AIRFOIL SHAPE FOR FIRST STAGE COMPRESSOR STATOR VANE

Abstract
A system is provided, including an airfoil. The airfoil includes a first suction portion of a nominal airfoil profile substantially in accordance with Cartesian coordinate values of X, Y, and Z of a suction side as set forth in TABLE I to a maximum of three decimal places, wherein the X and Y values of the suction side are coordinate values that couple together to define suction side sections of the first suction portion of the nominal airfoil profile at each Z coordinate value, the suction side sections of the first suction portion of the nominal airfoil profile are coupled together to define the first suction portion, the airfoil includes an airfoil length along a Z axis, the first suction portion comprises a first portion length along the Z axis, the first portion length is less than or equal to the airfoil length, and the Cartesian coordinate values of X, Y, and Z are non-dimensional values convertible to dimensional distances.
Description
BACKGROUND OF THE INVENTION

The subject matter disclosed herein relates to compressor stator vanes, and more specifically, to a first stage compressor stator vane.


Compressors are used in a variety of industries and systems to compress a gas, such as air. For example, gas turbine engines typically include a compressor to provide compressed air for combustion and cooling. Compressors typically include a rotor assembly and a stator assembly. In multi-stage compressors, the rotor assembly may include multiple rows (e.g., rotor stages) each row having multiple rotor blades. Likewise, the stator assembly may include multiple rows (e.g., stator stages) each row having multiple stator vanes. The rotor assembly is designed to rotate with respect to the stator assembly, compressing an intake fluid as the fluid traverses the compressor.


BRIEF DESCRIPTION OF THE INVENTION

Certain embodiments commensurate in scope with the originally claimed subject matter are summarized below. These embodiments are not intended to limit the scope of the claimed invention, but rather these embodiments are intended only to provide a brief summary of possible forms of the subject matter. Indeed, the invention may encompass a variety of forms that may be similar to or different from the embodiments set forth below.


In a first embodiment, a system includes an airfoil. The airfoil includes a first suction portion of a nominal airfoil profile substantially in accordance with Cartesian coordinate values of X, Y, and Z of a suction side as set forth in TABLE I to a maximum of three decimal places, wherein the X and Y values of the suction side are coordinate values that couple together to define suction side sections of the first suction portion of the nominal airfoil profile at each Z coordinate value, the suction side sections of the first suction portion of the nominal airfoil profile are coupled together to define the first suction portion, the airfoil includes an airfoil length along a Z axis, the first suction portion comprises a first portion length along the Z axis, the first portion length is less than or equal to the airfoil length, and the Cartesian coordinate values of X, Y, and Z are non-dimensional values convertible to dimensional distances.


In a second embodiment, a system includes an airfoil. The airfoil includes a suction side of a nominal airfoil profile substantially in accordance with Cartesian coordinate values of X, Y, and Z of the suction side as set forth in TABLE I to a maximum of three decimal places, wherein the X and Y values of the suction side are coordinate values that couple together to define suction side sections of the suction side of the nominal airfoil profile at each Z coordinate value, the suction side sections of the suction side of the nominal airfoil profile are coupled together to define the suction side, and the Cartesian coordinate values of X, Y, and Z are non-dimensional values convertible to dimensional distances.


In a third embodiment, a system includes an airfoil. The airfoil includes a nominal airfoil profile substantially in accordance with Cartesian coordinate values of X, Y, and Z as set forth in TABLE I to a maximum of three decimal places, wherein the X and Y values are coordinate values that couple together to define airfoil sections of the nominal airfoil profile at each Z coordinate value, the airfoil sections of the nominal airfoil profile are coupled together to define an entirety of the airfoil, and the Cartesian coordinate values of X, Y, and Z are non-dimensional values convertible to dimensional distances.





BRIEF DESCRIPTION OF THE DRAWINGS

These and other features, aspects, and advantages of the present subject matter will become better understood when the following detailed description is read with reference to the accompanying drawings in which like characters represent like parts throughout the drawings, wherein:



FIG. 1 is a block diagram of an embodiment of a gas turbine system having a multi-stage axial compressor;



FIG. 2 is a cross-sectional side view of an embodiment of the gas turbine engine of FIG. 1, illustrating stages of blades and vanes of the multi-stage axial compressor;



FIG. 3 is side view of an embodiment of an airfoil of a compressor rotor blade or a compressor stator vane;



FIG. 4 is side view of an embodiment of an airfoil of a compressor rotor blade or a compressor stator vane;



FIG. 5 is a side view of an embodiment of an airfoil of the compressor rotor blade or a compressor stator vane; and



FIG. 6 is an axial view of an embodiment of the airfoil of the compressor rotor blade or compressor stator vane of FIGS. 3-5.





DETAILED DESCRIPTION OF THE INVENTION

One or more specific embodiments of the present subject matter will be described below. In an effort to provide a concise description of these embodiments, all features of an actual implementation may not be described in the specification. It should be appreciated that in the development of any such actual implementation, as in any engineering or design project, numerous implementation-specific decisions must be made to achieve the developers' specific goals, such as compliance with system-related and business-related constraints, which may vary from one implementation to another. Moreover, it should be appreciated that such a development effort might be complex and time consuming, but would nevertheless be a routine undertaking of design, fabrication, and manufacture for those of ordinary skill having the benefit of this disclosure.


When introducing elements of various embodiments of the present subject matter, the articles “a,” “an,” “the,” and “said” are intended to mean that there are one or more of the elements. The terms “comprising,” “including,” and “having” are intended to be inclusive and mean that there may be additional elements other than the listed elements.


The disclosed embodiments include a multi-stage axial compressor, which may be a standalone unit or part of a multi-stage rotary machine such as a gas turbine system. In certain embodiments, the multi-stage axial compressor includes a plurality of rotor stages and corresponding stator stages, each rotor stage and stator stage including a plurality of airfoils (e.g., blades or vanes) with a specific airfoil profile. During operation, a compressible fluid (e.g., gas such as air, oxygen, oxygen enriched air, oxygen reduced air, exhaust gas, nitrogen, etc.) may enter the multi-stage axial compressor through an inlet system, and each stage of the multi-stage axial compressor will generally increase the pressure and temperature of the compressible fluid by a certain amount. In a gas turbine system, a compressed fluid may then be delivered, for example, via an outlet system, to a combustor for combustion with a fuel. The amount of pressure and temperature increase at each stage of the multi-stage axial compressor may depend on particular operating conditions, such as speed, inlet boundary conditions (e.g., flow, pressure, temperature, composition, and so forth), outlet boundary conditions (e.g., flow resistance, and so forth), and stage efficiency.


During compression, an energy level of the compressible fluid may increase as the compressible fluid flows through the multi-stage axial compressor due to the exertion of a torque on the fluid by the rotating rotor blades. The stator's stationary vanes slow the compressible fluid, converting a circumferential component of the flow into pressure. An airfoil profile or design of the airfoil (e.g., rotor blades and/or stator vanes) may directly affect compression of the compressible fluid. Airfoil profiles described herein may be more optimized and matched for specific velocities and turning speeds. Further, the airfoil profiles described herein may be more optimized for specific stages of the multi-stage axial compressor with a specific total number of stages. Additionally, the airfoil profiles described herein may be designed for compressor rotor blades, compressor stator vanes, or any combination thereof. In certain embodiments, the airfoil profiles described herein may be designed for compressor rotor blades and/or compressor stator vanes in any one or more stages of a multi-stage axial compressor with 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, or 20 stages. More specifically, in certain embodiments, the airfoil profiles described herein may be designed for compressor rotor blades and/or compressor stator vanes in stage 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, and/or 14 of a 14 stage axial compressor. For example, in certain embodiments, the airfoil profiles described herein may be more optimized for a first stage airfoil (e.g., a rotor blade or stator vane) of a 14 stage axial compressor. The airfoils (e.g., blades or vanes) described herein may be described in terms of X, Y, and Z values set forth in certain table(s) described herein that define airfoil sections of the airfoils. In certain embodiments the X, Y, and Z values may describe suction side airfoil surfaces, pressure side airfoil surfaces, or a combination thereof. The X, Y, and Z values may include coordinate values in a Cartesian coordinate system, including negative and positive values denoting sides that are opposite to each other from a certain axis (e.g., X, Y, Z axis).


Turning now to FIG. 1, the figure is a block diagram of an embodiment of a turbine system 10 that includes a gas turbine engine 12 and a controller 14 (e.g., electronic and/or processor-based controller). The controller 14 may be communicatively coupled to a variety of sensors 16 and actuators 18 disposed in various components of the gas turbine engine 12. Signals received via the sensors 16 may be used to derive control actions executable via the actuators 18. The illustrated gas turbine engine 12 includes a compressor 20 (e.g., a multi-stage axial compressor or compressor section), a turbine 22 (e.g., a multi-stage turbine or turbine section), and fuel nozzles 24 coupled to one or more combustors 26 (e.g., compressor section). The compressor 20 and turbine 22 each may have any number of rows stages of rotor blades and stator vanes (e.g., 1 to 20). As discussed in detail below, an embodiment of an airfoil profile is provided for use with airfoils (e.g., rotor blades or stator vanes) in one or more stages of the compressor 20. However, before presenting details of the airfoil profile, the following discussion provides a brief description of the gas turbine engine 12 and its operation.


