4430


1.8747
−1.6442
13.4430


1.7078
−1.5272
13.4430


1.5356
−1.4039
13.4430


1.3577
−1.2750
13.4430


1.1739
−1.1410
13.4430


0.9843
−1.0016
13.4430


0.7949
−0.8619
13.4430


0.6058
−0.7219
13.4430


0.4167
−0.5817
13.4430


0.2279
−0.4413
13.4430


0.0392
−0.3006
13.4430


−0.1492
−0.1596
13.4430


−0.3375
−0.0184
13.4430


−0.5254
0.1233
13.4430


−0.7129
0.2654
13.4430


−0.9000
0.4082
13.4430


−1.0866
0.5516
13.4430


−1.2665
0.6909
13.4430


−1.4397
0.8259
13.4430


−1.6064
0.9565
13.4430


−1.7667
1.0827
13.4430


−1.9205
1.2044
13.4430


−2.0677
1.3217
13.4430


−2.2086
1.4345
13.4430


−2.3428
1.5430
13.4430


−2.4642
1.6423
13.4430


−2.5731
1.7322
13.4430


−2.6694
1.8127
13.4430


−2.7591
1.8889
13.4430


−2.8362
1.9557
13.4430


−2.8950
2.0076
13.4430


−2.9418
2.0494
13.4430


−2.9767
2.0809
13.4430


−3.0015
2.1060
13.4430


−3.0127
2.1221
13.4430


−3.0173
2.1337
13.4430


−3.0176
2.1399
13.4430


−3.0167
2.1429
13.4430


−2.9601
2.3369
15.0640


−2.9588
2.3379
15.0640


−2.9556
2.3387
15.0640


−2.9492
2.3378
15.0640


−2.9376
2.3324
15.0640


−2.9214
2.3207
15.0640


−2.8935
2.2981
15.0640


−2.8561
2.2682
15.0640


−2.8060
2.2285
15.0640


−2.7429
2.1796
15.0640


−2.6602
2.1169
15.0640


−2.5639
2.0458
15.0640


−2.4605
1.9709
15.0640


−2.3437
1.8872
15.0640


−2.2134
1.7949
15.0640


−2.0698
1.6939
15.0640


−1.9195
1.5884
15.0640


−1.7628
1.4782
15.0640


−1.5998
1.3629
15.0640


−1.4309
1.2424
15.0640


−1.2560
1.1164
15.0640


−1.0755
0.9846
15.0640


−0.8895
0.8467
15.0640


−0.6983
0.7026
15.0640


−0.5083
0.5569
15.0640


−0.3196
0.4095
15.0640


−0.1322
0.2604
15.0640


0.0539
0.1097
15.0640


0.2387
−0.0425
15.0640


0.4224
−0.1962
15.0640


0.6049
−0.3511
15.0640


0.7864
−0.5073
15.0640


0.9668
−0.6649
15.0640


1.1462
−0.8235
15.0640


1.3249
−0.9829
15.0640


1.4971
−1.1376
15.0640


1.6633
−1.2871
15.0640


1.8236
−1.4312
15.0640


1.9780
−1.5698
15.0640


2.1270
−1.7027
15.0640


2.2706
−1.8294
15.0640


2.4092
−1.9499
15.0640


2.5367
−2.0588
15.0640


2.6527
−2.1565
15.0640


2.7572
−2.2431
15.0640


2.8498
−2.3190
15.0640


2.9303
−2.3845
15.0640


2.9986
−2.4397
15.0640


3.0571
−2.4868
15.0640


3.1063
−2.5262
15.0640


3.1469
−2.5585
15.0640


3.1793
−2.5844
15.0640


3.2043
−2.6043
15.0640


3.2231
−2.6192
15.0640


3.2387
−2.6316
15.0640


3.2487
−2.6437
15.0640


3.2470
−2.6554
15.0640


3.2372
−2.6621
15.0640


3.2221
−2.6577
15.0640


3.2043
−2.6483
15.0640


3.1831
−2.6371
15.0640


3.1548
−2.6220
15.0640


3.1181
−2.6022
15.0640


