AIRFOIL SHAPE FOR COMPRESSOR INLET GUIDE VANE

Information

  • Patent Application
  • 20120051927
  • Publication Number
    20120051927
  • Date Filed
    August 31, 2010
    14 years ago
  • Date Published
    March 01, 2012
    12 years ago
Abstract
An article of manufacture having a nominal profile substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in TABLE A. 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 profile sections at the Z distances can be joined smoothly with one another to form a complete inlet guide vane airfoil shape.
Description
BACKGROUND OF THE INVENTION

The present invention relates to airfoils for a vane of a gas turbine. In particular, the invention relates to compressor airfoil profiles for an inlet guide vane (IGV).


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. A turbine hot gas path requires that the compressor airfoil IGV meet design goals and desired requirements of efficiency, reliability, and loading. For example, and in no way limiting of the invention, a IGV of a compressor should achieve thermal and mechanical operating requirements. Further, for example, and in no way limiting of the invention, an IGV of a compressor should achieve thermal and mechanical operating requirements for that particular stage.


Past efforts to meet design goals and desired requirements have provided coatings on the airfoil, but the coatings may not be robust enough or permanent to provide design goals and desired requirements. Accordingly, it is desirable to provide an airfoil configuration, particularly for an IGV, with a profile meet to design goals and desired requirements.


BRIEF DESCRIPTION OF THE INVENTION

In one embodiment of the invention, an article of manufacture comprises an IGV 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 A. X and Y are distances which, when connected by smooth continuing arcs, define airfoil profile sections at each distance Z in inches. The profile sections at the Z distances are joined smoothly with one another to form a complete airfoil shape.


In another embodiment according to the invention, an IGV of a compressor includes an airfoil having an uncoated nominal airfoil profile substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in TABLE A. X and Y are distances in inches which, when connected by smooth continuing arcs, define airfoil profile sections at each Z distance in inches. The profile sections at the Z distances are joined smoothly with one another to form a complete airfoil shape. X and Y distances are scalable as a function of a constant to provide a scaled-up or scaled-down airfoil.


In a further embodiment of the invention, an IGV for a compressor comprises a compressor wheel having an IGV. Each IGV has an airfoil shape. The airfoil comprises a nominal profile substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in TABLE A. X and Y are distances in inches which, when connected by smooth continuing arcs, define the airfoil profile sections at each distance Z in inches. The profile sections at the Z distances are joined smoothly with one another to form a complete IGV airfoil shape.


In a yet further embodiment of the invention, a compressor comprises a compressor wheel having an IGV, and each IGV includes an airfoil having an uncoated nominal airfoil profile substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in TABLE A. X and Y are distances which, when connected by smooth continuing arcs, define airfoil profile sections at each distance Z in inches. The profile sections at the Z distances are joined smoothly with one another to form a complete IGV airfoil shape. The X, Y and Z distances are scalable as a function of a constant to provide a scaled-up or scaled-down IGV airfoil.





BRIEF DESCRIPTION OF THE DRAWINGS


FIG. 1 is a schematic side view of a gas turbine in which an inlet guide vane according to an embodiment of the invention can be used.



FIG. 2 is a schematic front view of the gas turbine in which an inlet guide vane according to an embodiment of the invention can be used shown in FIG. 1 and taken along the line 2-2.



FIG. 3 is a schematic isometric view of an inlet guide vane according to an embodiment of the invention.



FIG. 4 is a side elevational view of an inlet guide vane according to an embodiment of the invention.



FIGS. 5 and 6 are respective top and bottom elevational views of the inlet guide vane of FIG. 4.



FIG. 7 is a side elevational view of an inlet guide vane according to an embodiment of the invention from the other side of the inlet guide vane of FIG. 4.





DETAILED DESCRIPTION OF THE INVENTION

In accordance with one embodiment of the instant invention, an article of manufacture has a nominal profile substantially 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 profile sections at the Z distances being joined smoothly with one another to form a complete IGV airfoil shape.


In accordance with one embodiment of the instant invention, there is provided an airfoil compressor shape for an IGV of a gas turbine that enhances the performance of the gas turbine. The IGV airfoil shape hereof also improves the interaction between various stages of the compressor and affords improved aerodynamic efficiency, while simultaneously reducing stage airfoil thermal and mechanical stresses.


The IGV airfoil profile, as embodied by the invention, is defined by a unique loci of points to achieve the necessary efficiency and loading requirements whereby improved compressor performance is obtained. These unique loci of points define the nominal airfoil IGV profile and are identified by the X, Y and Z Cartesian coordinates of the TABLE A that follows. The points for the coordinate values shown in TABLE A are relative to the engine centerline and for a cold, i.e., room temperature IGV vane at various cross-sections of the vane's airfoil along its length. The positive X, Y and Z directions are axial toward the exhaust end of the turbine, tangential in the direction of engine rotation and radially outwardly toward the static case, respectively. The X, Y, and Z coordinates are given in distance dimensions, e.g., units of inches, and are joined smoothly at each Z location to form a smooth continuous airfoil cross-section. Each defined IGV airfoil section in the X, Y plane is joined smoothly with adjacent airfoil sections in the Z direction to form the complete IGV airfoil shape.


It will be appreciated that an IGV airfoil heats up during use, as known by a person of ordinary skill in the art. The IGV airfoil profile will thus change as a result of mechanical loading and temperature. Accordingly, the cold or room temperature profile, for manufacturing purposes, is given by X, Y and Z coordinates. A distance of plus or minus about 0.160 inches (+/−0.160″) from the IGV nominal profile in a direction normal to any surface location along the nominal profile and which includes any coating, defines a profile envelope for this IGV airfoil, because a manufactured IGV airfoil profile may be different from the nominal airfoil profile given by the following table. The IGV airfoil shape is robust to this variation, without impairment of the mechanical and aerodynamic functions of the IGV.


The IGV airfoil, as embodied by the invention, can be scaled up or scaled down geometrically for introduction into similar turbine designs. Consequently, the X, Y and Z coordinates of the nominal IGV 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 IGV airfoil profile, while retaining the IGV airfoil section shape, as embodied by the invention.


With reference to the accompanying FIG.s, examples of an inlet guide vane according to embodiments of the invention are disclosed. For purposes of explanation, numerous specific details are shown in the drawings and set forth in the detailed description that follows in order to provide a thorough understanding of embodiments of the invention. It will be apparent, however, that embodiments of the invention may be practiced without these specific details. In other instances, well-known structures and devices are schematically shown in order to simplify the drawing.


Referring now to the drawings, FIG. 1 illustrates a flow path 1 of a gas turbine 2. The gas turbine 2 includes a compressor including a plurality of airfoils such as, but not limited to, airfoils that are part of alternating rotors 3 and stators 4, each rotor/stator pair 5 comprising a stage of the compressor. The airfoils impart kinetic energy to the airflow and therefore bring about a desired flow across the compressor including a desired pressure rise. Each airfoil has a profile that varies over the length of the blade. The airfoils turn the fluid flow, slow the fluid flow velocity (in the respective airfoil frame of reference), and yield a rise in the static pressure of the fluid flow. The configuration of the airfoil (along with its interaction with surrounding airfoils), as embodied by the invention, including its peripheral surface provides 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, among other desirable aspects of the invention. Typically, as indicated above, multiple rows of airfoil stages, such as, but not limited to, rotor/stator airfoils, are stacked to achieve a desired discharge to inlet pressure ratio. Airfoils can be secured to wheels or a case by an appropriate attachment configuration, often known as a “root”, “base” or “dovetail.”


The configuration of the airfoil and any interaction with surrounding airfoils, as embodied by the invention, that provide the desirable aspects fluid flow dynamics and laminar flow of the invention can be determined by various means. For a given airfoil downstream of the inlet guide vanes, fluid flow from a preceding/upstream airfoil intersects with the airfoil, and via the configuration of the instant airfoil, flow over and around the airfoil, as embodied by the invention, is enhanced. In particular, the fluid dynamics and laminar flow from the airfoil, as embodied by the invention, is enhanced. There is a smooth transition fluid flow from the preceding/upstream airfoil(s) and a smooth transition fluid flow to the adjacent/downstream airfoil(s). Moreover, the flow from the airfoil, as embodied by the invention, proceeds to the adjacent/downstream airfoil(s) and is enhanced due to the enhanced laminar fluid flow off of the airfoil, as embodied by the invention. Therefore, the configuration of the airfoil, as embodied by the invention, assists in the prevention of turbulent fluid flow in the unit comprising the airfoil, as embodied by the invention.


For example, but in no way limiting of the invention, the airfoil configuration (with or without fluid flow interaction) can be determined by computational Fluid Dynamics (CFD); traditional fluid dynamics analysis; Euler and Navier-Stokes equations; for transfer functions, algorithms, manufacturing: manual positioning, flow testing (for example in wind tunnels), and modification of the airfoil; in-situ testing; modeling: application of scientific principles to design or develop the airfoils, machines, apparatus, or manufacturing processes; airfoil flow testing and modification; combinations thereof, and other design processes and practices. These methods of determination are merely exemplary, and are not intended to limit the invention in any manner.


As noted above, the airfoil configuration (along with its interaction with surrounding airfoils), as embodied by the invention, including its peripheral surface, provides 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, among other desirable aspects of the invention, compared to other similar airfoils, which have like applications. Moreover, and in no way limiting of the invention, in conjunction with other airfoils, which are conventional or enhanced (similar to the enhancements herein), the airfoil, as embodied by the invention, provides an increased efficiency compared to previous individual sets of airfoils. This increased efficiency provides, in addition to the above-noted advantages, a power output with a decrease the required fuel, therefore inherently decreasing emissions to produce energy. Of course, other such advantages are within the scope of the invention.


Referring again to FIG. 1, at the inlet 8 of the gas turbine 2, a plurality of inlet guide vanes (IGVs) 10 are arranged about the axis of the gas turbine, spanning at least part of the flow path between the casing 6 and inner barrel or center structure 7. The IGVs 10 condition the airflow by changing its speed and direction in conjunction with the surfaces of the inlet itself. The IGVs 10 are mounted so that their rotational orientation can be changed, such as with an actuator 9, which allows throttling of the gas turbine 2 by varying airflow through the inlet 8 and the rest of the gas turbine 2. Thus, IGVs 10 are mounted in a different manner than rotor and stator blades 3, 4, as is explained below.


With reference to FIGS. 3, 4, and 7, each IGV 10 includes an airfoil 11 whose profile 12 varies along its length as will be described below. At one end of the airfoil is a hub 13 from which projects a top shaft portion 14. The top shaft portion 14 is mounted via a projection 15 in the casing or housing 6 of the gas turbine 2 for rotation about the longitudinal axis z of the top shaft portion. A top end 16 of the projection includes a feature 17, such as a flattened portion, that enables manipulation of the projection 15 and the top shaft portion 14. An actuator 9 interacts with the feature 17 of the projection 15 to change the rotational position of the top shaft portion 14 and the IGV 10. At the other end of the IGV 10 is a bottom shaft portion 18 that is coaxial with the top shaft portion 14. The bottom shaft portion 18 is mounted for rotation about its longitudinal axis z in the inlet portion of the center structure 7.


As can particularly be seen in FIGS. 5 and 6, each IGV 10 is an airfoil 11 with a varying profile 12. At the top, the airfoil 11 is thicker and longer than it is at the bottom, and the angle of attack changes along the length of the IGV 10. FIG. 8 shows the profile of an IGV of an embodiment as it appears at specific cross sections A-A, B-B, N-N, and BB-BB of the IGV 10 as seen in FIG. 7.


To define the airfoil shape or profile 12 of the IGV 10, a unique set of points in space were derived by analytical means, such as by iteration of mechanical and aerodynamic loadings and flow conditions in a modeling computer software application. More specifically, to define the airfoil profiles 12 of the IGV 10, a unique set of points in space were derived using modeling computer software at respective spanwise positions on the blade. Local inflow distortions at each spanwise position were considered and each profile was derived with the goals of minimizing total pressure drop, broadening the separation-free range of operation vs. angle of attack to match the predicted inflow distortion, and satisfying mechanical requirements for strength, vibrational stress, and ease of manufacture. The profiles are interpolated to define the entire blade surface. This process is carried out in a computer software environment, such as a proprietary computer software environment. Fully three-dimensional computer analyses and scale model testing of the combined IGV and engine inlet were conducted to validate the design. The unique set of points is described using the Cartesian coordinate system of three mutually perpendicular axes x, y, and z. An example unique set of points is set forth in TABLE A below and is sufficient to enable manufacture of the IGV 10, such as with a “CNC” machine or other suitable apparatus, or by another method, such as casting, for example. Producing an IGV following the unique set of points yields an IGV that drives the initiation of flow separation from the IGVs to lower flow conditions than previous IGVs. As a result, vibration resulting from flow separation is significantly reduced, increasing reliability and reducing vibration-induced stresses on the IGVs and other components of the gas turbine.


The compressor vanes, including an IGV, impart kinetic energy to the airflow and therefore bring about a desired pressure rise. Directly following IGV, rotor airfoils and a stage of stator airfoils are provided. Both the rotor and stator airfoils turn the airflow, slow the airflow velocity (in the respective airfoil frame of reference), and yield a rise in the static pressure of the airflow. Typically, multiple rows of rotor/stator stages are stacked in axial flow compressors to achieve a desired discharge to inlet pressure ratio. Rotor and stator airfoils can be secured to rotor wheels or stator case by an appropriate attachment configuration, often known as a “root”, “base” or “dovetail” (see FIGS. 2-5).