In operation, the compressor 20 is configured to compress a compressible fluid (e.g., gas such as air, oxygen, and/or exhaust gas), and deliver the compressed fluid to the fuel nozzles 24 and/or combustors 26. Although the compressible fluid may include any suitable gas, the following discussion may generally refer to the compressible fluid as an oxidant (e.g., air) as one non-limiting example. The fuel nozzles 24 are configured to supply fuel (e.g., from one or more fuel supplies) into the one or more combustors 26 (e.g., in combustion chambers), which combust the fuel with the oxidant (e.g., air) to generate hot combustion gases to drive the turbine 22. The fuel nozzles 24 may be designed as pre-mix fuel nozzles 24 and/or diffusion fuel nozzles 24. Pre-mix fuel nozzles 24 mix the fuel with the oxidant (e.g., air) to create pre-mix type flames. Diffusion fuel nozzles 24 do not premix the fuel with the oxidant, and thus create diffusion type flames. Regardless of the type of flames, the hot combustion gas flows from the combustors 26 into the turbine 22, thereby driving rotation of one or more stages of turbine blades coupled to a turbine rotor and shaft 30 along an axis 32. Eventually, the hot combustion gas exits the turbine 22 through an exhaust outlet 28 (e.g., exhaust stack, exhaust end). In the illustrated embodiment, the shaft 30 is coupled to the compressor 20 and a load 36, such that rotation of the shaft 30 also drives rotation of the compressor 20 and the load 36. The compressor 20 may intake the oxidant (e.g., air) through an air intake 34, which may include filters, thermal control systems, or any other preconditioning systems. The load 36 may include an electrical generator, a rotary machine, a propulsion system of a vehicle, or any other suitable device.


The airfoil profile described in further detail below may be used in any stage of the compressor 20 (e.g., multi-stage axial compressor with any number of stages of rotor blades and stator vanes). The compressor 20 may include rotating blades and stationary vanes (e.g., airfoils) that may be disposed in rows or stages, described in more detail below. The oxidant (e.g., air) may be progressively compressed in stages or rows of rotating blades and corresponding stator vanes as the air moves downstream in the compressor 20. In the depicted embodiment, the compressor 20 is a multi-stage axial compressor 20 having at least two rows or stages of blades and vanes. For example, in certain embodiments, the multi-stage axial compressor 20 may have 14 rows or stages of compressor blades and vanes.


It may be beneficial to illustrate a more detailed view of certain components of the gas turbine engine 12. Accordingly, FIG. 2 is a cross-sectional side view of an embodiment of the compressor 20 of the gas turbine engine 12 of FIG. 1. Throughout the discussion of FIG. 2, a set of axes will be referenced. These axes are based on a cylindrical coordinate system and point in an axial direction 38 (e.g., downstream), a radial direction 40, and a circumferential direction 42. For example, the axial direction 38 extends downstream through the compressor 20 generally parallel to the axis 32, the radial direction 40 extends away from the axis 32, and the circumferential direction 42 extends around the axis 32.


In operation, air enters the compressor 20 in the axial direction 38 through the air intake 34 and may be pressurized in the multi-stage axial compressor 20. The compressed air may then be mixed with fuel for combustion within the combustor 26 to drive the turbine 22 to rotate the shaft 30 in the circumferential direction 42 and, thus, the multi-stage axial compressor 20 and the load 36. The rotation of the shaft 30 also causes one or more blades 44 (e.g., compressor rotor blades) within the multi-stage axial compressor 20 to draw in and pressurize the air received by the air intake 34.


The multi-stage axial compressor 20 may include a rotor assembly 46 having multiple rotor blades 44 surrounded by a static casing 48 having multiple stator vanes 50 (e.g., variable stator vanes and/or fixed stator vanes). In some embodiments, the static casing 48 of the compressor 20 or the air intake 34 may have one or more sets of inlet guide vanes 52 (IGVs) (e.g., variable IGV stator vanes) that may control flows into the compressor 20. Each variable stator vane 50 (including each variable IGV stator vane 52) may be configured to vary its vane angle relative to the gas flow (e.g. air flow) by rotating the vane 50, 52 about an axis of rotation (e.g., radially oriented vane shaft). However, each variable stator vane 50 may be otherwise stationary relative to the rotor blades 44. In certain embodiments, each variable stator vane 50 may be coupled to an actuator 18 (e.g., electric drive, pneumatic drive, or hydraulic drive), which is coupled to a controller 14 configured to vary the vane angle in response to feedback from sensors 16. Each fixed stator vane 50 may be configured to remain in a fixed angular position, such that the vane angle does not vary. The compressor 20 may include a plurality of rows or stages 54, such as between 2 to 30, 2 to 25, 2 to 20, 2 to 14, or 2 to 10 rows or stages, or any specific number or range therebetween. In each stage, the multi-stage axial compressor 20 may include 2 to 1000, 5 to 500, or 10 to 100 rotor blades 44, and 2 to 1000, 5 to 500, or 10 to 100 stator vanes 50. In particular, the illustrated embodiment of the multi-stage axial compressor 20 includes 14 stages. It may be appreciated that each stage 54 has a set of rotor blades 44 disposed at a first axial position and a set of stator vanes 50 disposed at a second axial position along the length of the compressor 20. In other words, each stage 54 has the rotor blades 44 and stator vanes 50 axially offset from one another, such that the compressor 20 has an alternating arrangement of rotor blades 44 and stator vanes 50 one set after another along the length of the compressor 20. Each set of rotor blades 44 extends (e.g., in a spaced arrangement) in the circumferential direction 42 about the shaft 30, and each set of stator vanes 50 extends (e.g., in a spaced arrangement) in the circumferential direction 42 within the static casing 48. While the compressor 20 may include greater or fewer stages 54 than 14, FIG. 2 illustrates an embodiment of the compressor 20 with 14 stages 54 identified as follows: first stage 54a, second stage 54b, third stage 54c, fourth stage 54d, fifth stage 54e, sixth stage 54f, seventh stage 54g, eighth stage 54h, ninth stage 54i, tenth stage 54j, eleventh stage 54k, twelfth stage 54l, thirteenth stage 54m, and fourteenth stage 54n. In certain embodiments, each stage 54 may include rotor blades 44 and stator vanes 50 (e.g., fixed stator vanes 50 and/or variable stator vanes 50). For example, in certain embodiments, earlier stages 54 (e.g., 54a, 54b, 54c, etc.) may include variable stator vanes 50, while later stages 54 may include fixed stator vanes 50.


The airfoil described in the TABLE I below may describe either a rotor blade 44 or a stator vane 50 of the compressor 20. For example, the airfoil described in the TABLE I below may be placed as a stator vane 50 of the first stage 54a. In use, the rotor blades 44 may rotate circumferentially about the static casing 48 and the stator vanes 50. Rotation of the rotor blades 44 may result in air entering the air intake 34. The air is then subsequently compressed as it traverses the various stages 54 (e.g., first stage 54a to fourteenth stage 54n) of the compressor 20 and moves in the axial direction 38 downstream of the multi-stage axial compressor 20. The compressed air may then exit through an outlet 56 of the multi-stage axial compressor 20. The outlet 56 may have a set of exit guide vanes 58 (EGVs). The compressed air that exits the compressor 20 may be mixed with fuel, directed to the combustor 26, directed to the turbine 22, or elsewhere in the turbine system 10.


Certain designs of the rotor blades 44 and stator vanes 50 (e.g., airfoils) provide for a more efficient multi-stage axial compressor 20 system. For example, certain rotor blade and/or stator vane (e.g., airfoil) designs may improve compressor 20 efficiency and enable improved operations for the turbine system 10. Referring now to FIG. 3, the figure is a side view of an embodiment of an airfoil 82 that may be included in the multi-stage axial compressor 20 as a rotor blade 44 or stator vane 50. In the particular embodiment, the airfoil 82 may be included in the first stage 54a of the multi-stage axial compressor 20 as a stator vane 50. In the depicted embodiment, the airfoil 82 is disposed on a base 60, which may, in certain embodiments, be removably coupled as a rotor blade 44 to the rotor assembly 46. That is, the base 60 having the airfoil 82 may be removed from the rotor assembly 46, for example, to inspect, repair, and/or replace the airfoil 82. Additionally, or in the alternative, the airfoil 82 may be removably coupled as a stator vane 50 to the static casing 48. That is, the base 60 having the airfoil 82 may be removed from the static casing 48, for example, to inspect, repair, and/or replace the airfoil 82. The base 60 may include a removable mount or coupling 59, such as a dovetail joint. For example, the coupling 59 may include a T-shaped structure, a hook, one or more lateral protrusions, one or more lateral slots, or any combination thereof. The coupling 59 (e.g., dovetail joint) may be configured to mount into the rotor assembly 46 or the static casing 48 in an axial direction 38, a radial direction 40, and/or a circumferential direction 42 (e.g., into an axial slot or opening, a radial slot or opening, and/or a circumferential slot or opening).