3.0724
−2.5774
15.0640


3.0169
−2.5469
15.0640


2.9513
−2.5099
15.0640


2.8750
−2.4658
15.0640


2.7853
−2.4127
15.0640


2.6827
−2.3504
15.0640


2.5675
−2.2780
15.0640


2.4404
−2.1949
15.0640


2.3018
−2.1005
15.0640


2.1520
−1.9942
15.0640


1.9977
−1.8803
15.0640


1.8390
−1.7591
15.0640


1.6756
−1.6306
15.0640


1.5073
−1.4953
15.0640


1.3335
−1.3539
15.0640


1.1540
−1.2071
15.0640


0.9682
−1.0551
15.0640


0.7824
−0.9032
15.0640


0.5966
−0.7513
15.0640


0.4110
−0.5992
15.0640


0.2256
−0.4467
15.0640


0.0406
−0.2939
15.0640


−0.1441
−0.1406
15.0640


−0.3284
0.0131
15.0640


−0.5124
0.1672
15.0640


−0.6961
0.3216
15.0640


−0.8796
0.4762
15.0640


−1.0630
0.6310
15.0640


−1.2401
0.7809
15.0640


−1.4107
0.9260
15.0640


−1.5750
1.0663
15.0640


−1.7329
1.2017
15.0640


−1.8844
1.3323
15.0640


−2.0295
1.4580
15.0640


−2.1683
1.5787
15.0640


−2.3005
1.6949
15.0640


−2.4201
1.8012
15.0640


−2.5272
1.8975
15.0640


−2.6218
1.9837
15.0640


−2.7097
2.0653
15.0640


−2.7852
2.1368
15.0640


−2.8429
2.1922
15.0640


−2.8888
2.2369
15.0640


−2.9229
2.2707
15.0640


−2.9470
2.2974
15.0640


−2.9578
2.3141
15.0640


−2.9620
2.3262
15.0640


−2.9621
2.3326
15.0640


−2.9610
2.3356
15.0640


−2.9426
2.4170
15.6890


−2.9413
2.4180
15.6890


−2.9381
2.4187
15.6890


−2.9317
2.4177
15.6890


−2.9200
2.4121
15.6890


−2.9038
2.4001
15.6890


−2.8759
2.3768
15.6890


−2.8386
2.3459
15.6890


−2.7886
2.3051
15.6890


−2.7256
2.2546
15.6890


−2.6429
2.1901
15.6890


−2.5465
2.1167
15.6890


−2.4431
2.0394
15.6890


−2.3262
1.9532
15.6890


−2.1959
1.8579
15.6890


−2.0522
1.7537
15.6890


−1.9018
1.6448
15.6890


−1.7450
1.5311
15.6890


−1.5818
1.4124
15.6890


−1.4126
1.2883
15.6890


−1.2375
1.1586
15.6890


−1.0569
1.0228
15.6890


−0.8709
0.8807
15.6890


−0.6797
0.7322
15.6890


−0.4897
0.5822
15.6890


−0.3010
0.4305
15.6890


−0.1136
0.2772
15.6890


0.0724
0.1223
15.6890


0.2570
−0.0342
15.6890


0.4403
−0.1923
15.6890


0.6224
−0.3518
15.6890


0.8032
−0.5128
15.6890


0.9828
−0.6752
15.6890


1.1615
−0.8385
15.6890


1.3395
−1.0026
15.6890


1.5113
−1.1616
15.6890


1.6770
−1.3153
15.6890


1.8368
−1.4634
15.6890


1.9907
−1.6060
15.6890


2.1388
−1.7431
15.6890


2.2815
−1.8741
15.6890


2.4189
−1.9988
15.6890


2.5452
−2.1119
15.6890


2.6600
−2.2135
15.6890


2.7634
−2.3038
15.6890


2.8551
−2.3828
15.6890


2.9349
−2.4509
15.6890


3.0026
−2.5084
15.6890


3.0605
−2.5574
15.6890


3.1093
−2.5984
15.6890


3.1495
−2.6321
15.6890


3.1817
−2.6590
15.6890


3.2065