The instant invention is directed to an inlet guide vane (IGV) airfoil shape. Inlet guide vanes (IGVs) modulate flow to the first stage, usually a first rotor stage, of the compressor. A variety of parameters define the shape and position of each IGV in a compressor. These parameters include but are not limited to the meanline of the IGV profile; the thickness distribution of the IGV profile; the lift coefficient, which is a multiplier of the meanline; and the stagger angle, which is the angle of the IGV relative to the axial direction of the compressor. By varying the IGV parameters, multiple IGV profile and stagger angle combinations are possible for any given IGV exit condition, the IGV exit condition being the angle at which a gas, usually air, exits the IGV.


To define the airfoil shape of the IGV airfoil, a unique set or loci of points in space are provided. This unique set or loci of points meet the stage requirements so the IGV can be manufactured. This unique loci of points also meets the desired requirements for stage efficiency and reduced thermal and mechanical stresses. The loci of points are arrived at by iteration between aerodynamic and mechanical loadings enabling the compressor to run in an efficient, safe and smooth manner.


The loci, as embodied by the invention, defines the IGV airfoil profile and can comprise a set of points relative to the axis of rotation of the engine. For example, a set of points can be provided to define an IGV airfoil profile. Furthermore, the vane airfoil profile, as embodied by the invention, can comprise an IGV of a compressor.


A Cartesian coordinate system of X, Y and Z values given in TABLE A below defines a profile of an IGV airfoil at various locations along its 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. The Cartesian coordinate system has orthogonally-related X, Y and Z axes. The X axis lies parallel to the compressor rotor centerline, such as the rotary axis. A positive X coordinate value is axial toward the aft, for example the exhaust end of the compressor. A positive Y coordinate value directed aft extends tangentially in the direction of rotation of the rotor. A positive Z coordinate value is directed radially outward toward the static casing of the compressor.


TABLE A values are generated and shown to three decimal places for determining the profile of an IGV airfoil. There are typical manufacturing tolerances as well as coatings, which should be accounted for in the actual profile of an IGV. Accordingly, the values for the profile given are for a nominal IGV airfoil. It will therefore be appreciated that +/−typical manufacturing tolerances, such as, +/−values, including any coating thicknesses, are additive to the X and Y values. Therefore, a distance of about +/−0.160 inches in a direction normal to any surface location along the IGV airfoil profile defines an IGV airfoil profile envelope for a vane airfoil design and compressor. In other words, a distance of about +/−0.160 inches in a direction normal to any surface location along an IGV profile defines a range of variation between measured points on the actual an IGV 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 IGV airfoil design, as embodied by the invention, is robust to this range of variation without impairment of mechanical and aerodynamic functions.


The coordinate values given in the TABLE A below provide the nominal profile envelope for an exemplary an IGV.