As further described herein, the airfoil 82 includes a suction side 62 and a pressure side 64 disposed opposite from one another on the airfoil 82 (i.e., opposite faces). The airfoil 82 also includes leading and trailing edges 61 and 63 disposed opposite from one another on the airfoil 82 (e.g., opposite upstream and downstream edges). The suction side 62, the pressure side 64, the leading edge 61, and the trailing edge 63 generally extend from the base 60 to a tip 68 of the airfoil 82. The leading and trailing edges, 61 and 63 respectively, may be described as the dividing or intersecting lines between the suction side 62 and the pressure side 64. In other words, the suction side 62 and the pressure sides 64 couple together with one another along the leading edge 61 and the trailing edge 63, thereby defining an airfoil shaped cross-section that gradually changes lengthwise along the airfoil 82. The airfoil profile described in further detail below may be utilized along any portion or the entirety of the airfoil 82 between the base 60 and the tip 68. For example, the portion having the disclosed airfoil profile may include all or part of the suction side 62, all or part of the pressure side 64, or a combination thereof.


In operation, the rotor blades 44 rotate about an axis 66 exerting a torque on a working fluid, such as air, thus increasing energy levels of the fluid as the working fluid traverses the various stages 54 of the multi-stage axial compressor 20 on its way to the combustor 26. The suction side 62 creates and/or increases a suction force on the working fluid, while the pressure side 64 creates and/or increases a pressure bias on the working fluid. The rotor blades 44 may be adjacent (e.g., upstream and/or downstream) to the one or more stationary stator vanes 50. The stator vanes 50 slow the working fluid during rotation of the rotor blades 44, converting a circumferential component of movement of the working fluid flow into pressure. Accordingly, continuous rotation of the rotor blade 44 creates a continuous flow of compressed working fluid, suitable for combustion via the combustor 26.


The airfoil 82 (e.g., rotor blade 44, stator vane 50) includes an airfoil length L measured from the tip 68 of the airfoil 82 to a bottom region 70 of the airfoil 82 adjacent the base 60 (e.g., at an intersection of the airfoil 82 with the base 60). An X axis 72 lies parallel to the base 60 and to the rotational axis 66. The rotational axis 66 may be parallel to the axis 32 or the shaft 30. The X axis 72 is orthogonal to a Z axis 74 which bisects the airfoil 82. A Y axis 76 (shown coming out of the plane of the drawing) is orthogonal to both the X axis 72 and the Z axis 74. The X axis 72 and the Y axis 76 may be used to define an airfoil profile, shape, or section, for example, taken through line 6-6 at a point along the Z axis 74. That is, the airfoil profile may include an outline of the surface (e.g., section) of the airfoil 82 (e.g., rotor blade 44, stator vane 50) at a point along the Z axis 74. The airfoil profile may include X, Y, and Z values for the suction side 62, and X, Y, and Z values for the pressure side 64. A Cartesian coordinate system point 78 (e.g., origin) may be used to define a zero point for the X axis 72, the Z axis 74, and the Y axis 76 of the respective airfoil 82. TABLE I below lists various non-dimensionalized airfoil shapes for the suction side 62 and the corresponding pressure side 64 disposed at locations along the Z axis 74 from the bottom region 70 to the tip 68 of the airfoil 82.


The airfoil 82 may be described in terms of certain airfoil sections containing various air foil shapes and corresponding rows of the TABLE I. For example, as illustrated in FIG. 4, the airfoil 82 may be described via airfoil shapes disposed on one or more portions 80. In certain embodiments, the portion 80 of the airfoil 82 may be described as an area of interest, an area of greater importance, or a sweet spot, wherein the particular airfoil profile may have a greater impact on the performance, efficiency, and other attributes of the airfoil 82 as compared with other areas of the airfoil 82. However, the portion 80 may include any area of the airfoil 82, regardless of importance. The one or more portions 80 may include a suction side portion of the suction side 62, a pressure side portion of the pressure side 64, or any combination thereof. For example, the one or more portions 80 may include suction side portions 62 and pressure side portions 64 that are offset from one another without any overlap along the Z axis 74, suction side portions 62 and pressure side portions 64 that partially overlap along the Z axis 74, or suction side portions 62 and pressure side portions 64 that completely overlap along the Z axis 74. Portion 80 is shown as a rectangle in dashed lines. More specifically, FIG. 4 is a side view of an embodiment of the airfoil 82 illustrating the portion 80. As described above, the airfoil 82 may be the rotor blade 44 or the stator vane 50, such as the stator vane 50 of the first stage 54a. Because the figure depicts like elements to FIG. 3, the like elements are illustrated with like numbers. In the depicted embodiment, the airfoil 82 includes the length L (e.g., total length), as mentioned previously, measured along the Z axis 74 (e.g., in the radial direction 40) from the tip 68 of the airfoil 82 to the bottom region 70 of the airfoil 82.


The portion 80 may begin at a distance or position d and include a length l extending away from the base 60 in the Z direction along the Z axis 74. As appreciated, in embodiments having one or more suction side portions 80 on the suction side 62 and/or one or more pressure side portions 80 on the pressure side 64, each portion 80 may be defined by a length l and a position d. A zero value of the position d corresponds to the bottom region 70 of the airfoil 82 adjacent the base 60 (e.g., at an intersection of the airfoil 82 with the base 60), which also corresponds to the coordinate origin 78. When d is zero and l is equal to L, the portion 80 includes the entirety of the airfoil 82 from the bottom region 70 to the tip 68 of the airfoil 82. By varying values for d and 1, portions 80 having varying lengths and start locations from the coordinate origin 78 may be provided for defining the area of interest (e.g., sweet spot) along the airfoil 82. Each portion 80 may include one or more adjacent airfoil shapes (e.g., airfoil sections or airfoil shapes 110) “stacked” on top of each other along the Z axis 74, described in more detail below with respect to FIG. 6 and TABLE I below. Each airfoil section or airfoil shape 110 corresponds to Cartesian coordinate values of X, Y, and Z for a common Cartesian coordinate value of Z in TABLE I. Furthermore, adjacent airfoil sections or airfoil shapes 110 correspond to the Cartesian coordinate values of X, Y, and Z for adjacent Cartesian coordinate values of Z in the TABLE I.


With reference to TABLE I, the position d may be used to define a start position (e.g., first Cartesian coordinate value of Z) of the portion 80 in the Z direction along the Z axis 74, while a sum of the position d and the length l may be used to define an end position (e.g., last Cartesian coordinate value of Z) of the portion 80 in the Z direction along the Z axis 74. In certain embodiments, the position d (e.g., start position) may be selected directly from one of the Cartesian coordinate values of Z in TABLE I, and the sum of the position d and the length l (e.g., end position) may be selected directly from one of the Cartesian coordinate values of Z in TABLE I. In other embodiments, the desired values of the position d and the length l may be initially selected without referencing TABLE I, and then TABLE I may be subsequently analyzed to select best fits of the Cartesian coordinate values of Z in TABLE I based on the desired values of d and l. For example, with reference to TABLE I, the start position of the portion 80 may correspond to the Cartesian coordinate value of Z equal to or nearest to the value of the position d (e.g., start Z value). If the position d is midway between adjacent Cartesian coordinate values of Z in TABLE I, then the lesser or greater Cartesian coordinate value of Z may be selected for the start position of the portion 80 (e.g., start Z value). Alternatively, in some embodiments, if a specific value of the position d is desired but does not match the specific Cartesian coordinate values of Z in TABLE I, then regression analysis and/or curve fitting may be used to analyze the data in TABLE I and interpolate new Cartesian coordinate values of X, Y, Z to enable use of the desired d value. Similarly, with reference to TABLE I, the end position (e.g., end Z value) may correspond to the Cartesian coordinate value of Z equal to or nearest to the sum of the position d and the length l. If the sum of the position d and the length l is midway between adjacent Cartesian coordinate values of Z in TABLE I, then the lesser or greater Cartesian coordinate value of Z may be selected for the end position (e.g., end Z value). Alternatively, in some embodiments, if a specific value of the length l is desired but the sum of the position d and the length l does not match the specific Cartesian coordinate values of Z in TABLE I, then regression analysis and/or curve fitting may be used to analyze the data in TABLE I and interpolate new Cartesian coordinate values of X, Y, Z to enable use of the desired l value.