−2.6797
15.6890


3.2251
−2.6953
15.6890


3.2406
−2.7082
15.6890


3.2504
−2.7204
15.6890


3.2485
−2.7320
15.6890


3.2385
−2.7386
15.6890


3.2233
−2.7339
15.6890


3.2054
−2.7244
15.6890


3.1840
−2.7129
15.6890


3.1555
−2.6976
15.6890


3.1185
−2.6774
15.6890


3.0724
−2.6521
15.6890


3.0165
−2.6210
15.6890


2.9504
−2.5831
15.6890


2.8737
−2.5378
15.6890


2.7838
−2.4832
15.6890


2.6809
−2.4190
15.6890


2.5655
−2.3443
15.6890


2.4381
−2.2586
15.6890


2.2991
−2.1611
15.6890


2.1490
−2.0513
15.6890


1.9944
−1.9337
15.6890


1.8352
−1.8087
15.6890


1.6716
−1.6766
15.6890


1.5032
−1.5376
15.6890


1.3296
−1.3922
15.6890


1.1503
−1.2410
15.6890


0.9651
−1.0843
15.6890


0.7800
−0.9275
15.6890


0.5949
−0.7707
15.6890


0.4100
−0.6136
15.6890


0.2254
−0.4563
15.6890


0.0410
−0.2987
15.6890


−0.1431
−0.1406
15.6890


−0.3268
0.0178
15.6890


−0.5102
0.1767
15.6890


−0.6932
0.3360
15.6890


−0.8758
0.4957
15.6890


−1.0583
0.6556
15.6890


−1.2345
0.8105
15.6890


−1.4043
0.9603
15.6890


−1.5677
1.1052
15.6890


−1.7247
1.2451
15.6890


−1.8753
1.3800
15.6890


−2.0194
1.5100
15.6890


−2.1573
1.6349
15.6890


−2.2886
1.7550
15.6890


−2.4073
1.8649
15.6890


−2.5136
1.9643
15.6890


−2.6076
2.0533
15.6890


−2.6949
2.1375
15.6890


−2.7698
2.2113
15.6890


−2.8271
2.2684
15.6890


−2.8725
2.3145
15.6890


−2.9063
2.3493
15.6890


−2.9302
2.3767
15.6890


−2.9407
2.3939
15.6890


−2.9447
2.4062
15.6890


−2.9447
2.4126
15.6890


−2.9436
2.4157
15.6890


−2.9337
2.4848
16.1940


−2.9323
2.4858
16.1940


−2.9291
2.4866
16.1940


−2.9226
2.4855
16.1940


−2.9109
2.4797
16.1940


−2.8946
2.4675
16.1940


−2.8668
2.4436
16.1940


−2.8295
2.4119
16.1940


−2.7794
2.3701
16.1940


−2.7163
2.3184
16.1940


−2.6336
2.2522
16.1940


−2.5373
2.1769
16.1940


−2.4338
2.0975
16.1940


−2.3168
2.0090
16.1940


−2.1862
1.9115
16.1940


−2.0419
1.8050
16.1940


−1.8909
1.6938
16.1940


−1.7335
1.5777
16.1940


−1.5697
1.4564
16.1940


−1.3998
1.3297
16.1940


−1.2242
1.1970
16.1940


−1.0432
1.0580
16.1940


−0.8569
0.9125
16.1940


−0.6655
0.7603
16.1940


−0.4755
0.6065
16.1940


−0.2867
0.4510
16.1940


−0.0994
0.2938
16.1940


0.0865
0.1350
16.1940


0.2709
−0.0254
16.1940


0.4538
−0.1876
16.1940


0.6355
−0.3512
16.1940


0.8160
−0.5161
16.1940


0.9952
−0.6824
16.1940


1.1737
−0.8496
16.1940


1.3517
−1.0173
16.1940


1.5234
−1.1797
16.1940


1.6891
−1.3367
16.1940


1.8488
−1.4882
16.1940


2.0021
−1.6345
16.1940


2.1494
−1.7753
16.1940


2.2911
−1.9102
16.1940


2.4275
−2.0388