TABLE A





X
Y
Z

















−3.8515
0.5190
−1.0653


−3.8512
0.5173
−1.0653


−3.8504
0.5139
−1.0653


−3.8483
0.5072
−1.0653


−3.8428
0.4944
−1.0653


−3.8306
0.4763
−1.0653


−3.8017
0.4498
−1.0653


−3.7560
0.4248
−1.0653


−3.6901
0.4040
−1.0653


−3.6056
0.3892
−1.0653


−3.4946
0.3755
−1.0653


−3.3663
0.3612
−1.0653


−3.2293
0.3472
−1.0653


−3.0752
0.3319
−1.0653


−2.9039
0.3145
−1.0653


−2.7157
0.2944
−1.0653


−2.5191
0.2719
−1.0653


−2.3142
0.2469
−1.0653


−2.1011
0.2190
−1.0653


−1.8800
0.1878
−1.0653


−1.6508
0.1530
−1.0653


−1.4135
0.1149
−1.0653


−1.1682
0.0731
−1.0653


−0.9150
0.0269
−1.0653


−0.6624
−0.0229
−1.0653


−0.4106
−0.0762
−1.0653


−0.1594
−0.1327
−1.0653


0.0912
−0.1922
−1.0653


0.3413
−0.2547
−1.0653


0.5908
−0.3199
−1.0653


0.8398
−0.3875
−1.0653


1.0883
−0.4574
−1.0653


1.3362
−0.5293
−1.0653


1.5835
−0.6031
−1.0653


1.8301
−0.6791
−1.0653


2.0677
−0.7549
−1.0653


2.2964
−0.8306
−1.0653


2.5162
−0.9060
−1.0653


2.7270
−0.9810
−1.0653


2.9288
−1.0555
−1.0653


3.1217
−1.1294
−1.0653


3.3056
−1.2025
−1.0653


3.4727
−1.2713
−1.0653


3.6233
−1.3352
−1.0653


3.7573
−1.3939
−1.0653


3.8751
−1.4470
−1.0653


3.9766
−1.4941
−1.0653


4.0620
−1.5349
−1.0653


4.1347
−1.5705
−1.0653


4.1956
−1.6008
−1.0653


4.2456
−1.6259
−1.0653


4.2855
−1.6462
−1.0653


4.3180
−1.6572
−1.0653


4.3438
−1.6544
−1.0653


4.3632
−1.6447
−1.0653


4.3759
−1.6329
−1.0653


4.3833
−1.6220
−1.0653


4.3886
−1.6096
−1.0653


4.3918
−1.5919
−1.0653


4.3891
−1.5695
−1.0653


4.3764
−1.5458
−1.0653


4.3476
−1.5244
−1.0653


4.3070
−1.5007
−1.0653


4.2563
−1.4712
−1.0653


4.1947
−1.4352
−1.0653


4.1215
−1.3921
−1.0653


4.0360
−1.3415
−1.0653


3.9353
−1.2811
−1.0653


3.8193
−1.2111
−1.0653


3.6880
−1.1316
−1.0653


3.5412
−1.0426
−1.0653


3.3789
−0.9444
−1.0653


3.2009
−0.8373
−1.0653


3.0147
−0.7264
−1.0653


2.8200
−0.6121
−1.0653


2.6168
−0.4951
−1.0653


2.4046
−0.3761
−1.0653


2.1833
−0.2555
−1.0653


1.9524
−0.1343
−1.0653


1.7117
−0.0133
−1.0653


1.4687
0.1027
−1.0653


1.2234
0.2134
−1.0653


0.9755
0.3185
−1.0653


0.7252
0.4179
−1.0653


0.4723
0.5115
−1.0653


0.2166
0.5989
−1.0653


−0.0420
0.6797
−1.0653


−0.3038
0.7533
−1.0653


−0.5682
0.8192
−1.0653


−0.8341
0.8766
−1.0653


−1.1018
0.9246
−1.0653


−1.3624
0.9610
−1.0653


−1.6157
0.9854
−1.0653


−1.8595
0.9986
−1.0653


−2.0935
1.0015
−1.0653


−2.3178
0.9949
−1.0653


−2.5324
0.9799
−1.0653


−2.7375
0.9573
−1.0653


−2.9330
0.9272
−1.0653


−3.1102
0.8927
−1.0653


−3.2691
0.8552
−1.0653


−3.4097
0.8144
−1.0653


−3.5393
0.7690
−1.0653


−3.6502
0.7258
−1.0653


−3.7336
0.6881
−1.0653


−3.7939
0.6472
−1.0653


−3.8304
0.6061
−1.0653


−3.8482
0.5691
−1.0653


−3.8528
0.5466
−1.0653


−3.8531
0.5319
−1.0653


−3.8524
0.5245
−1.0653


−3.8519
0.5209
−1.0653


−3.7666
0.4810
0.0000


−3.7663
0.4793
0.0000


−3.7655
0.4760
0.0000


−3.7635
0.4695
0.0000


−3.7580
0.4570
0.0000


−3.7459
0.4395
0.0000


−3.7174
0.4140
0.0000


−3.6724
0.3902
0.0000


−3.6079
0.3707
0.0000


−3.5249
0.3569
0.0000


−3.4160
0.3439
0.0000


−3.2901
0.3303
0.0000


−3.1558
0.3168
0.0000


−3.0046
0.3020
0.0000


−2.8367
0.2850
0.0000


−2.6522
0.2652
0.0000


−2.4594
0.2430
0.0000


−2.2586
0.2182
0.0000


−2.0498
0.1905
0.0000


−1.8330
0.1596
0.0000


−1.6083
0.1253
0.0000


−1.3756
0.0878
0.0000


−1.1350
0.0468
0.0000


−0.8866
0.0014
0.0000


−0.6388
−0.0473
0.0000


−0.3917
−0.0995
0.0000


−0.1452
−0.1548
0.0000


0.1009
−0.2130
0.0000


0.3464
−0.2740
0.0000


0.5914
−0.3377
0.0000


0.8357
−0.4039
0.0000


1.0793
−0.4724
0.0000


1.3223
−0.5431
0.0000


1.5646
−0.6159
0.0000


1.8063
−0.6908
0.0000


2.0392
−0.7657
0.0000


2.2633
−0.8403
0.0000


2.4787
−0.9147
0.0000


2.6854
−0.9885
0.0000


2.8832
−1.0617
0.0000


3.0724
−1.1341
0.0000


3.2528
−1.2056
0.0000


3.4168
−1.2728
0.0000


3.5646
−1.3351
0.0000


3.6962
−1.3923
0.0000


3.8118
−1.4440
0.0000


3.9115
−1.4898
0.0000


3.9955
−1.5295
0.0000


4.0669
−1.5641
0.0000


4.1268
−1.5935
0.0000


4.1759
−1.6180
0.0000


4.2151
−1.6377
0.0000


4.2469
−1.6488
0.0000


4.2725
−1.6464
0.0000


4.2918
−1.6370
0.0000


4.3044
−1.6253
0.0000


4.3117
−1.6145
0.0000


4.3168
−1.6023
0.0000


4.3197
−1.5848
0.0000


4.3166
−1.5630
0.0000


4.3037
−1.5400
0.0000


4.2753
−1.5194
0.0000


4.2354
−1.4966
0.0000


4.1856
−1.4680
0.0000


4.1252
−1.4332
0.0000


4.0533
−1.3916
0.0000


3.9695
−1.3426
0.0000


3.8706
−1.2843
0.0000


3.7567
−1.2166
0.0000


3.6278
−1.1397
0.0000


3.4838
−1.0537
0.0000


3.3245
−0.9588
0.0000


3.1498
−0.8553
0.0000


2.9670
−0.7481
0.0000


2.7760
−0.6378
0.0000


2.5767
−0.5248
0.0000


2.3688
−0.4099
0.0000


2.1520
−0.2934
0.0000


1.9260
−0.1762
0.0000


1.6906
−0.0590
0.0000


1.4532
0.0537
0.0000


1.2139
0.1614
0.0000


0.9724
0.2640
0.0000


0.7287
0.3612
0.0000


0.4826
0.4528
0.0000


0.2341
0.5385
0.0000


−0.0171
0.6176
0.0000


−0.2712
0.6899
0.0000


−0.5283
0.7547
0.0000


−0.7887
0.8119
0.0000


−1.0521
0.8603
0.0000


−1.3081
0.8973
0.0000


−1.5564
0.9230
0.0000


−1.7969
0.9378
0.0000


−2.0289
0.9427
0.0000


−2.2512
0.9382
0.0000


−2.4637
0.9252
0.0000


−2.6665
0.9046
0.0000


−2.8597
0.8765
0.0000


−3.0346
0.8436
0.0000


−3.1913
0.8074
0.0000


−3.3294
0.7684
0.0000


−3.4567
0.7255
0.0000


−3.5652
0.6826
0.0000


−3.6462
0.6443
0.0000


−3.7055
0.6045
0.0000


−3.7427
0.5654
0.0000


−3.7620
0.5300
0.0000


−3.7674
0.5081
0.0000


−3.7681
0.4937
0.0000


−3.7675
0.4864
0.0000


−3.7670
0.4828
0.0000


−3.7321
0.4656
0.4347


−3.7317
0.4639
0.4347


−3.7309
0.4606
0.4347


−3.7289
0.4541
0.4347


−3.7234
0.4418
0.4347


−3.7114
0.4244
0.4347


−3.6829
0.3994
0.4347


−3.6382
0.3761
0.4347


−3.5741
0.3571
0.4347


−3.4917
0.3437
0.4347


−3.3836
0.3309
0.4347


−3.2588
0.3176
0.4347


−3.1255
0.3044
0.4347


−2.9756
0.2898
0.4347


−2.8090
0.2729
0.4347


−2.6259
0.2532
0.4347


−2.4348
0.2311
0.4347


−2.2356
0.2064
0.4347


−2.0285
0.1787
0.4347


−1.8135
0.1479
0.4347


−1.5905
0.1138
0.4347


−1.3597
0.0766
0.4347


−1.1210
0.0359
0.4347


−0.8745
−0.0091
0.4347


−0.6287
−0.0575
0.4347


−0.3835
−0.1092
0.4347


−0.1388
−0.1640
0.4347


0.1054
−0.2216
0.4347


0.3490
−0.2821
0.4347


0.5921
−0.3451
0.4347


0.8345
−0.4106
0.4347


1.0761
−0.4785
0.4347


1.3171
−0.5486
0.4347


1.5574
−0.6209
0.4347


1.7970
−0.6956
0.4347


2.0280
−0.7701
0.4347


2.2502
−0.8444
0.4347


2.4638
−0.9184
0.4347


2.6687
−0.9918
0.4347


2.8650
−1.0644
0.4347


3.0526
−1.1363
0.4347


3.2316
−1.2072
0.4347


3.3944
−1.2737
0.4347


3.5410
−1.3354
0.4347


3.6716
−1.3919
0.4347


3.7864
−1.4430
0.4347


3.8853
−1.4884
0.4347


3.9687
−1.5276
0.4347


4.0396
−1.5617
0.4347


4.0990
−1.5908
0.4347


4.1478
−1.6150
0.4347


4.1867
−1.6344
0.4347


4.2183
−1.6455
0.4347


4.2437
−1.6430
0.4347


4.2628
−1.6337
0.4347


4.2752
−1.6220
0.4347


4.2824
−1.6114
0.4347


4.2874
−1.5992
0.4347


4.2902
−1.5819
0.4347


4.2870
−1.5603
0.4347


4.2742
−1.5376
0.4347


4.2458
−1.5173
0.4347


4.2062
−1.4948
0.4347


4.1568
−1.4666
0.4347


4.0968
−1.4323
0.4347


4.0255
−1.3913
0.4347


3.9422
−1.3430
0.4347


3.8441
−1.2855
0.4347


3.7310
−1.2187
0.4347


3.6031
−1.1428
0.4347


3.4601
−1.0580
0.4347


3.3019
−0.9644
0.4347


3.1284
−0.8623
0.4347


2.9469
−0.7567
0.4347


2.7574
−0.6479
0.4347


2.5594
−0.5366
0.4347


2.3530
−0.4232
0.4347


2.1378
−0.3083
0.4347


1.9135
−0.1926
0.4347


1.6799
−0.0768
0.4347


1.4444
0.0347
0.4347


1.2070
0.1415
0.4347


0.9675
0.2432
0.4347


0.7258
0.3398
0.4347


0.4818
0.4308
0.4347


0.2353
0.5159
0.4347


−0.0138
0.5945
0.4347


−0.2659
0.6662
0.4347


−0.5210
0.7306
0.4347


−0.7793
0.7873
0.4347


−1.0403
0.8353
0.4347


−1.2938
0.8722
0.4347


−1.5398
0.8979
0.4347


−1.7781
0.9131
0.4347


−2.0078
0.9185
0.4347


−2.2280
0.9146
0.4347


−2.4386
0.9025
0.4347


−2.6397
0.8827
0.4347


−2.8313
0.8555
0.4347


−3.0049
0.8234
0.4347


−3.1604
0.7878
0.4347


−3.2972
0.7497
0.4347


−3.4236
0.7078
0.4347


−3.5309
0.6651
0.4347


−3.6107
0.6264
0.4347


−3.6695
0.5867
0.4347


−3.7068
0.5485
0.4347


−3.7267
0.5139
0.4347


−3.7325
0.4924
0.4347


−3.7334
0.4781
0.4347


−3.7329
0.4709
0.4347


−3.7324
0.4674
0.4347


−3.6150
0.4101
1.9347


−3.6146
0.4085
1.9347


−3.6139
0.4052
1.9347


−3.6119
0.3990
1.9347


−3.6065
0.3870
1.9347


−3.5946
0.3703
1.9347


−3.5665
0.3464
1.9347


−3.5226
0.3246
1.9347


−3.4600
0.3075
1.9347


−3.3797
0.2955
1.9347


−3.2745
0.2838
1.9347


−3.1530
0.2717
1.9347


−3.0234
0.2595
1.9347


−2.8775
0.2458
1.9347


−2.7155
0.2298
1.9347


−2.5375
0.2109
1.9347


−2.3516
0.1895
1.9347


−2.1580
0.1654
1.9347


−1.9566
0.1384
1.9347


−1.7475
0.1083
1.9347


−1.5307
0.0751
1.9347


−1.3061
0.0389
1.9347


−1.0739
−0.0009
1.9347


−0.8342
−0.0448
1.9347


−0.5950
−0.0920
1.9347


−0.3564
−0.1424
1.9347


−0.1182
−0.1959
1.9347


0.1194
−0.2521
1.9347


0.3564
−0.3109
1.9347


0.5926
−0.3721
1.9347


0.8282
−0.4357
1.9347


1.0631
−0.5016
1.9347


1.2974
−0.5698
1.9347


1.5310
−0.6402
1.9347


1.7639
−0.7131
1.9347


1.9884
−0.7858
1.9347


2.2045
−0.8584
1.9347


2.4121
−0.9305
1.9347


2.6112
−1.0020
1.9347


2.8020
−1.0727
1.9347


2.9845
−1.1423
1.9347


3.1588
−1.2109
1.9347


3.3173
−1.2750
1.9347


3.4601
−1.3344
1.9347


3.5874
−1.3888
1.9347


3.6992
−1.4378
1.9347


3.7957
−1.4814
1.9347


3.8769
−1.5190
1.9347


3.9461
−1.5517
1.9347


4.0041
−1.5796
1.9347


4.0517
−1.6027
1.9347


4.0897
−1.6214
1.9347


4.1203
−1.6314
1.9347


4.1443
−1.6286
1.9347


4.1622
−1.6193
1.9347


4.1738
−1.6082
1.9347


4.1805
−1.5980
1.9347


4.1852
−1.5861
1.9347


4.1876
−1.5693
1.9347


4.1842
−1.5484
1.9347


4.1713
−1.5266
1.9347


4.1435
−1.5074
1.9347


4.1049
−1.4860
1.9347


4.0566
−1.4592
1.9347


3.9981
−1.4265
1.9347


3.9285
−1.3875
1.9347


3.8472
−1.3415
1.9347


3.7514
−1.2867
1.9347


3.6411
−1.2231
1.9347


3.5163
−1.1508
1.9347


3.3767
−1.0699
1.9347


3.2224
−0.9808
1.9347