In certain embodiments, the portion 80 may be defined by the Cartesian coordinate values of X, Y, and Z corresponding to the start Z value, the end Z value, and all intermediate Z values in TABLE I. However, in some embodiments, if the Z values do not match the desired start and end positions, then the portion 80 may be defined by the Cartesian coordinate values of X, Y, and Z in TABLE I in the Z direction between the start and end positions (e.g., based on the position d and length l). Furthermore, as discussed herein, the portion 80 may include the Cartesian coordinate values of X, Y, and Z for the suction side 62 (e.g., suction side profile 112—see FIG. 6), the pressure side 64 (e.g., pressure side profile—see FIG. 6), or a combination thereof.


In certain embodiments, the portion 80 may include the airfoil profile of TABLE I only for the suction side 62 according to the position d and length l, only for the pressure side 64 according to the position d and length l, or for both the suction and pressure sides 62 and 64 according to the position d and length l. The position d of the portion 80 may be greater than or equal to approximately 0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, or 75 percent of the length L of the airfoil 82. Furthermore, the length l of the portion 80 may be greater than or equal to approximately 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, or 100 percent of the length L of the airfoil 82. For example, the portion 80 selected from TABLE I may be the suction side 62 of the outer third of the airfoil 82. In another example, the portion 80 selected from TABLE I may be both the suction side 62 and the pressure side 64 of an interior portion 80 of the airfoil 82, where d is greater than 0 and l is less than L (e.g., l=0.3 L).


Additionally or alternatively, a portion of the airfoil 82, such as portion 80, may be described in terms of a start height (e.g., first position) and a stop height (e.g., second position) along the Z axis 74 (e.g., in the radial direction 40) as illustrated in FIG. 5. Collectively, the start and stop heights (e.g., first and second positions) define a range along the Z axis 74. Again, the portion (e.g., 80) of the airfoil 82 may be described as an area of interest, an area of greater importance, or a sweet spot, wherein the particular airfoil profile may have a greater impact on the performance, efficiency, and other attributes of the airfoil 82 as compared with other areas of the airfoil 82. However, the portion (e.g., 80) may include any area of the airfoil 82, regardless of importance. For example, as shown in FIG. 5, an embodiment of the airfoil 82 is illustrated with multiple defined heights 90, 92, 94, 96, 98, and 100 along the Z axis 74. The heights 90, 92, 94, 96, 98, and 100 may divide the airfoil 82 into a plurality of portions along the Z axis 74, wherein the plurality of portions may have equal lengths along the Z axis 74 (e.g., five portions each being 20 percent of the total length L of the airfoil 82). However, in some embodiments, the plurality of portions defined by the heights 90, 92, 94, 96, 98, and 100 may have different lengths along the Z axis 74. Although the illustrated embodiment includes 6 heights (e.g., 90, 92, 94, 96, 98, and 100) defining 5 portions, certain embodiments may include any number of heights (e.g., 2 to 100 or more) defining any number of portions (e.g., 2 to 100 or more) with equal or different lengths along the Z axis 74.


For example, certain embodiments may include 11 heights to define 10 portions with equal or different lengths along the Z axis 74 (e.g., 10 portions each being 10 percent of the total length L of the airfoil 82). By further example, certain embodiments may include 101 heights to define 100 portions with equal or different lengths along the Z axis 74 (e.g., 100 portions each being 1 percent of the total length L of the airfoil 82). In this manner, the heights may be used to define a specific portion (e.g., 80) of the airfoil 82, wherein the specific portion (e.g., area of interest) may track the airfoil profile described below in TABLE I. Again, similar to the discussion of FIG. 4, the specific portion (e.g., 80) defined by the heights in FIG. 5 may track the airfoil profile of TABLE I along only the suction side 62, only the pressure side 64, or both the suction and pressure sides 62 and 64. Because FIG. 5 depicts like elements to FIG. 4, the like elements are illustrated with like numbers.


In the illustrated embodiment, the portion (e.g., 80) may be defined by the start height and the stop height, wherein the start height is closer to the bottom region 70 than the stop height, and each of the start and stop heights may be selected from one of the heights 90, 92, 94, 96, 98, or 100. Multiple start and stop heights 90, 92, 94, 96, 98, 100 may be defined to divide the airfoil 82 and define the portion (e.g., 80). For example, a first start height 92 and a first stop height 90 may describe a first section or segment 102 (e.g., portion 80) of the airfoil 82, a second start height 96 and a second stop height 92 may describe a second section or segment 104 (e.g., portion 80) of the airfoil 82, and a third start height 96 and a third stop height 94 may describe a third section or segment 106 (e.g., portion 80) of the airfoil 82. As shown in FIG. 5, each height 90, 92, 94, 96, 98, 100 may define a start height for a segment, a stop height for the segment, or a start height for one segment and a stop height for another segment. Each of the heights 90, 92, 94, 96, 98, 100 may be selected to correspond to a different Cartesian coordinate value of Z in TABLE I. In certain embodiments, each of the heights 90, 92, 94, 96, 98, 100 may be selected directly from one of the Cartesian coordinate values of Z in TABLE I. In other embodiments, the desired values of the heights 90, 92, 94, 96, 98, 100 may be initially selected without referencing TABLE I, and then TABLE I may be subsequently analyzed to select best fits of the Cartesian coordinate values of Z in TABLE I based on the desired values of the heights 90, 92, 94, 96, 98, 100. For example, each of the heights 90, 92, 94, 96, 98, 100 may correspond to the Cartesian coordinate value of Z equal to or nearest to the value of the particular height 90, 92, 94, 96, 98, or 100. If the height 90, 92, 94, 96, 98, or 100 is midway between adjacent Cartesian coordinate values of Z in TABLE I, then the lesser or greater Cartesian coordinate value of Z may be selected for the particular height 90, 92, 94, 96, 98, or 100. Alternatively, in some embodiments, if specific heights are desired but do not match the specific Cartesian coordinate values of Z in TABLE I, then regression analysis and/or curve fitting may be used to analyze the data in TABLE I and interpolate new Cartesian coordinate values of X, Y, Z to enable use of the desired heights. In some embodiments, if the Z values do not match the desired heights, then the portion 80 may be defined by the Cartesian coordinate values of X, Y, and Z in TABLE I in the Z direction between the start and stop heights. Furthermore, with reference to TABLE I, the overall height dimension of each segment (e.g., 102, 104, 106) may be equal to an absolute value of the difference between the start and stop heights (e.g., Cartesian coordinate values of Z) for the particular segment. In certain embodiments, an offset or correction value may be used to account for negative values in TABLE I. For example, certain components of the airfoil 82, such as the bottom region 70, may be disposed below the origin point 78 by a distance 108, and thus certain Z values may be negative denoting sections of airfoil 82 below the origin point 78. Accordingly, the offset may be equal to an absolute value of the smallest negative value given in TABLE I.


As mentioned earlier with respect to the portion 80 of FIG. 4, the sections 102, 104, and 106 (e.g., portion 80) of FIG. 5 may include one or more airfoil shapes, profiles, or sections, such as an airfoil shape shown in FIG. 6. More specifically, FIG. 6 is a cross-sectional top view depicting an embodiment of an airfoil shape 110 taken through line 6-6 of FIGS. 3, 4, and 5, wherein the airfoil shape 110 may be included, for example, in the portion 80 of the airfoil 82 (e.g., rotor blade 44, stator vane 50). As mentioned earlier, the airfoil 82 may be described in terms of one or more airfoil shapes (e.g., sections) “stacked” on top of each other along the Z axis 74, such as the depicted airfoil shape 110. To define the airfoil shape 110, a unique set or loci of points in space are provided in TABLE I.


A Cartesian coordinate system of X, Y, and Z values given in TABLE I below defines a suction side profile 112 and a pressure side profile 114 of the airfoil shape 110 at various locations along the airfoil 82. For example, point 116 defines a first pair of suction side X and Y values at the Z value of line 6-6 of FIGS. 3-5, while point 118 defines a second pair of pressure side X and Y values at the same Z value of FIGS. 3-5. The X, Y, and Z values of TABLE I are set forth in non-dimensionalized units, and thus a variety of units of dimensions may be used when the values are appropriately scaled by a scale factor F. The scale factor F may be substantially equal to 1, greater than 1, or less than 1. For example, the Cartesian coordinate values of X, Y, and Z may be convertible to dimensional distances by multiplying the X, Y, and Z values by a constant number (e.g., 100). The number, used to convert the non-dimensional values to dimensional distances, may be a fraction (e.g., ½, ¼, etc.), decimal fraction (e.g., 0.5, 1.5, 10.25, etc.), integer (e.g., 1, 2, 10, 100, etc.) or a mixed number (e.g., 1½, 10¼, etc.). The dimensional distances may be any suitable format (e.g., inches, feet, millimeters, centimeters, etc.) These values exclude a coated region or coatings 120 of the airfoil 82. In other words, these values correspond to the bare surface of the airfoil 82. The coated region 120 may include one or more coating layers, surface treatments, or a combination thereof, over the bare surface of the airfoil 82. The Cartesian coordinate system of FIG. 6 utilizes the same orthogonally-related X axis 72, Y axis 76, and Z 74 as the Cartesian coordinate system of FIGS. 3-5 to define locations on the airfoil shape 110 for both the suction side profile 112 and the pressure side profile 114 along the length L of the airfoil 82.