16.1940


2.5528
−2.1554
16.1940


2.6667
−2.2604
16.1940


2.7692
−2.3536
16.1940


2.8604
−2.4351
16.1940


2.9397
−2.5054
16.1940


3.0069
−2.5647
16.1940


3.0644
−2.6153
16.1940


3.1129
−2.6576
16.1940


3.1529
−2.6924
16.1940


3.1849
−2.7202
16.1940


3.2095
−2.7416
16.1940


3.2280
−2.7576
16.1940


3.2434
−2.7709
16.1940


3.2533
−2.7834
16.1940


3.2513
−2.7952
16.1940


3.2411
−2.8017
16.1940


3.2258
−2.7967
16.1940


3.2078
−2.7870
16.1940


3.1862
−2.7753
16.1940


3.1575
−2.7596
16.1940


3.1202
−2.7391
16.1940


3.0738
−2.7133
16.1940


3.0175
−2.6815
16.1940


2.9509
−2.6430
16.1940


2.8737
−2.5967
16.1940


2.7831
−2.5410
16.1940


2.6796
−2.4753
16.1940


2.5636
−2.3990
16.1940


2.4358
−2.3112
16.1940


2.2965
−2.2114
16.1940


2.1462
−2.0988
16.1940


1.9916
−1.9783
16.1940


1.8323
−1.8505
16.1940


1.6681
−1.7155
16.1940


1.4991
−1.5737
16.1940


1.3248
−1.4256
16.1940


1.1447
−1.2717
16.1940


0.9589
−1.1119
16.1940


0.7734
−0.9517
16.1940


0.5882
−0.7912
16.1940


0.4035
−0.6302
16.1940


0.2191
−0.4687
16.1940


0.0350
−0.3070
16.1940


−0.1487
−0.1448
16.1940


−0.3319
0.0179
16.1940


−0.5147
0.1811
16.1940


−0.6971
0.3448
16.1940


−0.8790
0.5090
16.1940


−1.0606
0.6735
16.1940


−1.2359
0.8329
16.1940


−1.4049
0.9871
16.1940


−1.5676
1.1360
16.1940


−1.7241
1.2797
16.1940


−1.8741
1.4183
16.1940


−2.0176
1.5519
16.1940


−2.1548
1.6803
16.1940


−2.2855
1.8038
16.1940


−2.4034
1.9170
16.1940


−2.5090
2.0194
16.1940


−2.6022
2.1111
16.1940


−2.6887
2.1979
16.1940


−2.7630
2.2738
16.1940


−2.8197
2.3326
16.1940


−2.8648
2.3800
16.1940


−2.8984
2.4157
16.1940


−2.9219
2.4439
16.1940


−2.9322
2.4615
16.1940


−2.9360
2.4740
16.1940


−2.9359
2.4805
16.1940


−2.9347
2.4835
16.1940


−2.9250
2.5693
16.8140


−2.9236
2.5703
16.8140


−2.9203
2.5711
16.8140


−2.9138
2.5699
16.8140


−2.9019
2.5640
16.8140


−2.8856
2.5515
16.8140


−2.8577
2.5269
16.8140


−2.8204
2.4943
16.8140


−2.7702
2.4513
16.8140


−2.7071
2.3981
16.8140


−2.6243
2.3298
16.8140


−2.5280
2.2521
16.8140


−2.4244
2.1702
16.8140


−2.3071
2.0790
16.8140


−2.1759
1.9787
16.8140


−2.0307
1.8696
16.8140


−1.8788
1.7557
16.8140


−1.7204
1.6366
16.8140


−1.5558
1.5121
16.8140


−1.3852
1.3819
16.8140


−1.2090
1.2454
16.8140


−1.0274
1.1024
16.8140


−0.8409
0.9525
16.8140


−0.6493
0.7956
16.8140


−0.4591
0.6370
16.8140


−0.2703
0.4767
16.8140


−0.0829
0.3149
16.8140


0.1031
0.1514
16.8140


0.2875
−0.0137
16.8140


0.4705
−0.1805
16.8140


0.6522
−0.3487
16.8140