3.0530
−0.8837
1.9347


2.8758
−0.7832
1.9347


2.6908
−0.6798
1.9347


2.4976
−0.5738
1.9347


2.2962
−0.4658
1.9347


2.0863
−0.3562
1.9347


1.8677
−0.2456
1.9347


1.6402
−0.1347
1.9347


1.4110
−0.0275
1.9347


1.1800
0.0754
1.9347


0.9472
0.1737
1.9347


0.7123
0.2671
1.9347


0.4751
0.3552
1.9347


0.2356
0.4376
1.9347


−0.0065
0.5139
1.9347


−0.2513
0.5837
1.9347


−0.4990
0.6465
1.9347


−0.7497
0.7020
1.9347


−1.0023
0.7492
1.9347


−1.2478
0.7858
1.9347


−1.4860
0.8120
1.9347


−1.7169
0.8282
1.9347


−1.9393
0.8350
1.9347


−2.1524
0.8330
1.9347


−2.3565
0.8229
1.9347


−2.5515
0.8053
1.9347


−2.7375
0.7806
1.9347


−2.9061
0.7509
1.9347


−3.0572
0.7175
1.9347


−3.1901
0.6815
1.9347


−3.3130
0.6420
1.9347


−3.4171
0.6012
1.9347


−3.4945
0.5638
1.9347


−3.5517
0.5260
1.9347


−3.5886
0.4897
1.9347


−3.6088
0.4567
1.9347


−3.6150
0.4360
1.9347


−3.6162
0.4222
1.9347


−3.6158
0.4153
1.9347


−3.6153
0.4118
1.9347


−3.5579
0.3838
2.6847


−3.5576
0.3822
2.6847


−3.5569
0.3791
2.6847


−3.5550
0.3729
2.6847


−3.5496
0.3611
2.6847


−3.5378
0.3447
2.6847


−3.5099
0.3214
2.6847


−3.4663
0.3005
2.6847


−3.4046
0.2842
2.6847


−3.3253
0.2731
2.6847


−3.2216
0.2620
2.6847


−3.1018
0.2504
2.6847


−2.9740
0.2389
2.6847


−2.8302
0.2258
2.6847


−2.6706
0.2103
2.6847


−2.4951
0.1919
2.6847


−2.3120
0.1709
2.6847


−2.1212
0.1472
2.6847


−1.9228
0.1205
2.6847


−1.7167
0.0907
2.6847


−1.5030
0.0580
2.6847


−1.2817
0.0222
2.6847


−1.0529
−0.0170
2.6847


−0.8166
−0.0603
2.6847


−0.5808
−0.1068
2.6847


−0.3456
−0.1566
2.6847


−0.1108
−0.2094
2.6847


0.1233
−0.2648
2.6847


0.3567
−0.3228
2.6847


0.5894
−0.3832
2.6847


0.8214
−0.4460
2.6847


1.0529
−0.5109
2.6847


1.2838
−0.5779
2.6847


1.5140
−0.6471
2.6847


1.7437
−0.7185
2.6847


1.9651
−0.7898
2.6847


2.1781
−0.8608
2.6847


2.3828
−0.9314
2.6847


2.5793
−1.0012
2.6847


2.7674
−1.0703
2.6847


2.9475
−1.1384
2.6847


3.1194
−1.2055
2.6847


3.2757
−1.2682
2.6847


3.4166
−1.3262
2.6847


3.5422
−1.3794
2.6847


3.6525
−1.4274
2.6847


3.7478
−1.4699
2.6847


3.8280
−1.5067
2.6847


3.8963
−1.5386
2.6847


3.9535
−1.5658
2.6847


4.0005
−1.5884
2.6847


4.0380
−1.6066
2.6847


4.0682
−1.6169
2.6847


4.0920
−1.6143
2.6847


4.1099
−1.6052
2.6847


4.1215
−1.5941
2.6847


4.1281
−1.5839
2.6847


4.1327
−1.5722
2.6847


4.1349
−1.5557
2.6847


4.1313
−1.5351
2.6847


4.1184
−1.5138
2.6847


4.0907
−1.4952
2.6847


4.0526
−1.4743
2.6847


4.0050
−1.4482
2.6847


3.9471
−1.4164
2.6847


3.8784
−1.3783
2.6847


3.7981
−1.3335
2.6847


3.7035
−1.2802
2.6847


3.5945
−1.2183
2.6847


3.4712
−1.1478
2.6847


3.3333
−1.0691
2.6847


3.1808
−0.9823
2.6847


3.0135
−0.8877
2.6847


2.8385
−0.7898
2.6847


2.6557
−0.6890
2.6847


2.4650
−0.5857
2.6847


2.2661
−0.4804
2.6847


2.0589
−0.3735
2.6847


1.8431
−0.2657
2.6847


1.6185
−0.1575
2.6847


1.3922
−0.0530
2.6847


1.1643
0.0473
2.6847


0.9345
0.1432
2.6847


0.7027
0.2343
2.6847


0.4688
0.3204
2.6847


0.2326
0.4010
2.6847


−0.0060
0.4757
2.6847


−0.2473
0.5442
2.6847


−0.4913
0.6061
2.6847


−0.7381
0.6609
2.6847


−0.9864
0.7075
2.6847


−1.2277
0.7440
2.6847


−1.4620
0.7703
2.6847


−1.6890
0.7870
2.6847


−1.9075
0.7944
2.6847


−2.1170
0.7932
2.6847


−2.3177
0.7840
2.6847


−2.5095
0.7675
2.6847


−2.6925
0.7439
2.6847


−2.8585
0.7153
2.6847


−3.0073
0.6831
2.6847


−3.1381
0.6483
2.6847


−3.2591
0.6098
2.6847


−3.3618
0.5702
2.6847


−3.4382
0.5339
2.6847


−3.4948
0.4972
2.6847


−3.5314
0.4618
2.6847


−3.5516
0.4296
2.6847


−3.5579
0.4093
2.6847


−3.5591
0.3957
2.6847


−3.5587
0.3889
2.6847


−3.5582
0.3855
2.6847


−3.5018
0.3577
3.4347


−3.5015
0.3561
3.4347


−3.5008
0.3530
3.4347


−3.4989
0.3469
3.4347


−3.4936
0.3353
3.4347


−3.4818
0.3192
3.4347


−3.4541
0.2967
3.4347


−3.4110
0.2765
3.4347


−3.3500
0.2611
3.4347


−3.2718
0.2507
3.4347


−3.1697
0.2402
3.4347


−3.0516
0.2292
3.4347


−2.9257
0.2183
3.4347


−2.7840
0.2058
3.4347


−2.6267
0.1908
3.4347


−2.4539
0.1730
3.4347


−2.2735
0.1526
3.4347


−2.0856
0.1295
3.4347


−1.8901
0.1034
3.4347


−1.6871
0.0743
3.4347


−1.4765
0.0423
3.4347


−1.2585
0.0073
3.4347


−1.0330
−0.0312
3.4347


−0.8002
−0.0737
3.4347


−0.5678
−0.1193
3.4347


−0.3359
−0.1681
3.4347


−0.1047
−0.2199
3.4347


0.1259
−0.2743
3.4347


0.3558
−0.3311
3.4347


0.5850
−0.3904
3.4347


0.8136
−0.4520
3.4347


1.0416
−0.5156
3.4347


1.2691
−0.5812
3.4347


1.4960
−0.6489
3.4347


1.7224
−0.7186
3.4347


1.9407
−0.7880
3.4347


2.1508
−0.8571
3.4347


2.3527
−0.9258
3.4347


2.5464
−0.9937
3.4347


2.7320
−1.0609
3.4347


2.9096
−1.1272
3.4347


3.0792
−1.1924
3.4347


3.2335
−1.2535
3.4347


3.3725
−1.3100
3.4347


3.4965
−1.3618
3.4347


3.6053
−1.4085
3.4347


3.6993
−1.4499
3.4347


3.7785
−1.4858
3.4347


3.8459
−1.5169
3.4347


3.9024
−1.5434
3.4347


3.9488
−1.5654
3.4347


3.9859
−1.5831
3.4347


4.0156
−1.5934
3.4347


4.0392
−1.5909
3.4347


4.0568
−1.5820
3.4347


4.0682
−1.5710
3.4347


4.0747
−1.5609
3.4347


4.0791
−1.5493
3.4347


4.0812
−1.5330
3.4347


4.0774
−1.5128
3.4347


4.0644
−1.4920
3.4347


4.0370
−1.4740
3.4347


3.9993
−1.4537
3.4347


3.9523
−1.4283
3.4347


3.8952
−1.3974
3.4347


3.8273
−1.3605
3.4347


3.7480
−1.3170
3.4347


3.6546
−1.2652
3.4347


3.5469
−1.2050
3.4347


3.4250
−1.1367
3.4347


3.2888
−1.0602
3.4347


3.1381
−0.9760
3.4347


2.9728
−0.8842
3.4347


2.7999
−0.7892
3.4347


2.6194
−0.6914
3.4347


2.4310
−0.5911
3.4347


2.2346
−0.4889
3.4347


2.0299
−0.3852
3.4347


1.8168
−0.2806
3.4347


1.5950
−0.1756
3.4347


1.3717
−0.0743
3.4347


1.1467
0.0231
3.4347


0.9199
0.1161
3.4347


0.6912
0.2046
3.4347


0.4605
0.2883
3.4347


0.2277
0.3668
3.4347


−0.0075
0.4397
3.4347


−0.2452
0.5065
3.4347


−0.4855
0.5671
3.4347


−0.7282
0.6207
3.4347


−0.9721
0.6664
3.4347


−1.2093
0.7024
3.4347


−1.4396
0.7287
3.4347


−1.6626
0.7455
3.4347


−1.8771
0.7534
3.4347


−2.0830
0.7528
3.4347


−2.2802
0.7446
3.4347


−2.4687
0.7290
3.4347


−2.6487
0.7066
3.4347


−2.8120
0.6792
3.4347


−2.9584
0.6482
3.4347


−3.0872
0.6146
3.4347


−3.2063
0.5774
3.4347


−3.3074
0.5390
3.4347


−3.3828
0.5039
3.4347


−3.4389
0.4684
3.4347


−3.4752
0.4341
3.4347


−3.4953
0.4026
3.4347


−3.5016
0.3827
3.4347


−3.5029
0.3693
3.4347


−3.5026
0.3627
3.4347


−3.5021
0.3593
3.4347


−3.3926
0.3112
4.9347


−3.3923
0.3097
4.9347


−3.3916
0.3067
4.9347


−3.3897
0.3008
4.9347


−3.3843
0.2896
4.9347


−3.3723
0.2745
4.9347


−3.3446
0.2538
4.9347


−3.3022
0.2356
4.9347


−3.2429
0.2217
4.9347


−3.1670
0.2119
4.9347


−3.0679
0.2024
4.9347


−2.9534
0.1932
4.9347


−2.8312
0.1836
4.9347


−2.6939
0.1724
4.9347


−2.5413
0.1589
4.9347


−2.3738
0.1425
4.9347


−2.1989
0.1235
4.9347


−2.0166
0.1017
4.9347


−1.8271
0.0770
4.9347


−1.6303
0.0495
4.9347


−1.4261
0.0193
4.9347


−1.2147
−0.0139
4.9347


−0.9960
−0.0503
4.9347


−0.7701
−0.0907
4.9347


−0.5447
−0.1340
4.9347


−0.3198
−0.1803
4.9347


−0.0955
−0.2294
4.9347


0.1281
−0.2809
4.9347


0.3511
−0.3348
4.9347


0.5736
−0.3910
4.9347


0.7954
−0.4493
4.9347


1.0168
−0.5096
4.9347


1.2376
−0.5718
4.9347


1.4580
−0.6358
4.9347


1.6778
−0.7019
4.9347


1.8898
−0.7676
4.9347


2.0939
−0.8330
4.9347


2.2900
−0.8979
4.9347


2.4783
−0.9622
4.9347


2.6588
−1.0257
4.9347


2.8315
−1.0883
4.9347


2.9964
−1.1499
4.9347


3.1465
−1.2076
4.9347


3.2817
−1.2610
4.9347


3.4024
−1.3099
4.9347


3.5084
−1.3540
4.9347


3.5999
−1.3930
4.9347


3.6770
−1.4268
4.9347


3.7427
−1.4562
4.9347


3.7978
−1.4811
4.9347


3.8430
−1.5019
4.9347


3.8792
−1.5186
4.9347


3.9080
−1.5286
4.9347


3.9309
−1.5263
4.9347


3.9480
−1.5176
4.9347


3.9590
−1.5068
4.9347


3.9651
−1.4969
4.9347


3.9692
−1.4856
4.9347


3.9708
−1.4698
4.9347


3.9667
−1.4503
4.9347


3.9534
−1.4306
4.9347


3.9264
−1.4138
4.9347


3.8897
−1.3948
4.9347


3.8439
−1.3710
4.9347


3.7882
−1.3420
4.9347


3.7220
−1.3074
4.9347


3.6446
−1.2667
4.9347


3.5534
−1.2182
4.9347


3.4482
−1.1619
4.9347


3.3292
−1.0980
4.9347


3.1962
−1.0265
4.9347


3.0490
−0.9477
4.9347


2.8876
−0.8619
4.9347


2.7188
−0.7731
4.9347


2.5424
−0.6816
4.9347


2.3583
−0.5877
4.9347


2.1662
−0.4919
4.9347


1.9661
−0.3948
4.9347


1.7580
−0.2967
4.9347


1.5416
−0.1984
4.9347


1.3240
−0.1035
4.9347


1.1051
−0.0124
4.9347


0.8848
0.0746
4.9347


0.6631
0.1574
4.9347


0.4397
0.2357
4.9347


0.2147
0.3092
4.9347


−0.0121
0.3774
4.9347


−0.2409
0.4401
4.9347


−0.4717
0.4970
4.9347


−0.7047
0.5476
4.9347


−0.9400
0.5912
4.9347


−1.1695
0.6260
4.9347


−1.3918
0.6518
4.9347


−1.6069
0.6689
4.9347


−1.8149
0.6777
4.9347


−2.0150
0.6785
4.9347


−2.2068
0.6718
4.9347


−2.3905
0.6580
4.9347


−2.5654
0.6375
4.9347


−2.7236
0.6123
4.9347


−2.8649
0.5836
4.9347


−2.9892
0.5525
4.9347


−3.1043
0.5178
4.9347


−3.2021
0.4820
4.9347


−3.2753
0.4494
4.9347


−3.3299
0.4165
4.9347


−3.3656
0.3843
4.9347


−3.3857
0.3543
4.9347


−3.3921
0.3353
4.9347


−3.3935
0.3225
4.9347


−3.3933
0.3161
4.9347


−3.3928
0.3128
4.9347


−3.2902
0.2695
6.4347


−3.2899
0.2680
6.4347


−3.2892
0.2650
6.4347


−3.2873
0.2594
6.4347


−3.2819
0.2487
6.4347


−3.2700
0.2344
6.4347


−3.2427
0.2151
6.4347


−3.2013
0.1986
6.4347


−3.1436
0.1864
6.4347


−3.0701
0.1779
6.4347


−2.9741
0.1697
6.4347


−2.8633
0.1619
6.4347


−2.7450
0.1538
6.4347


−2.6120
0.1440
6.4347


−2.4644
0.1319
6.4347


−2.3021
0.1172
6.4347


−2.1327
0.1000
6.4347


−1.9560
0.0801
6.4347


−1.7722
0.0573
6.4347


−1.5813
0.0319
6.4347


−1.3834
0.0039
6.4347


−1.1784
−0.0269
6.4347


−0.9665
−0.0609
6.4347


−0.7477
−0.0984
6.4347


−0.5293
−0.1388
6.4347


−0.3115
−0.1820
6.4347


−0.0941
−0.2278
6.4347


0.1229
−0.2759
6.4347


0.3394
−0.3263
6.4347


0.5553
−0.3788
6.4347


0.7707
−0.4333
6.4347


0.9856
−0.4896
6.4347


1.2000
−0.5477
6.4347


1.4139
−0.6076
6.4347


1.6273
−0.6692
6.4347


1.8332
−0.7307
6.4347


2.0314
−0.7917
6.4347


2.2221
−0.8523
6.4347