The X axis 72 and the Y axis 76 lie parallel to the base 60, as illustrated in the previous figures. In some embodiments, a positive X coordinate value is axial in the downstream axial direction 38 toward the aft, for example the exhaust outlet 28 of the multi-stage axial compressor 20. In some embodiments, a positive Y coordinate value is directed normal to the X axis 72. A positive Z coordinate value is directed radially from the X axis 72 and the Y axis 76 outward toward tip 68 of the airfoil 82, which is towards the static casing 48 of the multi-stage axial compressor 20 for rotor blades 44, and directed radially inward towards the shaft 30 of the multi-stage axial compressor 20 for stator vanes 50.


By defining X and Y coordinate values at selected locations in a Z direction normal to the X-Y plane, the airfoil shape 110, with its suction side profile 112 and pressure side profile 114, may be defined, for example, by connecting each X and Y coordinate value to adjacent X and Y coordinate values with smooth continuing arcs. The suction side profile 112 is joined to the pressure side profile 114, as shown in FIG. 6, to define the airfoil shape 110. The airfoil shapes 110 (e.g., sections) of the airfoil 82 at various surface locations (e.g., heights) between the Z coordinate values may be determined by smoothly connecting the adjacent (e.g., “stacked”) airfoil shapes 110 to one another, thus forming the airfoil 82. It may be appreciated that the airfoil shape 110 of the airfoil 82 may change from the base 60 to the tip 68. For example, adjacent airfoil shapes 110 may taper or expand in one or more directions (e.g., X axis 72, Y axis 76), adjacent airfoil shapes 110 may rotate about an axis (e.g., Z axis 74) in a clockwise direction or a counter-clockwise direction, or any combination thereof. It is also to be noted that TABLE I values represent the Cartesian coordinate values for the airfoil 82 at ambient, non-operating or non-hot conditions. Additionally, TABLE I values represent the Cartesian coordinate values for an uncoated airfoil (i.e., without coatings 120). For a coated airfoil, a thickness t of the coating 120 may be added to each of the X, Y values of TABLE I below.


The X, Y, and Z coordinate values of TABLE I below are non-dimensional values convertible to dimensional distances with the scale factor F. That is, the X, Y, and Z values of TABLE I may be scaled as a function of the same scale factor F (e.g., constant or number) to provide a scaled-up or a scaled-down airfoil. Thus, TABLE I defines the relationships between the X, Y, and Z coordinate values without specifying the units of measure (e.g., dimensional units) for an embodiment of the airfoil 82. Accordingly, while different scale factors F may be applied to the X, Y, and Z coordinate values of TABLE I to define different embodiments of the airfoil 82, each embodiment of the airfoil 82 regardless of the particular scale factor F is considered to be defined by the X, Y, and Z coordinate values of TABLE I. For example, the X, Y, and Z coordinate values of TABLE I define a first embodiment of the airfoil 82 formed with a 1:1 inch scale factor F, a second embodiment of the airfoil 82 formed with a 1:2 inch scale factor F, and a third embodiment of the airfoil 82 formed with a 1:1 cm scale factor F. It may be appreciated that any scale factor F may be used with the X, Y, and Z coordinate values of TABLE I, according to the design considerations of a particular embodiment.


The TABLE I values below are computer-generated and shown to five decimal places. However, certain values in TABLE I may be shown to less than five decimal places (e.g., 0, 1, 2, 3, or 4 decimal places), because the values are rounded to significant figures, the additional decimal places would merely show trailing zeroes, or a combination thereof. Accordingly, in certain embodiments, any values having less than five decimal places may be shown with trailing zeroes out to 1, 2, 3, 4, or 5 decimal places. Furthermore, in some embodiments and in view of manufacturing constraints, actual values useful for forming the airfoil 82 are may be considered valid to fewer (e.g., one, two, three, or four) decimal places for determining the airfoil shape 110 of the airfoil 82. Further, there are typical manufacturing tolerances which may be accounted for in the airfoil shape 110. Accordingly, the X, Y, and Z values given in TABLE I are for the airfoil shape 110 of a nominal airfoil. It will therefore be appreciated that plus or minus typical manufacturing tolerances are applicable to these X, Y, and Z values and that an airfoil 82 having a profile substantially in accordance with those values includes such tolerances. For example, in certain embodiments, a manufacturing tolerance of about ±between 0.001 to 0.20 inches (e.g., between 0.025 to 5 mm) is within design limits for the airfoil 82, and a manufacturing tolerance of about ±0.0008 to 0.1 inches (e.g., 0.02 to 2.5 mm) may be maintained during manufacturing. Accordingly, the values of X and Y carried to three decimal places and having a manufacturing tolerance about ±0.010 inches (0.25 mm) and preferably about ±0.008 inches (0.20 mm) is acceptable to define the airfoil shape 110 of the airfoil 82 at each radial position (e.g., Z coordinate, height) throughout its entire length. As used herein, any reference to Cartesian coordinate values of X, Y, and Z as set forth in TABLE I to a maximum of N decimal places is intended to include: (1) values to N decimal places if shown in TABLE I with N or greater decimal places, and (2) values to less than N decimal places if shown in TABLE 1 with less than N decimal places, wherein N may be 0, 1, 2, 3, 4, or 5. For example, any reference to Cartesian coordinate values of X, Y, and Z as set forth in TABLE I to a maximum of three (3) decimal places is intended to include: (1) values to three (3) decimal places if shown in TABLE I with three (3) or greater decimal places, and (2) values to less than three (3) decimal places if shown in TABLE 1 with less than three (3) decimal places (e.g., 0, 1, or 2 decimal places). Furthermore, any reference to Cartesian coordinate values of X, Y, and Z as set forth in TABLE I all carried to N decimal places is intended to include: (1) values to N decimal places if shown in TABLE I with N or greater decimal places, and (2) values with trailing zeros to N decimal places if shown in TABLE 1 with less than N decimal places, wherein N may be 0, 1, 2, 3, 4, or 5.


As noted previously, the airfoil 82 may also be coated for protection against corrosion, erosion, wear, and oxidation after the airfoil 82 is manufactured, according to the values of TABLE I and within the tolerances explained above. For example, the coating region 120 may include one or more corrosion resistant layers, erosion resistant layers, wear resistant layers, oxidation resistant or anti-oxidation layers, or any combination thereof. An anti-corrosion coating may be provided with an average thickness t of 0.008 inches (0.20 mm), between 0.001 and 0.1 inches (between 0.25 and 2.5 mm), between, 0.0001 and 1 inches or more (between 0.0025 and 2.5 mm or more). For example, in certain embodiments, the coating 120 may increase X and Y values of a suction side in TABLE I by no greater than approximately 3.5 mm along a first suction portion, a first pressure portion, or both. It is to be noted that additional anti-oxidation coatings 120 may be provided, such as overcoats.