0.8326
−0.5182
16.8140


1.0118
−0.6892
16.8140


1.1900
−0.8611
16.8140


1.3676
−1.0338
16.8140


1.5386
−1.2013
16.8140


1.7035
−1.3633
16.8140


1.8621
−1.5199
16.8140


2.0143
−1.6712
16.8140


2.1605
−1.8168
16.8140


2.3012
−1.9563
16.8140


2.4366
−2.0894
16.8140


2.5610
−2.2101
16.8140


2.6742
−2.3187
16.8140


2.7760
−2.4152
16.8140


2.8666
−2.4997
16.8140


2.9454
−2.5725
16.8140


3.0122
−2.6340
16.8140


3.0694
−2.6865
16.8140


3.1176
−2.7304
16.8140


3.1573
−2.7665
16.8140


3.1891
−2.7953
16.8140


3.2135
−2.8175
16.8140


3.2319
−2.8341
16.8140


3.2472
−2.8480
16.8140


3.2570
−2.8609
16.8140


3.2548
−2.8728
16.8140


3.2444
−2.8793
16.8140


3.2290
−2.8741
16.8140


3.2110
−2.8639
16.8140


3.1893
−2.8517
16.8140


3.1605
−2.8353
16.8140


3.1231
−2.8140
16.8140


3.0763
−2.7873
16.8140


3.0197
−2.7544
16.8140


2.9527
−2.7147
16.8140


2.8749
−2.6673
16.8140


2.7835
−2.6104
16.8140


2.6789
−2.5433
16.8140


2.5619
−2.4655
16.8140


2.4330
−2.3759
16.8140


2.2926
−2.2739
16.8140


2.1415
−2.1587
16.8140


1.9863
−2.0352
16.8140


1.8265
−1.9039
16.8140


1.6619
−1.7652
16.8140


1.4926
−1.6194
16.8140


1.3179
−1.4671
16.8140


1.1374
−1.3090
16.8140


0.9511
−1.1448
16.8140


0.7652
−0.9803
16.8140


0.5796
−0.8154
16.8140


0.3946
−0.6497
16.8140


0.2101
−0.4836
16.8140


0.0260
−0.3171
16.8140


−0.1576
−0.1499
16.8140


−0.3406
0.0178
16.8140


−0.5231
0.1862
16.8140


−0.7049
0.3553
16.8140


−0.8862
0.5250
16.8140


−1.0669
0.6952
16.8140


−1.2411
0.8603
16.8140


−1.4092
1.0199
16.8140


−1.5711
1.1738
16.8140


−1.7268
1.3223
16.8140


−1.8761
1.4656
16.8140


−2.0188
1.6038
16.8140


−2.1552
1.7365
16.8140


−2.2850
1.8643
16.8140


−2.4018
1.9815
16.8140


−2.5062
2.0878
16.8140


−2.5983
2.1829
16.8140


−2.6838
2.2730
16.8140


−2.7572
2.3517
16.8140


−2.8132
2.4125
16.8140


−2.8578
2.4615
16.8140


−2.8910
2.4984
16.8140


−2.9141
2.5276
16.8140


−2.9241
2.5457
16.8140


−2.9276
2.5584
16.8140


−2.9273
2.5650
16.8140


−2.9260
2.5680
16.8140









It should be appreciated that the nominal airfoil profile disclosed in TABLE A may be scaled up or down geometrically for use in other similar airfoil designs. Consequently, the X, Y and Z coordinates of the nominal airfoil profile may be a function of a constant. That is, the X, Y and Z coordinate values may be multiplied or divided by the same constant or number to provide a “scaled-up” or “scaled-down” version of the airfoil profile, while retaining the airfoil section shape disclosed herein.