2.4051
−0.9123
6.4347


2.5806
−0.9715
6.4347


2.7486
−1.0299
6.4347


2.9090
−1.0874
6.4347


3.0551
−1.1411
6.4347


3.1868
−1.1908
6.4347


3.3042
−1.2363
6.4347


3.4075
−1.2774
6.4347


3.4967
−1.3138
6.4347


3.5719
−1.3452
6.4347


3.6360
−1.3725
6.4347


3.6897
−1.3958
6.4347


3.7339
−1.4151
6.4347


3.7691
−1.4306
6.4347


3.7970
−1.4397
6.4347


3.8188
−1.4372
6.4347


3.8350
−1.4286
6.4347


3.8452
−1.4181
6.4347


3.8509
−1.4086
6.4347


3.8546
−1.3976
6.4347


3.8558
−1.3823
6.4347


3.8512
−1.3636
6.4347


3.8377
−1.3450
6.4347


3.8112
−1.3297
6.4347


3.7754
−1.3121
6.4347


3.7307
−1.2900
6.4347


3.6764
−1.2632
6.4347


3.6118
−1.2312
6.4347


3.5364
−1.1935
6.4347


3.4473
−1.1486
6.4347


3.3447
−1.0966
6.4347


3.2285
−1.0374
6.4347


3.0987
−0.9713
6.4347


2.9550
−0.8985
6.4347


2.7975
−0.8192
6.4347


2.6327
−0.7371
6.4347


2.4607
−0.6526
6.4347


2.2811
−0.5659
6.4347


2.0939
−0.4774
6.4347


1.8991
−0.3876
6.4347


1.6964
−0.2971
6.4347


1.4859
−0.2062
6.4347


1.2742
−0.1185
6.4347


1.0614
−0.0341
6.4347


0.8473
0.0466
6.4347


0.6318
0.1234
6.4347


0.4150
0.1960
6.4347


0.1966
0.2643
6.4347


−0.0235
0.3277
6.4347


−0.2452
0.3861
6.4347


−0.4689
0.4392
6.4347


−0.6945
0.4864
6.4347


−0.9221
0.5273
6.4347


−1.1431
0.5598
6.4347


−1.3573
0.5842
6.4347


−1.5647
0.6006
6.4347


−1.7651
0.6093
6.4347


−1.9577
0.6106
6.4347


−2.1427
0.6048
6.4347


−2.3197
0.5924
6.4347


−2.4883
0.5738
6.4347


−2.6409
0.5506
6.4347


−2.7772
0.5242
6.4347


−2.8973
0.4955
6.4347


−3.0085
0.4633
6.4347


−3.1031
0.4300
6.4347


−3.1742
0.3998
6.4347


−3.2276
0.3694
6.4347


−3.2628
0.3392
6.4347


−3.2828
0.3109
6.4347


−3.2894
0.2927
6.4347


−3.2910
0.2804
6.4347


−3.2908
0.2741
6.4347


−3.2904
0.2710
6.4347


−3.1908
0.2283
7.9347


−3.1906
0.2269
7.9347


−3.1899
0.2241
7.9347


−3.1881
0.2186
7.9347


−3.1827
0.2083
7.9347


−3.1710
0.1947
7.9347


−3.1441
0.1766
7.9347


−3.1038
0.1617
7.9347


−3.0477
0.1512
7.9347


−2.9764
0.1442
7.9347


−2.8836
0.1374
7.9347


−2.7764
0.1309
7.9347


−2.6620
0.1241
7.9347


−2.5334
0.1158
7.9347


−2.3906
0.1053
7.9347


−2.2337
0.0924
7.9347


−2.0699
0.0772
7.9347


−1.8992
0.0594
7.9347


−1.7215
0.0389
7.9347


−1.5370
0.0160
7.9347


−1.3455
−0.0094
7.9347


−1.1472
−0.0374
7.9347


−0.9420
−0.0684
7.9347


−0.7300
−0.1028
7.9347


−0.5186
−0.1399
7.9347


−0.3077
−0.1796
7.9347


−0.0974
−0.2217
7.9347


0.1125
−0.2660
7.9347


0.3220
−0.3123
7.9347


0.5311
−0.3607
7.9347


0.7398
−0.4109
7.9347


0.9481
−0.4629
7.9347


1.1559
−0.5165
7.9347


1.3633
−0.5717
7.9347


1.5703
−0.6285
7.9347


1.7699
−0.6851
7.9347


1.9621
−0.7413
7.9347


2.1471
−0.7971
7.9347


2.3248
−0.8524
7.9347


2.4952
−0.9070
7.9347


2.6583
−0.9607
7.9347


2.8142
−1.0136
7.9347


2.9561
−1.0630
7.9347


3.0842
−1.1088
7.9347


3.1984
−1.1506
7.9347


3.2989
−1.1884
7.9347


3.3857
−1.2219
7.9347


3.4590
−1.2508
7.9347


3.5214
−1.2759
7.9347


3.5738
−1.2972
7.9347


3.6168
−1.3149
7.9347


3.6511
−1.3292
7.9347


3.6782
−1.3381
7.9347


3.6996
−1.3359
7.9347


3.7154
−1.3274
7.9347


3.7253
−1.3170
7.9347


3.7307
−1.3076
7.9347


3.7340
−1.2969
7.9347


3.7347
−1.2821
7.9347


3.7297
−1.2643
7.9347


3.7160
−1.2469
7.9347


3.6900
−1.2329
7.9347


3.6551
−1.2168
7.9347


3.6115
−1.1966
7.9347


3.5586
−1.1720
7.9347


3.4957
−1.1427
7.9347


3.4221
−1.1081
7.9347


3.3353
−1.0671
7.9347


3.2353
−1.0194
7.9347


3.1220
−0.9652
7.9347


2.9953
−0.9047
7.9347


2.8553
−0.8380
7.9347


2.7017
−0.7654
7.9347


2.5411
−0.6902
7.9347


2.3734
−0.6128
7.9347


2.1985
−0.5334
7.9347


2.0163
−0.4525
7.9347


1.8267
−0.3703
7.9347


1.6296
−0.2874
7.9347


1.4249
−0.2041
7.9347


1.2192
−0.1237
7.9347


1.0125
−0.0464
7.9347


0.8046
0.0277
7.9347


0.5956
0.0982
7.9347


0.3852
0.1650
7.9347


0.1735
0.2277
7.9347


−0.0397
0.2861
7.9347


−0.2544
0.3398
7.9347


−0.4709
0.3886
7.9347


−0.6890
0.4321
7.9347


−0.9081
0.4696
7.9347


−1.1209
0.4994
7.9347


−1.3271
0.5219
7.9347


−1.5268
0.5371
7.9347


−1.7194
0.5452
7.9347


−1.9047
0.5464
7.9347


−2.0827
0.5411
7.9347


−2.2530
0.5297
7.9347


−2.4153
0.5125
7.9347


−2.5622
0.4911
7.9347


−2.6935
0.4665
7.9347


−2.8093
0.4400
7.9347


−2.9165
0.4100
7.9347


−3.0079
0.3790
7.9347


−3.0767
0.3511
7.9347


−3.1287
0.3229
7.9347


−3.1633
0.2947
7.9347


−3.1832
0.2679
7.9347


−3.1899
0.2506
7.9347


−3.1916
0.2387
7.9347


−3.1914
0.2328
7.9347


−3.1911
0.2298
7.9347


−3.0924
0.1898
9.4347


−3.0921
0.1884
9.4347


−3.0915
0.1857
9.4347


−3.0897
0.1805
9.4347


−3.0843
0.1706
9.4347


−3.0727
0.1578
9.4347


−3.0463
0.1411
9.4347


−3.0071
0.1279
9.4347


−2.9527
0.1190
9.4347


−2.8839
0.1133
9.4347


−2.7942
0.1079
9.4347


−2.6907
0.1028
9.4347


−2.5803
0.0975
9.4347


−2.4562
0.0908
9.4347


−2.3184
0.0820
9.4347


−2.1670
0.0711
9.4347


−2.0088
0.0579
9.4347


−1.8440
0.0422
9.4347


−1.6724
0.0241
9.4347


−1.4942
0.0037
9.4347


−1.3092
−0.0190
9.4347


−1.1176
−0.0441
9.4347


−0.9193
−0.0719
9.4347


−0.7146
−0.1029
9.4347


−0.5103
−0.1362
9.4347


−0.3064
−0.1721
9.4347


−0.1029
−0.2101
9.4347


0.1002
−0.2501
9.4347


0.3029
−0.2920
9.4347


0.5054
−0.3357
9.4347


0.7074
−0.3811
9.4347


0.9091
−0.4280
9.4347


1.1104
−0.4764
9.4347


1.3113
−0.5263
9.4347


1.5118
−0.5776
9.4347


1.7053
−0.6287
9.4347


1.8918
−0.6796
9.4347


2.0713
−0.7300
9.4347


2.2437
−0.7799
9.4347


2.4090
−0.8293
9.4347


2.5674
−0.8779
9.4347


2.7188
−0.9257
9.4347


2.8567
−0.9704
9.4347


2.9812
−1.0118
9.4347


3.0923
−1.0498
9.4347


3.1900
−1.0840
9.4347


3.2745
−1.1143
9.4347


3.3458
−1.1405
9.4347


3.4066
−1.1633
9.4347


3.4576
−1.1826
9.4347


3.4995
−1.1987
9.4347


3.5329
−1.2117
9.4347


3.5592
−1.2198
9.4347


3.5796
−1.2173
9.4347


3.5946
−1.2090
9.4347


3.6039
−1.1988
9.4347


3.6087
−1.1897
9.4347


3.6116
−1.1793
9.4347


3.6119
−1.1650
9.4347


3.6064
−1.1481
9.4347


3.5925
−1.1319
9.4347


3.5670
−1.1194
9.4347


3.5331
−1.1048
9.4347


3.4906
−1.0865
9.4347


3.4391
−1.0642
9.4347


3.3778
−1.0377
9.4347


3.3062
−1.0064
9.4347


3.2216
−0.9693
9.4347


3.1241
−0.9261
9.4347


3.0136
−0.8772
9.4347


2.8902
−0.8224
9.4347


2.7537
−0.7622
9.4347


2.6040
−0.6966
9.4347


2.4475
−0.6287
9.4347


2.2841
−0.5588
9.4347


2.1138
−0.4872
9.4347


1.9364
−0.4142
9.4347


1.7519
−0.3401
9.4347


1.5600
−0.2653
9.4347


1.3607
−0.1901
9.4347


1.1605
−0.1175
9.4347


0.9593
−0.0476
9.4347


0.7571
0.0194
9.4347


0.5536
0.0832
9.4347


0.3491
0.1436
9.4347


0.1438
0.2002
9.4347


−0.0621
0.2528
9.4347


−0.2688
0.3009
9.4347


−0.4763
0.3445
9.4347


−0.6846
0.3833
9.4347


−0.8938
0.4167
9.4347


−1.0970
0.4434
9.4347


−1.2941
0.4636
9.4347


−1.4852
0.4774
9.4347


−1.6702
0.4848
9.4347


−1.8489
0.4859
9.4347


−2.0203
0.4809
9.4347


−2.1843
0.4704
9.4347


−2.3408
0.4545
9.4347


−2.4823
0.4346
9.4347


−2.6090
0.4119
9.4347


−2.7208
0.3873
9.4347


−2.8244
0.3596
9.4347


−2.9128
0.3308
9.4347


−2.9795
0.3050
9.4347


−3.0303
0.2791
9.4347


−3.0643
0.2530
9.4347


−3.0843
0.2278
9.4347


−3.0912
0.2113
9.4347


−3.0930
0.1999
9.4347


−3.0929
0.1941
9.4347


−3.0926
0.1913
9.4347


−2.9962
0.1540
10.9347


−2.9959
0.1526
10.9347


−2.9953
0.1500
10.9347


−2.9935
0.1450
10.9347


−2.9881
0.1356
10.9347


−2.9765
0.1236
10.9347


−2.9505
0.1085
10.9347


−2.9124
0.0969
10.9347


−2.8597
0.0898
10.9347


−2.7933
0.0857
10.9347


−2.7068
0.0818
10.9347


−2.6070
0.0783
10.9347


−2.5006
0.0746
10.9347


−2.3809
0.0696
10.9347


−2.2480
0.0628
10.9347


−2.1019
0.0539
10.9347


−1.9494
0.0430
10.9347


−1.7903
0.0297
10.9347


−1.6248
0.0142
10.9347


−1.4527
−0.0035
10.9347


−1.2741
−0.0233
10.9347


−1.0891
−0.0454
10.9347


−0.8978
−0.0698
10.9347


−0.7003
−0.0972
10.9347


−0.5031
−0.1267
10.9347


−0.3063
−0.1586
10.9347


−0.1099
−0.1924
10.9347


0.0862
−0.2280
10.9347


0.2820
−0.2653
10.9347


0.4775
−0.3042
10.9347


0.6728
−0.3447
10.9347


0.8678
−0.3866
10.9347


1.0625
−0.4299
10.9347


1.2570
−0.4744
10.9347


1.4512
−0.5203
10.9347


1.6386
−0.5660
10.9347


1.8192
−0.6113
10.9347


1.9930
−0.6564
10.9347


2.1601
−0.7009
10.9347


2.3204
−0.7450
10.9347


2.4740
−0.7884
10.9347


2.6210
−0.8311
10.9347


2.7548
−0.8710
10.9347


2.8757
−0.9080
10.9347


2.9836
−0.9419
10.9347


3.0786
−0.9724
10.9347


3.1607
−0.9995
10.9347


3.2300
−1.0229
10.9347


3.2892
−1.0433
10.9347


3.3388
−1.0605
10.9347


3.3796
−1.0749
10.9347


3.4122
−1.0865
10.9347


3.4376
−1.0938
10.9347


3.4570
−1.0911
10.9347


3.4712
−1.0828
10.9347


3.4798
−1.0728
10.9347


3.4842
−1.0639
10.9347


3.4867
−1.0539
10.9347


3.4865
−1.0402
10.9347


3.4806
−1.0242
10.9347


3.4666
−1.0092
10.9347


3.4416
−0.9982
10.9347


3.4086
−0.9852
10.9347


3.3674
−0.9689
10.9347


3.3173
−0.9491
10.9347


3.2577
−0.9255
10.9347


3.1881
−0.8977
10.9347


3.1059
−0.8646
10.9347


3.0110
−0.8262
10.9347


2.9036
−0.7827
10.9347


2.7836
−0.7340
10.9347


2.6508
−0.6804
10.9347


2.5052
−0.6221
10.9347


2.3531
−0.5617
10.9347


2.1944
−0.4996
10.9347


2.0290
−0.4360
10.9347


1.8568
−0.3712
10.9347


1.6779
−0.3054
10.9347


1.4922
−0.2391
10.9347


1.2995
−0.1725
10.9347


1.1062
−0.1082
10.9347


0.9122
−0.0463
10.9347


0.7176
0.0130
10.9347


0.5221
0.0695
10.9347


0.3259
0.1229
10.9347


0.1288
0.1730
10.9347


−0.0692
0.2197
10.9347


−0.2683
0.2626
10.9347


−0.4684
0.3016
10.9347


−0.6697
0.3362
10.9347


−0.8722
0.3663
10.9347


−1.0693
0.3903
10.9347


−1.2608
0.4084
10.9347


−1.4457
0.4207
10.9347


−1.6241
0.4272
10.9347


−1.7959
0.4280
10.9347


−1.9607
0.4232
10.9347


−2.1183
0.4134
10.9347


−2.2688
0.3987
10.9347


−2.4050
0.3804
10.9347


−2.5270
0.3594
10.9347


−2.6346
0.3368
10.9347


−2.7345
0.3113
10.9347


−2.8199
0.2849
10.9347


−2.8845
0.2613
10.9347


−2.9340
0.2377
10.9347


−2.9675
0.2138
10.9347


−2.9875
0.1902
10.9347


−2.9947
0.1745
10.9347


−2.9967
0.1637
10.9347


−2.9967
0.1581
10.9347


−2.9964