TABLE I







SuctionSide or Surface
PressureSide or Surface












X
Y
Z
X
Y
Z















−4.41006
4.5608
−1.23843
5.84571
−6.38972
−1.23843


−4.42983
4.54661
−1.23843
5.84706
−6.38702
−1.23843


−4.44774
4.51923
−1.23843
5.84943
−6.38127
−1.23843


−4.46633
4.48306
−1.23843
5.85382
−6.36978
−1.23843


−4.48712
4.43879
−1.23843
5.86075
−6.34646
−1.23843


−4.50571
4.3771
−1.23843
5.86684
−6.3086
−1.23843


−4.5123
4.29226
−1.23843
5.86261
−6.24033
−1.23843


−4.515
4.18562
−1.23843
5.82425
−6.15768
−1.23843


−4.51771
4.056
−1.23843
5.73214
−6.07893
−1.23843


−4.50993
3.90204
−1.23843
5.61317
−5.98514
−1.23843


−4.49016
3.72223
−1.23843
5.45836
−5.86346
−1.23843


−4.4589
3.51148
−1.23843
5.28074
−5.72183
−1.23843


−4.41648
3.26998
−1.23843
5.09366
−5.56787
−1.23843


−4.36003
2.9984
−1.23843
4.88528
−5.39195
−1.23843


−4.28111
2.69876
−1.23843
4.65527
−5.19472
−1.23843


−4.18224
2.37039
−1.23843
4.40397
−4.97587
−1.23843


−4.06428
2.0133
−1.23843
4.14405
−4.74434
−1.23843


−3.92469
1.64572
−1.23843
3.87635
−4.49912
−1.23843


−3.76448
1.27088
−1.23843
3.6019
−4.23903
−1.23843


−3.58483
0.88843
−1.23843
3.32068
−3.96423
−1.23843


−3.38372
0.4999
−1.23843
3.03169
−3.67541
−1.23843


−3.15979
0.10579
−1.23843
2.73358
−3.37459
−1.23843


−2.91305
−0.29389
−1.23843
2.42464
−3.06296
−1.23843


−2.64181
−0.69814
−1.23843
2.10506
−2.74067
−1.23843


−2.35518
−1.09343
−1.23843
1.78633
−2.41755
−1.23843


−2.0542
−1.48027
−1.23843
1.46844
−2.0934
−1.23843


−1.74138
−1.85647
−1.23843
1.14802
−1.77197
−1.23843


−1.41825
−2.22218
−1.23843
0.8232
−1.45475
−1.23843


−1.08616
−2.57843
−1.23843
0.49686
−1.1394
−1.23843


−0.74512
−2.92556
−1.23843
0.17407
−0.8205
−1.23843


−0.39293
−3.26102
−1.23843
−0.14314
−0.49652
−1.23843


−0.02552
−3.58077
−1.23843
−0.45478
−0.16765
−1.23843


0.35777
−3.88413
−1.23843
−0.76168
0.16562
−1.23843


0.75391
−4.1743
−1.23843
−1.06352
0.50345
−1.23843


1.15866
−4.45247
−1.23843
−1.36045
0.84568
−1.23843


1.55666
−4.70783
−1.23843
−1.64285
1.18063
−1.23843


1.94806
−4.94038
−1.23843
−1.91071
1.50833
−1.23843


2.33203
−5.15163
−1.23843
−2.16506
1.8279
−1.23843


2.7067
−5.34513
−1.23843
−2.40656
2.13819
−1.23843


3.0709
−5.52343
−1.23843
−2.63539
2.43935
−1.23843


3.42394
−5.6877
−1.23843
−2.85306
2.72969
−1.23843


3.76532
−5.83912
−1.23843
−3.0611
3.00854
−1.23843


4.09504
−5.97753
−1.23843
−3.24953
3.26424
−1.23843


4.39823
−6.09668
−1.23843
−3.41938
3.4961
−1.23843


4.67386
−6.19824
−1.23843
−3.57266
3.70262
−1.23843


4.92077
−6.28477
−1.23843
−3.70887
3.88413
−1.23843


5.15332
−6.36386
−1.23843
−3.82819
4.04028
−1.23843


5.35527
−6.43079
−1.23843
−3.93145
4.17092
−1.23843


5.5116
−6.47963
−1.23843
−4.02457
4.27824
−1.23843


5.6375
−6.51529
−1.23843
−4.10704
4.36459
−1.23843


5.73316
−6.50363
−1.23843
−4.17362
4.4371
−1.23843


5.79417
−6.4629
−1.23843
−4.23058
4.48999
−1.23843


5.82104
−6.43231
−1.23843
−4.28212
4.51991
−1.23843


5.83523
−6.41017
−1.23843
−4.3237
4.53866
−1.23843


5.84149
−6.39868
−1.23843
−4.35868
4.5532
−1.23843


5.84436
−6.39276
−1.23843
−4.38758
4.56199
−1.23843


−4.55675
4.60187
0
6.22579
−6.01539
0


−4.57753
4.58734
0
6.22714
−6.01251
0


−4.59663
4.55962
0
6.22951
−6.00694
0


−4.61319
4.52092
0
6.23373
−5.99544
0


−4.6284
4.47292
0
6.24016
−5.97195
0


−4.6404
4.40735
0
6.24506
−5.93393
0


−4.64344
4.32116
0
6.23678
−5.86582
0


−4.64192
4.21283
0
6.19233
−5.78656
0


−4.63652
4.08186
0
6.09718
−5.71068
0


−4.62046
3.92739
0
5.9755
−5.61874
0


−4.59207
3.74791
0
5.81681
−5.4996
0


−4.55049
3.537
0
5.63463
−5.36085
0


−4.49557
3.29466
0
5.44265
−5.2101
0


−4.42493
3.02324
0
5.22852
−5.03823
0


−4.33012
2.72631
0
4.99175
−4.84574
0


−4.21469
2.40267
0
4.73268
−4.63246
0


−4.07865
2.052
0
4.46397
−4.40684
0


−3.92097
1.69287
0
4.18664
−4.16822
0


−3.74149
1.32496
0
3.90137
−3.91522
0


−3.54072
0.94826
0
3.60866
−3.6477
0


−3.31629
0.56412
0
3.30733
−3.36699
0


−3.06904
0.17677
0
2.99603
−3.07445
0


−2.79915
−0.21294
0
2.67324
−2.77194
0


−2.50576
−0.60401
0
2.33879
−2.45963
0


−2.19886
−0.98375
0
2.00468
−2.14681
0


−1.87945
−1.35285
0
1.6704
−1.83416
0


−1.54804
−1.71197
0
1.33307
−1.52489
0


−1.20548
−2.06163
0
0.99135
−1.22035
0


−0.85261
−2.40267
0
0.64778
−0.91801
0


−0.48942
−2.73493
0
0.30674
−0.61263
0


−0.11577
−3.05383
0
−0.02941
−0.302
0


0.26888
−3.35465
0
−0.36065
0.01369
0


0.66468
−3.63773
0
−0.68699
0.33445
0


1.06909
−3.90644
0
−1.00809
0.65995
0


1.48044
−4.16416
0
−1.32412
0.99034
0


1.88503
−4.40194
0
−1.62477
1.31414
0


2.28268
−4.61995
0
−1.91038
1.63119
0


2.6729
−4.81937
0
−2.18162
1.94063
0


3.05434
−5.0024
0
−2.43952
2.24195
0


3.42529
−5.17123
0
−2.68423
2.53449
0


3.78492
−5.32739
0
−2.91677
2.8174
0


4.13205
−5.47171
0
−3.13833
3.08932
0


4.46633
−5.60421
0
−3.3391
3.33893
0


4.77256
−5.71896
0
−3.52027
3.56522
0


5.04972
−5.81732
0
−3.68319
3.76701
0


5.29731
−5.90148
0
−3.82802
3.94412
0


5.53002
−5.97905
0
−3.9546
4.09673
0


5.73197
−6.04496
0
−4.06377
4.22416
0


5.88796
−6.09363
0
−4.16095
4.32961
0


6.0137
−6.1298
0
−4.24646
4.41462
0


6.10969
−6.12422
0
−4.31727
4.48408
0


6.17289
−6.08738
0
−4.37727
4.53562
0


6.20061
−6.05764
0
−4.42814
4.56773
0


6.21531
−6.03584
0
−4.46887
4.58784
0


6.22157
−6.02434
0
−4.50436
4.60136
0


6.22444
−6.01843
0
−4.53444
4.6061
0


−4.6884
4.61962
1.12757
6.57038
−5.67333
1.12757


−4.70935
4.60525
1.12757
6.57157
−5.67063
1.12757


−4.72963
4.57838
1.12757
6.57393
−5.66488
1.12757


−4.74484
4.53917
1.12757
6.57799
−5.65339
1.12757


−4.75431
4.48949
1.12757
6.58407
−5.62973
1.12757


−4.75921
4.42273
1.12757
6.58762
−5.59153
1.12757


−4.75938
4.33586
1.12757
6.57562
−5.5241
1.12757


−4.7538
4.2272
1.12757
6.52526
−5.44873
1.12757


−4.7413
4.09605
1.12757
6.4269
−5.37521
1.12757


−4.71814
3.94159
1.12757
6.30252
−5.2848
1.12757


−4.68231
3.76245
1.12757
6.14078
−5.16751
1.12757


−4.63178
3.55272
1.12757
5.95488
−5.03113
1.12757


−4.56638
3.31189
1.12757
5.75851
−4.88309
1.12757


−4.4834
3.042
1.12757
5.53898
−4.71459