It should also be appreciated that the airfoil profile defined by the coordinate values of TABLE A can generally be applied in any suitable gas turbine compressor known in the art including, but not limited to, various compressors provided by General Electric, such as “7F” compressors, “7FA” compressors, “7FA+” compressors, and “7FA+e” compressors. Additionally, it should be appreciated that the airfoil profile defined by the coordinates of TABLE A may also be applied in any other suitable machine using and/or component having an airfoil shape.


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 include 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. An article of manufacture, the article having a nominal profile generally in accordance with Cartesian coordinate values of X, Y and Z set forth in TABLE A, and wherein X and Y are distances in inches which, when connected by smooth continuing arcs, define airfoil profile sections at each distance Z in inches, the airfoil profile sections at the Z distances being joined smoothly with one another to form a complete airfoil shape.
  • 2. The article of claim 1, wherein the article comprises an airfoil.
  • 3. The article of claim 1, wherein the nominal profile lies in an envelope within +/−0.160 inches in a direction normal to any article surface location.
  • 4. The article of claim 1, wherein the article comprises a rotor blade.
  • 5. The article of claim 4, wherein the rotor blade comprises a Stage Zero rotor blade of a compressor.
  • 6. The article of claim 1, wherein the article comprises a stator vane.
  • 7. A rotor blade including an airfoil, the airfoil having a nominal profile generally in accordance with Cartesian coordinate values of X, Y and Z set forth in TABLE A, and wherein X and Y are distances in inches which, when connected by smooth continuing arcs, define airfoil profile sections at each distance Z in inches, the airfoil profile sections at the Z distances being joined smoothly with one another to form a complete airfoil shape.
  • 8. The rotor blade of claim 7, wherein the rotor blade forms comprises a Stage Zero rotor blade of a compressor.
  • 9. The rotor blade of claim 7, wherein the nominal profile lies in an envelope within +/−0.160 inches in a direction normal to any airfoil surface location.
  • 10. A compressor comprising: a rotor wheel; anda plurality of rotor blades mounted to the rotor wheel, each of the plurality of rotor blades including an airfoil, the airfoil having a nominal profile generally in accordance with Cartesian coordinate values of X, Y and Z set forth in TABLE A, and wherein X and Y are distances in inches which, when connected by smooth continuing arcs, define airfoil profile sections at each distance Z in inches, the airfoil profile sections at the Z distances being joined smoothly with one another to form a complete airfoil shape.
  • 11. The compressor of claim 10, wherein the nominal profile lies in an envelope within +/−0.160 inches in a direction normal to any airfoil surface location.
  • 12. The compressor of claim 10, wherein the plurality of rotor blades forms part of a Stage Zero of the compressor.
US Referenced Citations (22)
Number Name Date Kind
6739839 Brown et al. May 2004 B1
6887041 Coke et al. May 2005 B2
6923623 Cleveland et al. Aug 2005 B2
7497665 King et al. Mar 2009 B2
7510378 LaMaster et al. Mar 2009 B2
7520729 McGowan et al. Apr 2009 B2
7524170 Devangada et al. Apr 2009 B2
7534092 Columbus et al. May 2009 B2
7534093 Spracher et al. May 2009 B2
7537434 Cheruku et al. May 2009 B2
7537435 Radhakrishnan et al. May 2009 B2
7540715 Latimer et al. Jun 2009 B2
7572104 Hudson et al. Aug 2009 B2
7837445 Benjamin et al. Nov 2010 B2
20080282541 Anderson et al. Nov 2008 A1
20090097982 Saindon et al. Apr 2009 A1
20090116967 Sleiman et al. May 2009 A1
20100008784 Shafique et al. Jan 2010 A1
20100061862 Bonini et al. Mar 2010 A1
20100092283 Hudson et al. Apr 2010 A1
20100092284 Bonini et al. Apr 2010 A1
20100092298 Hudson et al. Apr 2010 A1
Related Publications (1)
Number Date Country
20120308395 A1 Dec 2012 US