0.1553
10.9347


−2.8093
0.0865
13.9347


−2.8091
0.0853
13.9347


−2.8084
0.0829
13.9347


−2.8067
0.0782
13.9347


−2.8014
0.0698
13.9347


−2.7899
0.0594
13.9347


−2.7651
0.0469
13.9347


−2.7292
0.0383
13.9347


−2.6801
0.0341
13.9347


−2.6186
0.0323
13.9347


−2.5386
0.0310
13.9347


−2.4462
0.0302
13.9347


−2.3477
0.0293
13.9347


−2.2369
0.0275
13.9347


−2.1139
0.0244
13.9347


−1.9786
0.0198
13.9347


−1.8372
0.0135
13.9347


−1.6897
0.0054
13.9347


−1.5361
−0.0047
13.9347


−1.3765
−0.0164
13.9347


−1.2108
−0.0298
13.9347


−1.0392
−0.0449
13.9347


−0.8616
−0.0620
13.9347


−0.6781
−0.0812
13.9347


−0.4948
−0.1024
13.9347


−0.3117
−0.1254
13.9347


−0.1287
−0.1501
13.9347


0.0540
−0.1762
13.9347


0.2366
−0.2037
13.9347


0.4191
−0.2325
13.9347


0.6013
−0.2625
13.9347


0.7833
−0.2937
13.9347


0.9651
−0.3259
13.9347


1.1467
−0.3592
13.9347


1.3281
−0.3936
13.9347


1.5033
−0.4278
13.9347


1.6723
−0.4619
13.9347


1.8350
−0.4957
13.9347


1.9916
−0.5293
13.9347


2.1419
−0.5624
13.9347


2.2859
−0.5951
13.9347


2.4238
−0.6273
13.9347


2.5496
−0.6575
13.9347


2.6632
−0.6854
13.9347


2.7647
−0.7110
13.9347


2.8541
−0.7341
13.9347


2.9314
−0.7546
13.9347


2.9968
−0.7723
13.9347


3.0526
−0.7877
13.9347


3.0994
−0.8008
13.9347


3.1380
−0.8117
13.9347


3.1687
−0.8205
13.9347


3.1926
−0.8265
13.9347


3.2109
−0.8238
13.9347


3.2239
−0.8156
13.9347


3.2315
−0.8058
13.9347


3.2351
−0.7973
13.9347


3.2367
−0.7879
13.9347


3.2354
−0.7754
13.9347


3.2286
−0.7612
13.9347


3.2142
−0.7490
13.9347


3.1904
−0.7408
13.9347


3.1594
−0.7309
13.9347


3.1205
−0.7185
13.9347


3.0733
−0.7034
13.9347


3.0171
−0.6855
13.9347


2.9514
−0.6645
13.9347


2.8738
−0.6395
13.9347


2.7843
−0.6104
13.9347


2.6829
−0.5774
13.9347


2.5695
−0.5406
13.9347


2.4442
−0.5000
13.9347


2.3068
−0.4558
13.9347


2.1634
−0.4101
13.9347


2.0137
−0.3631
13.9347


1.8579
−0.3150
13.9347


1.6959
−0.2659
13.9347


1.5278
−0.2163
13.9347


1.3534
−0.1662
13.9347


1.1727
−0.1159
13.9347


0.9917
−0.0674
13.9347


0.8104
−0.0207
13.9347


0.6287
0.0239
13.9347


0.4467
0.0663
13.9347


0.2643
0.1063
13.9347


0.0814
0.1438
13.9347


−0.1019
0.1786
13.9347


−0.2858
0.2104
13.9347


−0.4701
0.2391
13.9347


−0.6551
0.2644
13.9347


−0.8406
0.2861
13.9347


−1.0207
0.3032
13.9347


−1.1951
0.3159
13.9347


−1.3641
0.3241
13.9347


−1.5274
0.3279
13.9347


−1.6853
0.3272
13.9347


−1.8376
0.3220
13.9347


−1.9842
0.3126
13.9347


−2.1243
0.2993
13.9347


−2.2513
0.2830
13.9347


−2.3650
0.2646
13.9347


−2.4655
0.2449
13.9347


−2.5590
0.2229
13.9347


−2.6390
0.2003
13.9347


−2.6998
0.1802
13.9347


−2.7470
0.1606
13.9347


−2.7795
0.1402
13.9347


−2.7996
0.1196
13.9347


−2.8072
0.1055
13.9347


−2.8096
0.0955
13.9347


−2.8097
0.0904
13.9347


−2.8095
0.0878
13.9347


−2.7157
0.0569
15.4347


−2.7154
0.0557
15.4347


−2.7148
0.0534
15.4347


−2.7131
0.0490
15.4347


−2.7079
0.0410
15.4347


−2.6967
0.0312
15.4347


−2.6726
0.0198
15.4347


−2.6379
0.0122
15.4347


−2.5907
0.0089
15.4347


−2.5316
0.0077
15.4347


−2.4548
0.0071
15.4347


−2.3661
0.0071
15.4347


−2.2715
0.0072
15.4347


−2.1651
0.0065
15.4347


−2.0469
0.0048
15.4347


−1.9169
0.0019
15.4347


−1.7810
−0.0024
15.4347


−1.6392
−0.0084
15.4347


−1.4916
−0.0159
15.4347


−1.3382
−0.0249
15.4347


−1.1789
−0.0352
15.4347


−1.0139
−0.0470
15.4347


−0.8430
−0.0604
15.4347


−0.6664
−0.0757
15.4347


−0.4900
−0.0927
15.4347


−0.3137
−0.1113
15.4347


−0.1375
−0.1312
15.4347


0.0386
−0.1524
15.4347


0.2146
−0.1749
15.4347


0.3904
−0.1984
15.4347


0.5660
−0.2230
15.4347


0.7415
−0.2486
15.4347


0.9168
−0.2751
15.4347


1.0920
−0.3025
15.4347


1.2671
−0.3308
15.4347


1.4362
−0.3591
15.4347


1.5993
−0.3873
15.4347


1.7565
−0.4153
15.4347


1.9077
−0.4432
15.4347


2.0529
−0.4707
15.4347


2.1922
−0.4980
15.4347


2.3255
−0.5248
15.4347


2.4471
−0.5500
15.4347


2.5570
−0.5733
15.4347


2.6552
−0.5947
15.4347


2.7417
−0.6141
15.4347


2.8167
−0.6313
15.4347


2.8800
−0.6462
15.4347


2.9340
−0.6591
15.4347


2.9794
−0.6702
15.4347


3.0167
−0.6793
15.4347


3.0466
−0.6867
15.4347


3.0696
−0.6917
15.4347


3.0867
−0.6887
15.4347


3.0988
−0.6805
15.4347


3.1057
−0.6711
15.4347


3.1088
−0.6629
15.4347


3.1100
−0.6539
15.4347


3.1082
−0.6419
15.4347


3.1010
−0.6287
15.4347


3.0866
−0.6178
15.4347


3.0635
−0.6110
15.4347


3.0334
−0.6025
15.4347


2.9958
−0.5920
15.4347


2.9501
−0.5793
15.4347


2.8957
−0.5641
15.4347


2.8320
−0.5462
15.4347


2.7568
−0.5250
15.4347


2.6701
−0.5003
15.4347


2.5719
−0.4722
15.4347


2.4621
−0.4409
15.4347


2.3407
−0.4063
15.4347


2.2077
−0.3687
15.4347


2.0688
−0.3298
15.4347


1.9240
−0.2898
15.4347


1.7733
−0.2489
15.4347


1.6166
−0.2072
15.4347


1.4539
−0.1649
15.4347


1.2853
−0.1223
15.4347


1.1106
−0.0796
15.4347


0.9357
−0.0383
15.4347


0.7605
0.0013
15.4347


0.5850
0.0391
15.4347


0.4091
0.0751
15.4347


0.2330
0.1089
15.4347


0.0564
0.1406
15.4347


−0.1205
0.1698
15.4347


−0.2979
0.1964
15.4347


−0.4757
0.2202
15.4347


−0.6541
0.2410
15.4347


−0.8329
0.2587
15.4347


−1.0064
0.2722
15.4347


−1.1745
0.2818
15.4347


−1.3372
0.2875
15.4347


−1.4945
0.2893
15.4347


−1.6463
0.2870
15.4347


−1.7919
0.2807
15.4347


−1.9312
0.2707
15.4347


−2.0642
0.2573
15.4347


−2.1846
0.2414
15.4347


−2.2925
0.2237
15.4347


−2.3879
0.2050
15.4347


−2.4767
0.1843
15.4347


−2.5528
0.1631
15.4347


−2.6106
0.1443
15.4347


−2.6556
0.1262
15.4347


−2.6867
0.1074
15.4347


−2.7061
0.0882
15.4347


−2.7136
0.0749
15.4347


−2.7159
0.0654
15.4347


−2.7161
0.0606
15.4347


−2.7158
0.0581
15.4347


−2.6214
0.0300
16.9347


−2.6212
0.0288
16.9347


−2.6206
0.0266
16.9347


−2.6189
0.0224
16.9347


−2.6138
0.0148
16.9347


−2.6029
0.0056
16.9347


−2.5795
−0.0049
16.9347


−2.5462
−0.0116
16.9347


−2.5009
−0.0142
16.9347


−2.4442
−0.0149
16.9347


−2.3706
−0.0149
16.9347


−2.2855
−0.0142
16.9347


−2.1949
−0.0134
16.9347


−2.0928
−0.0131
16.9347


−1.9795
−0.0136
16.9347


−1.8548
−0.0149
16.9347


−1.7245
−0.0174
16.9347


−1.5885
−0.0213
16.9347


−1.4469
−0.0264
16.9347


−1.2997
−0.0327
16.9347


−1.1468
−0.0401
16.9347


−0.9884
−0.0487
16.9347


−0.8244
−0.0585
16.9347


−0.6548
−0.0699
16.9347


−0.4853
−0.0827
16.9347


−0.3159
−0.0969
16.9347


−0.1465
−0.1122
16.9347


0.0227
−0.1286
16.9347


0.1919
−0.1460
16.9347


0.3609
−0.1644
16.9347


0.5299
−0.1837
16.9347


0.6987
−0.2037
16.9347


0.8675
−0.2246
16.9347


1.0361
−0.2462
16.9347


1.2047
−0.2686
16.9347


1.3675
−0.2910
16.9347


1.5246
−0.3133
16.9347


1.6761
−0.3356
16.9347


1.8218
−0.3578
16.9347


1.9617
−0.3799
16.9347


2.0960
−0.4017
16.9347


2.2246
−0.4233
16.9347


2.3419
−0.4435
16.9347


2.4480
−0.4624
16.9347


2.5428
−0.4797
16.9347


2.6263
−0.4954
16.9347


2.6987
−0.5094
16.9347


2.7599
−0.5215
16.9347


2.8121
−0.5321
16.9347


2.8559
−0.5411
16.9347


2.8920
−0.5486
16.9347


2.9209
−0.5547
16.9347


2.9431
−0.5590
16.9347


2.9597
−0.5560
16.9347


2.9713
−0.5480
16.9347


2.9777
−0.5387
16.9347


2.9805
−0.5307
16.9347


2.9813
−0.5220
16.9347


2.9792
−0.5106
16.9347


2.9716
−0.4983
16.9347


2.9572
−0.4887
16.9347


2.9349
−0.4832
16.9347


2.9058
−0.4762
16.9347


2.8695
−0.4675
16.9347


2.8253
−0.4569
16.9347


2.7727
−0.4443
16.9347


2.7112
−0.4295
16.9347


2.6385
−0.4119
16.9347


2.5547
−0.3913
16.9347


2.4598
−0.3679
16.9347


2.3537
−0.3418
16.9347


2.2364
−0.3130
16.9347


2.1079
−0.2816
16.9347


1.9737
−0.2492
16.9347


1.8339
−0.2159
16.9347


1.6883
−0.1817
16.9347


1.5371
−0.1470
16.9347


1.3801
−0.1118
16.9347


1.2174
−0.0763
16.9347


1.0488
−0.0407
16.9347


0.8801
−0.0065
16.9347


0.7111
0.0264
16.9347


0.5419
0.0578
16.9347


0.3724
0.0875
16.9347


0.2027
0.1154
16.9347


0.0326
0.1413
16.9347


−0.1378
0.1651
16.9347


−0.3086
0.1867
16.9347


−0.4798
0.2057
16.9347


−0.6514
0.2221
16.9347


−0.8234
0.2356
16.9347


−0.9902
0.2456
16.9347


−1.1518
0.2522
16.9347


−1.3078
0.2553
16.9347


−1.4581
0.2549
16.9347


−1.6025
0.2510
16.9347


−1.7411
0.2436
16.9347


−1.8736
0.2330
16.9347


−2.0001
0.2195
16.9347


−2.1147
0.2039
16.9347


−2.2173
0.1867
16.9347


−2.3081
0.1689
16.9347


−2.3926
0.1493
16.9347


−2.4651
0.1293
16.9347


−2.5202
0.1118
16.9347


−2.5633
0.0950
16.9347


−2.5931
0.0776
16.9347


−2.6119
0.0596
16.9347


−2.6192
0.0471
16.9347


−2.6216
0.0381
16.9347


−2.6218
0.0334
16.9347


−2.6216
0.0311
16.9347


−2.5283
0.0052
18.4347


−2.5281
0.0041
18.4347


−2.5275
0.0020
18.4347


−2.5259
−0.0020
18.4347


−2.5209
−0.0093
18.4347


−2.5104
−0.0180
18.4347


−2.4880
−0.0280
18.4347


−2.4560
−0.0342
18.4347


−2.4126
−0.0365
18.4347


−2.3584
−0.0371
18.4347


−2.2878
−0.0369
18.4347


−2.2064
−0.0359
18.4347


−2.1195
−0.0347
18.4347


−2.0218
−0.0337
18.4347


−1.9132
−0.0332
18.4347


−1.7938
−0.0332
18.4347


−1.6689
−0.0342
18.4347


−1.5386
−0.0361
18.4347


−1.4029
−0.0390
18.4347


−1.2618
−0.0427
18.4347


−1.1153
−0.0473
18.4347


−0.9634
−0.0526
18.4347


−0.8062
−0.0590
18.4347


−0.6435
−0.0664
18.4347


−0.4809
−0.0751
18.4347


−0.3183
−0.0850
18.4347


−0.1558
−0.0957
18.4347


0.0067
−0.1074
18.4347


0.1691
−0.1199
18.4347


0.3314
−0.1331
18.4347


0.4937
−0.1471
18.4347


0.6559
−0.1617
18.4347


0.8180
−0.1770
18.4347


0.9801
−0.1929
18.4347


1.1422
−0.2094
18.4347


1.2987
−0.2261
18.4347


1.4499
−0.2427
18.4347


1.5955
−0.2594
18.4347


1.7357
−0.2761
18.4347


1.8704
−0.2928
18.4347


1.9996
−0.3094
18.4347


2.1234
−0.3258
18.4347


2.2364
−0.3413
18.4347


2.3385
−0.3558
18.4347


2.4299
−0.3692
18.4347


2.5104
−0.3814
18.4347


2.5801
−0.3923
18.4347


2.6391
−0.4018
18.4347


2.6895
−0.4101
18.4347


2.7318
−0.4172
18.4347


2.7666
−0.4231
18.4347


2.7944
−0.4279
18.4347


2.8158
−0.4314
18.4347


2.8317
−0.4285
18.4347


2.8427
−0.4206
18.4347


2.8487
−0.4115
18.4347


2.8511
−0.4037
18.4347


2.8515
−0.3954
18.4347


2.8490
−0.3846