1.12757


−4.37524
2.74794
1.12757
5.29612
−4.52599
1.12757


−4.24477
2.42836
1.12757
5.03045
−4.31711
1.12757


−4.09234
2.08293
1.12757
4.75465
−4.09622
1.12757


−3.9181
1.72988
1.12757
4.46921
−3.86266
1.12757


−3.72189
1.36924
1.12757
4.17498
−3.61609
1.12757


−3.50405
1.00116
1.12757
3.87145
−3.35651
1.12757


−3.26187
0.62665
1.12757
3.55813
−3.08476
1.12757


−2.99553
0.24843
1.12757
3.23398
−2.80202
1.12757


−2.70637
−0.13047
1.12757
2.89801
−2.50948
1.12757


−2.39372
−0.50937
1.12757
2.55004
−2.20731
1.12757


−2.06805
−0.87576
1.12757
2.20173
−1.90564
1.12757


−1.73056
−1.23066
1.12757
1.85224
−1.60516
1.12757


−1.38191
−1.57491
1.12757
1.50021
−1.30789
1.12757


−1.02296
−1.90919
1.12757
1.14464
−1.01434
1.12757


−0.6542
−2.23384
1.12757
0.78754
−0.72298
1.12757


−0.27496
−2.54835
1.12757
0.4318
−0.42977
1.12757


0.11661
−2.85086
1.12757
0.0796
−0.1325
1.12757


0.51849
−3.13647
1.12757
−0.2682
0.17001
1.12757


0.92899
−3.40501
1.12757
−0.61127
0.47776
1.12757


1.34693
−3.65902
1.12757
−0.94961
0.79092
1.12757


1.77061
−3.9012
1.12757
−1.28322
1.10949
1.12757


2.18585
−4.12445
1.12757
−1.60111
1.42247
1.12757


2.59195
−4.32961
1.12757
−1.90362
1.72904
1.12757


2.98826
−4.51788
1.12757
−2.19125
2.02851
1.12757


3.37392
−4.69127
1.12757
−2.46453
2.3202
1.12757


3.74825
−4.85148
1.12757
−2.72411
2.60378
1.12757


4.11008
−4.9997
1.12757
−2.97068
2.87858
1.12757


4.4594
−5.13709
1.12757
−3.20525
3.14357
1.12757


4.79588
−5.26384
1.12757
−3.41786
3.38676
1.12757


5.10397
−5.37437
1.12757
−3.6095
3.60747
1.12757


5.38333
−5.47002
1.12757
−3.78171
3.80436
1.12757


5.6326
−5.55233
1.12757
−3.93449
3.97725
1.12757


5.86684
−5.62804
1.12757
−4.068
4.12614
1.12757


6.07031
−5.6926
1.12757
−4.18275
4.25052
1.12757


6.22714
−5.74042
1.12757
−4.28364
4.35412
1.12757


6.35322
−5.7771
1.12757
−4.37152
4.43794
1.12757


6.45022
−5.77845
1.12757
−4.44605
4.5047
1.12757


6.51563
−5.74482
1.12757
−4.50808
4.5554
1.12757


6.54469
−5.71558
1.12757
−4.55827
4.59089
1.12757


6.55974
−5.69412
1.12757
−4.59866
4.61269
1.12757


6.56616
−5.68246
1.12757
−4.63533
4.62452
1.12757


6.56903
−5.67637
1.12757
−4.66609
4.6257
1.12757


−4.81751
4.55624
2.31057
6.9241
−5.32063
2.31057


−4.83779
4.5412
2.31057
6.92528
−5.31775
2.31057


−4.85689
4.51331
2.31057
6.92765
−5.31201
2.31057


−4.86974
4.47326
2.31057
6.93154
−5.30052
2.31057


−4.87531
4.42307
2.31057
6.93694
−5.27669
2.31057


−4.87514
4.35614
2.31057
6.93914
−5.23832
2.31057


−4.87109
4.26911
2.31057
6.92292
−5.17174
2.31057


−4.8601
4.16061
2.31057
6.86512
−5.10177
2.31057


−4.84033
4.03031
2.31057
6.76372
−5.03113
2.31057


−4.80991
3.87686
2.31057
6.6368
−4.94291
2.31057


−4.76597
3.69941
2.31057
6.47202
−4.82799
2.31057


−4.70547
3.49171
2.31057
6.28258
−4.69448
2.31057


−4.62807
3.25376
2.31057
6.08163
−4.55049
2.31057


−4.53157
2.98826
2.31057
5.85653
−4.38707
2.31057


−4.40853
2.69978
2.31057
5.60742
−4.20404
2.31057


−4.26167
2.38662
2.31057
5.33482
−4.00108
2.31057


−4.09132
2.04879
2.31057
5.05141
−3.78678
2.31057


−3.89866
1.7042
2.31057
4.75752
−3.56083
2.31057


−3.68352
1.35285
2.31057
4.45298
−3.32339
2.31057


−3.44625
0.9949
2.31057
4.1378
−3.07445
2.31057


−3.18447
0.63172
2.31057
3.8118
−2.81436
2.31057


−2.89936
0.2677
2.31057
3.47413
−2.54396
2.31057


−2.59111
−0.09633
2.31057
3.12481
−2.26342
2.31057


−2.25953
−0.45968
2.31057
2.76332
−1.97358
2.31057


−1.91545
−0.81036
2.31057
2.40115
−1.68425
2.31057


−1.55987
−1.1492
2.31057
2.03763
−1.39679
2.31057


−1.19365
−1.4774
2.31057
1.67192
−1.11219
2.31057


−0.81762
−1.79529
2.31057
1.30333
−0.83114
2.31057


−0.43213
−2.10371
2.31057
0.93322
−0.55212
2.31057


−0.03617
−2.40115
2.31057
0.56362
−0.27243
2.31057


0.36927
−2.6844
2.31057
0.19655
0.01048
2.31057


0.78298
−2.95057
2.31057
−0.16697
0.29812
2.31057


1.20429
−3.20069
2.31057
−0.52644
0.59082
2.31057


1.63237
−3.43678
2.31057
−0.88184
0.88843
2.31057


2.06653
−3.66037
2.31057
−1.23302
1.19128
2.31057


2.49123
−3.86604
2.31057
−1.56815
1.48889
2.31057


2.90579
−4.05516
2.31057
−1.88773
1.78042
2.31057


3.30953
−4.22956
2.31057
−2.19193
2.06569
2.31057


3.70144
−4.39062
2.31057
−2.4816
2.3442
2.31057


4.08118
−4.53968
2.31057
−2.75673
2.61544
2.31057


4.44791
−4.67809
2.31057
−3.018
2.87875
2.31057


4.80146
−4.8067
2.31057
−3.2666
3.13309
2.31057


5.14132
−4.92584
2.31057
−3.49188
3.36682
2.31057


5.45211
−5.03045
2.31057
−3.69502
3.57908
2.31057


5.73299
−5.12155
2.31057
−3.87703
3.76853
2.31057


5.98345
−5.2003
2.31057
−4.03842
3.93517
2.31057


6.21886
−5.27212
2.31057
−4.17903
4.07865
2.31057


6.42318
−5.33313
2.31057
−4.2997
4.19864
2.31057


6.58086
−5.37876
2.31057
−4.40482
4.29902
2.31057


6.7071
−5.41442
2.31057
−4.4954
4.38065
2.31057


6.80377
−5.42152
2.31057
−4.57263
4.44521
2.31057


6.86968
−5.39059
2.31057
−4.63618
4.49439
2.31057


6.89892
−5.3622
2.31057
−4.68654
4.53005
2.31057


6.91379
−5.34091
2.31057
−4.72727
4.55185
2.31057


6.92004
−5.32958
2.31057
−4.76445
4.563
2.31057


6.92275
−5.32367
2.31057
−4.79521
4.56334
2.31057


−4.88596
4.50655
2.98657
7.11084
−5.13828
2.98657


−4.90573
4.49067
2.98657
7.11203
−5.1354
2.98657


−4.92331
4.46177
2.98657
7.11422
−5.12966
2.98657


−4.93412
4.42121
2.98657
7.11794
−5.118
2.98657


−4.93818
4.37085
2.98657
7.12318
−5.09417
2.98657


−4.93615
4.30392
2.98657
7.1242
−5.05564
2.98657


−4.92939
4.21706
2.98657
7.10527
−4.98956
2.98657


−4.91486
4.10924
2.98657
7.04274
−4.92331
2.98657


−4.8912
3.97978
2.98657
6.93982
−4.85402
2.98657


−4.85638
3.82734
2.98657
6.81138
−4.76732
2.98657


−4.80754
3.65091
2.98657
6.64457
−4.65426
2.98657


−4.74096
3.44473
2.98657
6.45276
−4.52312
2.98657


−4.65663
3.20931
2.98657
6.24878
−4.382
2.98657


−4.55235
2.94736
2.98657
6.02046
−4.22179
2.98657


−4.4207
2.66276
2.98657
5.76763
−4.04265
2.98657


−4.26438
2.35417
2.98657
5.49081
−3.84374
2.98657


−4.08338
2.02158
2.98657
5.20267
−3.63401
2.98657


−3.8799
1.68256
2.98657
4.90354
−3.41312
2.98657


−3.65378
1.33713
2.98657
4.59342