18.4347


2.8411
−0.3732
18.4347


2.8268
−0.3649
18.4347


2.8053
−0.3605
18.4347


2.7772
−0.3549
18.4347


2.7421
−0.3479
18.4347


2.6995
−0.3394
18.4347


2.6488
−0.3292
18.4347


2.5895
−0.3172
18.4347


2.5195
−0.3029
18.4347


2.4386
−0.2862
18.4347


2.3471
−0.2672
18.4347


2.2448
−0.2459
18.4347


2.1316
−0.2224
18.4347


2.0077
−0.1968
18.4347


1.8784
−0.1703
18.4347


1.7436
−0.1431
18.4347


1.6034
−0.1152
18.4347


1.4577
−0.0868
18.4347


1.3065
−0.0581
18.4347


1.1497
−0.0292
18.4347


0.9875
−0.0002
18.4347


0.8250
0.0277
18.4347


0.6624
0.0544
18.4347


0.4996
0.0798
18.4347


0.3367
0.1037
18.4347


0.1735
0.1261
18.4347


0.0100
0.1468
18.4347


−0.1537
0.1656
18.4347


−0.3177
0.1824
18.4347


−0.4821
0.1969
18.4347


−0.6467
0.2092
18.4347


−0.8117
0.2189
18.4347


−0.9716
0.2255
18.4347


−1.1260
0.2292
18.4347


−1.2749
0.2298
18.4347


−1.4184
0.2274
18.4347


−1.5562
0.2219
18.4347


−1.6883
0.2133
18.4347


−1.8147
0.2020
18.4347


−1.9354
0.1880
18.4347


−2.0446
0.1724
18.4347


−2.1425
0.1554
18.4347


−2.2291
0.1380
18.4347


−2.3097
0.1190
18.4347


−2.3788
0.0998
18.4347


−2.4314
0.0829
18.4347


−2.4725
0.0670
18.4347


−2.5012
0.0504
18.4347


−2.5192
0.0334
18.4347


−2.5262
0.0215
18.4347


−2.5284
0.0129
18.4347


−2.5286
0.0085
18.4347


−2.5284
0.0063
18.4347


−2.4751
−0.0060
19.1847


−2.4748
−0.0071
19.1847


−2.4743
−0.0091
19.1847


−2.4727
−0.0131
19.1847


−2.4679
−0.0202
19.1847


−2.4578
−0.0288
19.1847


−2.4360
−0.0387
19.1847


−2.4048
−0.0449
19.1847


−2.3624
−0.0474
19.1847


−2.3094
−0.0483
19.1847


−2.2405
−0.0483
19.1847


−2.1610
−0.0474
19.1847


−2.0761
−0.0461
19.1847


−1.9807
−0.0451
19.1847


−1.8747
−0.0443
19.1847


−1.7580
−0.0440
19.1847


−1.6361
−0.0444
19.1847


−1.5088
−0.0456
19.1847


−1.3763
−0.0476
19.1847


−1.2384
−0.0502
19.1847


−1.0953
−0.0534
19.1847


−0.9469
−0.0573
19.1847


−0.7933
−0.0620
19.1847


−0.6343
−0.0676
19.1847


−0.4754
−0.0743
19.1847


−0.3166
−0.0820
19.1847


−0.1577
−0.0905
19.1847


0.0011
−0.0998
19.1847


0.1599
−0.1098
19.1847


0.3186
−0.1205
19.1847


0.4772
−0.1318
19.1847


0.6359
−0.1437
19.1847


0.7944
−0.1561
19.1847


0.9530
−0.1691
19.1847


1.1115
−0.1827
19.1847


1.2646
−0.1963
19.1847


1.4125
−0.2101
19.1847


1.5550
−0.2240
19.1847


1.6921
−0.2379
19.1847


1.8240
−0.2518
19.1847


1.9505
−0.2658
19.1847


2.0716
−0.2797
19.1847


2.1822
−0.2928
19.1847


2.2822
−0.3051
19.1847


2.3716
−0.3166
19.1847


2.4505
−0.3270
19.1847


2.5188
−0.3364
19.1847


2.5765
−0.3447
19.1847


2.6259
−0.3519
19.1847


2.6673
−0.3580
19.1847


2.7014
−0.3632
19.1847


2.7286
−0.3674
19.1847


2.7496
−0.3705
19.1847


2.7651
−0.3675
19.1847


2.7758
−0.3597
19.1847


2.7815
−0.3507
19.1847


2.7837
−0.3431
19.1847


2.7840
−0.3350
19.1847


2.7812
−0.3245
19.1847


2.7733
−0.3135
19.1847


2.7591
−0.3059
19.1847


2.7379
−0.3020
19.1847


2.7105
−0.2971
19.1847


2.6761
−0.2908
19.1847


2.6344
−0.2832
19.1847


2.5847
−0.2742
19.1847


2.5266
−0.2635
19.1847


2.4580
−0.2507
19.1847


2.3788
−0.2358
19.1847


2.2892
−0.2187
19.1847


2.1889
−0.1996
19.1847


2.0782
−0.1785
19.1847


1.9568
−0.1555
19.1847


1.8301
−0.1317
19.1847


1.6982
−0.1072
19.1847


1.5608
−0.0821
19.1847


1.4182
−0.0566
19.1847


1.2701
−0.0308
19.1847


1.1167
−0.0048
19.1847


0.9579
0.0212
19.1847


0.7989
0.0462
19.1847


0.6398
0.0701
19.1847


0.4805
0.0928
19.1847


0.3211
0.1141
19.1847


0.1614
0.1340
19.1847


0.0016
0.1523
19.1847


−0.1585
0.1688
19.1847


−0.3189
0.1835
19.1847


−0.4795
0.1959
19.1847


−0.6404
0.2063
19.1847


−0.8016
0.2142
19.1847


−0.9577
0.2193
19.1847


−1.1083
0.2215
19.1847


−1.2536
0.2209
19.1847


−1.3935
0.2175
19.1847


−1.5280
0.2111
19.1847


−1.6568
0.2019
19.1847


−1.7801
0.1900
19.1847


−1.8977
0.1756
19.1847


−2.0042
0.1598
19.1847


−2.0996
0.1427
19.1847


−2.1840
0.1252
19.1847


−2.2625
0.1063
19.1847


−2.3298
0.0872
19.1847


−2.3810
0.0704
19.1847


−2.4211
0.0546
19.1847


−2.4489
0.0384
19.1847


−2.4663
0.0216
19.1847


−2.4731
0.0099
19.1847


−2.4752
0.0016
19.1847


−2.4754
−0.0027
19.1847


−2.4752
−0.0049
19.1847


−2.4159
−0.0161
19.9347


−2.4157
−0.0172
19.9347


−2.4151
−0.0192
19.9347


−2.4136
−0.0231
19.9347


−2.4091
−0.0300
19.9347


−2.3993
−0.0386
19.9347


−2.3782
−0.0486
19.9347


−2.3479
−0.0551
19.9347


−2.3067
−0.0579
19.9347


−2.2551
−0.0592
19.9347


−2.1880
−0.0596
19.9347


−2.1105
−0.0591
19.9347


−2.0278
−0.0581
19.9347


−1.9349
−0.0572
19.9347


−1.8316
−0.0564
19.9347


−1.7179
−0.0559
19.9347


−1.5991
−0.0559
19.9347


−1.4752
−0.0566
19.9347


−1.3460
−0.0578
19.9347


−1.2117
−0.0595
19.9347


−1.0723
−0.0615
19.9347


−0.9277
−0.0641
19.9347


−0.7779
−0.0671
19.9347


−0.6230
−0.0709
19.9347


−0.4682
−0.0757
19.9347


−0.3133
−0.0812
19.9347


−0.1585
−0.0875
19.9347


−0.0037
−0.0944
19.9347


0.1511
−0.1019
19.9347


0.3059
−0.1099
19.9347


0.4606
−0.1185
19.9347


0.6153
−0.1276
19.9347


0.7700
−0.1371
19.9347


0.9246
−0.1472
19.9347


1.0792
−0.1577
19.9347


1.2286
−0.1684
19.9347


1.3729
−0.1792
19.9347


1.5119
−0.1902
19.9347


1.6458
−0.2013
19.9347


1.7744
−0.2125
19.9347


1.8979
−0.2238
19.9347


2.0162
−0.2351
19.9347


2.1241
−0.2458
19.9347


2.2218
−0.2560
19.9347


2.3091
−0.2655
19.9347


2.3861
−0.2742
19.9347


2.4528
−0.2821
19.9347


2.5092
−0.2891
19.9347


2.5573
−0.2952
19.9347


2.5978
−0.3004
19.9347


2.6311
−0.3048
19.9347


2.6577
−0.3084
19.9347


2.6782
−0.3111
19.9347


2.6933
−0.3080
19.9347


2.7035
−0.3003
19.9347


2.7089
−0.2915
19.9347


2.7109
−0.2840
19.9347


2.7111
−0.2761
19.9347


2.7082
−0.2659
19.9347


2.7002
−0.2555
19.9347


2.6861
−0.2485
19.9347


2.6655
−0.2451
19.9347


2.6386
−0.2407
19.9347


2.6051
−0.2352
19.9347


2.5643
−0.2285
19.9347


2.5157
−0.2205
19.9347


2.4590
−0.2111
19.9347


2.3919
−0.1997
19.9347


2.3146
−0.1864
19.9347


2.2269
−0.1712
19.9347


2.1290
−0.1542
19.9347


2.0207
−0.1353
19.9347


1.9022
−0.1147
19.9347


1.7784
−0.0934
19.9347


1.6495
−0.0715
19.9347


1.5153
−0.0490
19.9347


1.3759
−0.0262
19.9347


1.2313
−0.0030
19.9347


1.0813
0.0202
19.9347


0.9261
0.0435
19.9347


0.7707
0.0658
19.9347


0.6153
0.0872
19.9347


0.4596
0.1074
19.9347


0.3039
0.1263
19.9347


0.1479
0.1439
19.9347


−0.0082
0.1599
19.9347


−0.1645
0.1742
19.9347


−0.3210
0.1868
19.9347


−0.4776
0.1973
19.9347


−0.6343
0.2057
19.9347


−0.7911
0.2119
19.9347


−0.9428
0.2155
19.9347


−1.0894
0.2163
19.9347


−1.2306
0.2145
19.9347


−1.3666
0.2100
19.9347


−1.4973
0.2027
19.9347


−1.6225
0.1928
19.9347


−1.7422
0.1802
19.9347


−1.8564
0.1654
19.9347


−1.9598
0.1492
19.9347


−2.0524
0.1319
19.9347


−2.1344
0.1144
19.9347


−2.2105
0.0953
19.9347


−2.2759
0.0762
19.9347


−2.3255
0.0594
19.9347


−2.3642
0.0436
19.9347


−2.3910
0.0274
19.9347


−2.4077
0.0108
19.9347


−2.4141
−0.0006
19.9347


−2.4161
−0.0088
19.9347


−2.4162
−0.0130
19.9347


−2.4160
−0.0151
19.9347


−2.2907
−0.0328
21.4347


−2.2905
−0.0338
21.4347


−2.2900
−0.0357
21.4347


−2.2887
−0.0394
21.4347


−2.2847
−0.0462
21.4347


−2.2760
−0.0548
21.4347


−2.2567
−0.0655
21.4347


−2.2285
−0.0731
21.4347


−2.1897
−0.0775
21.4347


−2.1410
−0.0803
21.4347


−2.0776
−0.0825
21.4347


−2.0044
−0.0835
21.4347


−1.9263
−0.0838
21.4347


−1.8385
−0.0839
21.4347


−1.7409
−0.0840
21.4347


−1.6335
−0.0839
21.4347


−1.5212
−0.0839
21.4347


−1.4041
−0.0841
21.4347


−1.2821
−0.0845
21.4347


−1.1552
−0.0849
21.4347


−1.0234
−0.0852
21.4347


−0.8867
−0.0855
21.4347


−0.7452
−0.0858
21.4347


−0.5988
−0.0865
21.4347


−0.4523
−0.0877
21.4347


−0.3059
−0.0894
21.4347


−0.1595
−0.0915
21.4347


−0.0131
−0.0940
21.4347


0.1333
−0.0968
21.4347


0.2797
−0.0999
21.4347


0.4261
−0.1033
21.4347


0.5724
−0.1070
21.4347


0.7188
−0.1110
21.4347


0.8652
−0.1153
21.4347


1.0115
−0.1199
21.4347


1.1530
−0.1247
21.4347


1.2896
−0.1298
21.4347


1.4212
−0.1351
21.4347


1.5480
−0.1407
21.4347


1.6699
−0.1465
21.4347


1.7869
−0.1526
21.4347


1.8990
−0.1589
21.4347


2.0013
−0.1650
21.4347


2.0939
−0.1710
21.4347


2.1766
−0.1768
21.4347


2.2497
−0.1822
21.4347


2.3129
−0.1873
21.4347


2.3664
−0.1919
21.4347


2.4121
−0.1960
21.4347


2.4505
−0.1995
21.4347


2.4821
−0.2026
21.4347


2.5074
−0.2050
21.4347


2.5268
−0.2069
21.4347


2.5411
−0.2040
21.4347


2.5508
−0.1965
21.4347


2.5558
−0.1880
21.4347


2.5576
−0.1808
21.4347


2.5574
−0.1733
21.4347


2.5543
−0.1638
21.4347


2.5463
−0.1542
21.4347


2.5327
−0.1484
21.4347


2.5131
−0.1458
21.4347


2.4876
−0.1425
21.4347


2.4558
−0.1383
21.4347


2.4171
−0.1331
21.4347


2.3710
−0.1269
21.4347


2.3171
−0.1196
21.4347


2.2535
−0.1106
21.4347


2.1801
−0.1001
21.4347


2.0970
−0.0880
21.4347


2.0041
−0.0742
21.4347


1.9014
−0.0590
21.4347


1.7890
−0.0423
21.4347


1.6716
−0.0250
21.4347


1.5494
−0.0071
21.4347


1.4222
0.0112
21.4347


1.2901
0.0299
21.4347


1.1531
0.0488
21.4347


1.0111
0.0678
21.4347


0.8641
0.0867
21.4347


0.7170
0.1049
21.4347


0.5699
0.1221
21.4347


0.4226
0.1383
21.4347


0.2752
0.1534
21.4347


0.1277
0.1672
21.4347


−0.0200
0.1796
21.4347


−0.1678
0.1905
21.4347


−0.3159
0.1997
21.4347


−0.4641
0.2070
21.4347


−0.6125
0.2124
21.4347


−0.7610
0.2158
21.4347


−0.9045
0.2167
21.4347


−1.0431
0.2151
21.4347


−1.1767
0.2111
21.4347


−1.3052
0.2045
21.4347


−1.4286
0.1954
21.4347


−1.5469
0.1837
21.4347


−1.6599
0.1698
21.4347


−1.7677
0.1537
21.4347


−1.8652
0.1364
21.4347


−1.9524
0.1181
21.4347


−2.0295
0.0998
21.4347


−2.1011
0.0799
21.4347


−2.1623
0.0600
21.4347


−2.2087
0.0426
21.4347


−2.2447
0.0262
21.4347


−2.2692
0.0097
21.4347


−2.2841
−0.0069
21.4347


−2.2895
−0.0180
21.4347


−2.2910
−0.0258
21.4347


−2.2910
−0.0298
21.4347


−2.2908
−0.0318
21.4347


−2.1635
−0.0473
22.9347


−2.1633
−0.0482
22.9347


−2.1629
−0.0501
22.9347


−2.1617
−0.0536
22.9347


−2.1582
−0.0602
22.9347


−2.1507
−0.0689
22.9347


−2.1333
−0.0804
22.9347


−2.1073
−0.0896
22.9347


−2.0711
−0.0959
22.9347


−2.0254
−0.1008
22.9347


−1.9658
−0.1052
22.9347


−1.8969
−0.1083
22.9347


−1.8234
−0.1103
22.9347


−1.7406
−0.1121
22.9347


−1.6487
−0.1135
22.9347


−1.5476
−0.1144
22.9347


−1.4418
−0.1150
22.9347


−1.3315
−0.1155
22.9347


−1.2166
−0.1156
22.9347


−1.0971
−0.1152
22.9347


−0.9730
−0.1143
22.9347


−0.8443
−0.1129
22.9347


−0.7109
−0.1110
22.9347


−0.5730
−0.1090
22.9347


−0.4351
−0.1071
22.9347


−0.2972
−0.1055
22.9347


−0.1593
−0.1039
22.9347


−0.0214
−0.1023
22.9347


0.1165
−0.1007
22.9347


0.2544
−0.0992
22.9347


0.3923
−0.0978
22.9347


0.5303
−0.0964
22.9347


0.6682
−0.0951
22.9347


0.8061
−0.0939
22.9347


0.9440
−0.0929
22.9347


1.0773
−0.0921
22.9347


1.2061
−0.0916
22.9347


1.3302
−0.0915
22.9347


1.4497
−0.0917
22.9347


1.5646
−0.0924
22.9347


1.6750
−0.0935
22.9347


1.7807
−0.0949
22.9347


1.8772
−0.0967
22.9347


1.9646
−0.0988
22.9347


2.0427
−0.1010
22.9347


2.1116
−0.1034
22.9347


2.1713
−0.1058
22.9347


2.2218
−0.1082
22.9347


2.2650
−0.1105
22.9347


2.3013
−0.1124
22.9347


2.3311
−0.1141
22.9347


2.3550
−0.1156
22.9347


2.3733
−0.1168
22.9347


2.3868
−0.1138
22.9347


2.3957
−0.1066
22.9347


2.4002
−0.0984
22.9347


2.4017
−0.0916
22.9347


2.4013
−0.0846
22.9347


2.3980
−0.0757
22.9347


2.3901
−0.0670
22.9347


2.3770
−0.0622
22.9347


2.3584
−0.0604
22.9347


2.3343
−0.0579
22.9347


2.3042
−0.0548
22.9347


2.2676
−0.0510
22.9347


2.2241
−0.0463
22.9347


2.1732
−0.0407
22.9347


2.1131
−0.0338
22.9347


2.0437
−0.0255
22.9347


1.9651
−0.0158
22.9347


1.8774
−0.0047
22.9347


1.7804
0.0077
22.9347


1.6741
0.0213
22.9347


1.5633
0.0356
22.9347


1.4478
0.0504
22.9347


1.3277
0.0656
22.9347


1.2030
0.0811
22.9347


1.0736
0.0968
22.9347


0.9395
0.1126
22.9347


0.8007
0.1283
22.9347


0.6619
0.1433
22.9347


0.5230
0.1573
22.9347


0.3840
0.1705
22.9347


0.2449
0.1825
22.9347


0.1057
0.1933
22.9347


−0.0336
0.2028
22.9347


−0.1731
0.2109
22.9347


−0.3127
0.2173
22.9347


−0.4525
0.2218
22.9347


−0.5924
0.2246
22.9347


−0.7323
0.2254
22.9347


−0.8675
0.2239
22.9347


−0.9980
0.2200
22.9347


−1.1238
0.2138
22.9347


−1.2448
0.2051
22.9347


−1.3608
0.1939
22.9347


−1.4720
0.1804
22.9347


−1.5781
0.1647
22.9347


−1.6792
0.1470
22.9347


−1.7706
0.1282
22.9347


−1.8523
0.1087
22.9347


−1.9244
0.0892
22.9347


−1.9911
0.0682
22.9347


−2.0480
0.0471
22.9347


−2.0909
0.0287
22.9347


−2.1239
0.0114
22.9347


−2.1458
−0.0056
22.9347


−2.1586
−0.0223
22.9347


−2.1629
−0.0332
22.9347


−2.1640
−0.0407
22.9347


−2.1639
−0.0445
22.9347


−2.1636
−0.0464
22.9347









In the exemplary embodiments, as embodied by the invention, for example an IGV for a compressor, there are many airfoils, which are un-cooled. For reference purposes only, there is established point-0 passing through the intersection of an IGV and the platform along the stacking axis.


Moreover, the IGV, as embodied by the invention, defines a spouting angle into the first compressor rotor stage. This spouting angle defined by the IGV, as embodied by the invention, is an important factor to providing that a compressor meets flow requirements, and proportional output requirements at base load.


It will also be appreciated that the exemplary IGV airfoil(s) disclosed in the above TABLE A may be scaled up or down geometrically for use in other similar compressor designs. Consequently, the coordinate values set forth in TABLE A may be scaled upwardly or downwardly such TABLE A the IGV airfoil profile shape remains unchanged. A scaled version of the coordinates in the TABLE A would be represented by X, Y and Z coordinate values of the TABLE A multiplied or divided by a constant.


In particular, as embodied by the invention, the airfoil as defined by TABLE A, can be applied in a compressor of a turbine, for example, but not limited to, as General Electric “7FA+e” or 7FA.05 compressor. This compressor is merely illustrative of the intended applications for the airfoil, as embodied by the invention. Moreover, it is envisioned that the IGV airfoil of TABLE A, as embodied by the invention, can also be used as an IGV in GE Frame F-class turbines, as well as GE's Frame 6 and 9 turbines, given the scaling of the airfoil, as embodied by the invention.


An IGV airfoil can impart kinetic energy to the airflow and therefore bring about a desired flow across the compressor. The IGV airfoils turn the fluid flow, slow the fluid flow velocity (in the respective airfoil frame of reference), and yield a rise in the static pressure of the fluid flow. The configuration of the IGV airfoil (along with its interaction with surrounding airfoils), as embodied by the invention, including its peripheral surface provides 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, among other desirable aspects of the invention. Typically, multiple rows of airfoil stages, such as, but not limited to, rotor/stator airfoils, are stacked to achieve a desired discharge to inlet pressure ratio. Airfoils can be secured to wheels or a case by an appropriate attachment configuration, often known as a “root”, “base” or “dovetail”.


The configuration of an IGV airfoil and any interaction with surrounding airfoils, as embodied by the invention, that provide the desirable aspects fluid flow dynamics and laminar flow of the invention can be determined by various means. Fluid flow from an IGV airfoil, as embodied by the invention, and via the configuration of the instant airfoil, flow over and around subsequent airfoils, as embodied by the invention, is enhanced. In particular, the fluid dynamics and laminar flow from an IGV airfoil, as embodied by the invention, is enhanced. There is a smooth transition fluid flow to any subsequent or downstream airfoils. Moreover, the flow from an IGV, as embodied by the invention, proceeds to the adjacent/downstream airfoil(s) is enhanced due to the enhanced laminar fluid flow off of the IGV airfoil, as embodied by the invention. Therefore, the configuration of the IGV airfoil, as embodied by the invention, assists in the prevention of turbulent fluid flow in the unit comprising the airfoil, as embodied by the invention.


For example, but in no way limiting of the invention, an IGV airfoil configuration (with or without fluid flow interaction) can be determined by computational modeling, Fluid Dynamics (CFD); traditional fluid dynamics analysis; Euler and Navier-Stokes equations; for transfer functions, algorithms, manufacturing: manual positioning, flow testing (for example in wind tunnels), and modification of an IGV; in-situ testing; modeling: application of scientific principles to design or develop the airfoils, machines, apparatus, or manufacturing processes; IGV airfoil flow testing and modification; combinations thereof, and other design processes and practices. These methods of determination are merely exemplary, and are not intended to limit the invention in any manner.


As noted above, the IGV airfoil configuration (along with its interaction with surrounding airfoils), as embodied by the invention, including its peripheral surface provides for airflow efficiency, enhanced aeromechanics, smooth laminar flow from stage to stage, reduced thermal stresses, enhanced interrelation of the stages to effectively pass the IGV airflow from stage to stage, and reduced mechanical stresses, among other desirable aspects of the invention, compared to other similar airfoils, which have like applications. Of course, other such advantages are within the scope of the invention.


While various embodiments are described herein, it will be appreciated from the specification that various combinations of elements, variations or improvements therein may be made by those skilled in the art, and are within the scope of the invention.

Claims
  • 1. An article of manufacture, the article having a nominal profile substantially 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 profile sections at the Z distances being joined smoothly with one another to form a complete inlet guide vane airfoil shape.
  • 2. An article of manufacture according to claim 1, wherein the inlet guide vane airfoil shape comprises an airfoil.
  • 3. An article of manufacture according to claim 2, wherein said airfoil shape lies in an envelope within ±0.160 inches in a direction normal to any article surface location.
  • 4. A compressor comprising a compressor wheel having a plurality of blades, each of said blades cooperating with a plurality of stator vanes, the compressor comprising an inlet guide vane having an airfoil shape, said airfoil shape having a nominal profile substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in TABLE A, wherein X and Y are distances in inches which, when connected by smooth continuing arcs, define the airfoil profile sections at each distance Z in inches, the profile sections at the Z distances being joined smoothly with one another to form a complete inlet guide vane airfoil shape.
  • 5. A compressor comprising a compressor wheel having a plurality of blades, each of said blades cooperating with a plurality of stator vanes, the compressor comprising an inlet guide vane comprising an airfoil having an uncoated nominal airfoil profile substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in TABLE A, 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 profile sections at the Z distances being joined smoothly with one another to form a complete inlet guide vane airfoil shape, the X and Y distances being scalable as a function of the same constant or number to provide at least one of a scaled up inlet guide vane airfoil and scaled down inlet guide vane airfoil.
  • 6. A compressor according to claim 5 wherein said airfoil shape lies in an envelope within ±0.160 inches in a direction normal to any airfoil surface location.