−3.18126
2.98657


−3.40484
0.98544
2.98657
4.27215
−2.93807
2.98657


−3.13275
0.63037
2.98657
3.9399
−2.68423
2.98657


−2.83785
0.27513
2.98657
3.59598
−2.41974
2.98657


−2.52013
−0.07994
2.98657
3.24024
−2.14512
2.98657


−2.17892
−0.43433
2.98657
2.87232
−1.86103
2.98657


−1.82588
−0.77639
2.98657
2.5039
−1.57762
2.98657


−1.46168
−1.10695
2.98657
2.1343
−1.29572
2.98657


−1.08701
−1.4267
2.98657
1.7625
−1.01704
2.98657


−0.70287
−1.73664
2.98657
1.38783
−0.74174
2.98657


−0.30944
−2.03696
2.98657
1.01147
−0.46881
2.98657


0.09312
−2.32578
2.98657
0.63527
−0.1957
2.98657


0.50345
−2.59956
2.98657
0.26127
0.08028
2.98657


0.92156
−2.85695
2.98657
−0.10951
0.36048
2.98657


1.34727
−3.09862
2.98657
−0.47692
0.64524
2.98657


1.77957
−3.32643
2.98657
−0.84078
0.93474
2.98657


2.21779
−3.54207
2.98657
−1.20091
1.2288
2.98657


2.64637
−3.73997
2.98657
−1.54517
1.51762
2.98657


3.06465
−3.92181
2.98657
−1.8737
1.8007
2.98657


3.47177
−4.08929
2.98657
−2.1872
2.07769
2.98657


3.86706
−4.24393
2.98657
−2.48565
2.34809
2.98657


4.25001
−4.3869
2.98657
−2.76957
2.61173
2.98657


4.61978
−4.51923
2.98657
−3.0393
2.86793
2.98657


4.97604
−4.64209
2.98657
−3.29567
3.11568
2.98657


5.3186
−4.756
2.98657
−3.52838
3.3435
2.98657


5.63125
−4.85622
2.98657
−3.73794
3.55035
2.98657


5.91348
−4.94376
2.98657
−3.92553
3.73541
2.98657


6.16495
−5.01964
2.98657
−4.09166
3.89799
2.98657


6.40121
−5.08893
2.98657
−4.23649
4.03809
2.98657


6.60638
−5.14757
2.98657
−4.36037
4.15537
2.98657


6.76439
−5.19185
2.98657
−4.46802
4.25356
2.98657


6.89114
−5.22649
2.98657
−4.56047
4.33384
2.98657


6.98798
−5.23731
2.98657
−4.63888
4.39721
2.98657


7.05541
−5.20841
2.98657
−4.70344
4.44555
2.98657


7.08516
−5.18036
2.98657
−4.75465
4.48019
2.98657


7.10037
−5.15889
2.98657
−4.79571
4.50165
2.98657


7.10662
−5.1474
2.98657
−4.83289
4.51298
2.98657


7.10949
−5.14132
2.98657
−4.86382
4.51365
2.98657


−4.961
4.49219
3.83157
7.29641
−4.93024
3.83157


−4.98026
4.47563
3.83157
7.29759
−4.92736
3.83157


−4.99598
4.44588
3.83157
7.29979
−4.92162
3.83157


−5.00477
4.40465
3.83157
7.3035
−4.90979
3.83157


−5.00646
4.35429
3.83157
7.30807
−4.88562
3.83157


−5.00172
4.28736
3.83157
7.3079
−4.84692
3.83157


−4.99125
4.20083
3.83157
7.28508
−4.78186
3.83157


−4.97266
4.09369
3.83157
7.21731
−4.71966
3.83157


−4.9441
3.96508
3.83157
7.11287
−4.65206
3.83157


−4.90404
3.81382
3.83157
6.9824
−4.56723
3.83157


−4.84912
3.63891
3.83157
6.81307
−4.45653
3.83157


−4.7756
3.43459
3.83157
6.61821
−4.32826
3.83157


−4.6835
3.20221
3.83157
6.41102
−4.19036
3.83157


−4.57027
2.94398
3.83157
6.17864
−4.03386
3.83157


−4.42915
2.66395
3.83157
5.92159
−3.85844
3.83157


−4.26252
2.36025
3.83157
5.64021
−3.66375
3.83157


−4.06986
2.03375
3.83157
5.34733
−3.45842
3.83157


−3.85455
1.70132
3.83157
5.04313
−3.2421
3.83157


−3.61643
1.36282
3.83157
4.72761
−3.01479
3.83157


−3.3555
1.01873
3.83157
4.40093
−2.7765
3.83157


−3.07225
0.67262
3.83157
4.06276
−2.52756
3.83157


−2.76687
0.32634
3.83157
3.71293
−2.26798
3.83157


−2.43918
−0.02011
3.83157
3.35127
−1.99843
3.83157


−2.0885
−0.36589
3.83157
2.9771
−1.71941
3.83157


−1.72667
−0.69949
3.83157
2.6026
−1.44089
3.83157


−1.3542
−1.02177
3.83157
2.22691
−1.16424
3.83157


−0.97192
−1.33341
3.83157
1.84886
−0.89046
3.83157


−0.58068
−1.63541
3.83157
1.46827
−0.6204
3.83157


−0.18066
−1.92795
3.83157
1.08583
−0.35304
3.83157


0.22832
−2.209
3.83157
0.70321
−0.08568
3.83157


0.6444
−2.47484
3.83157
0.32262
0.18421
3.83157


1.06791
−2.72445
3.83157
−0.05526
0.45799
3.83157


1.49835
−2.95868
3.83157
−0.43027
0.73583
3.83157


1.93505
−3.1794
3.83157
−0.80224
1.01772
3.83157


2.37699
−3.38828
3.83157
−1.17117
1.30367
3.83157


2.80912
−3.57993
3.83157
−1.52438
1.58404
3.83157


3.23027
−3.75619
3.83157
−1.86221
1.85866
3.83157


3.63975
−3.91843
3.83157
−2.185
2.1272
3.83157


4.03724
−4.06817
3.83157
−2.49309
2.38915
3.83157


4.42205
−4.20624
3.83157
−2.7863
2.64468
3.83157


4.79385
−4.33367
3.83157
−3.06515
2.89311
3.83157


5.15197
−4.45163
3.83157
−3.33015
3.1336
3.83157


5.49639
−4.56063
3.83157
−3.57046
3.35499
3.83157


5.81073
−4.65663
3.83157
−3.78678
3.55644
3.83157


6.09431
−4.74062
3.83157
−3.98029
3.73676
3.83157


6.34696
−4.81346
3.83157
−4.15149
3.89562
3.83157


6.58441
−4.88021
3.83157
−4.30037
4.03234
3.83157


6.79042
−4.93666
3.83157
−4.42763
4.14692
3.83157


6.94911
−4.97942
3.83157
−4.53782
4.24308
3.83157


7.0762
−5.01288
3.83157
−4.63229
4.32184
3.83157


7.17287
−5.02623
3.83157
−4.71189
4.3842
3.83157


7.24097
−4.9997
3.83157
−4.77729
4.43169
3.83157


7.27089
−4.97215
3.83157
−4.82934
4.46583
3.83157


7.2861
−4.95069
3.83157
−4.87058
4.48729
3.83157


7.29235
−4.93919
3.83157
−4.90793
4.49878
3.83157


7.29522
−4.93328
3.83157
−4.93869
4.49963
3.83157


−5.00679
4.56283
5.01457
7.4382
−4.65291
5.01457


−5.02505
4.54542
5.01457
7.43938
−4.65004
5.01457


−5.03874
4.51467
5.01457
7.44141
−4.64412
5.01457


−5.04465
4.47309
5.01457
7.44479
−4.63229
5.01457


−5.04347
4.4229
5.01457
7.44884
−4.60795
5.01457


−5.03519
4.35665
5.01457
7.44699
−4.56942
5.01457


−5.02031
4.27097
5.01457
7.41978
−4.50605
5.01457


−4.99632
4.16534
5.01457
7.34744
−4.44859
5.01457


−4.96184
4.03859
5.01457
7.24148
−4.38285
5.01457


−4.91553
3.88937
5.01457
7.10932
−4.30037
5.01457


−4.85402
3.71699
5.01457
6.93796
−4.19255
5.01457


−4.77324
3.51605
5.01457
6.74057
−4.06749
5.01457


−4.67319
3.28806
5.01457
6.53084
−3.93297
5.01457


−4.55134
3.03473
5.01457
6.29559
−3.78019
5.01457


−4.40161
2.75994
5.01457
6.0355
−3.60883
5.01457


−4.22618
2.46233
5.01457
5.75073
−3.41836
5.01457


−4.02372
2.14258
5.01457
5.45448
−3.21708
5.01457


−3.79861
1.81743
5.01457
5.14673
−3.00516
5.01457


−3.55103
1.48669
5.01457
4.82765
−2.78225
5.01457


−3.28114
1.15072
5.01457
4.49692
−2.54852
5.01457


−2.98978
0.81323
5.01457
4.1547
−2.30432
5.01457


−2.67713
0.47506
5.01457
3.80064
−2.0498
5.01457


−2.34268
0.13655
5.01457
3.43442
−1.78549
5.01457


−1.98626
−0.20162
5.01457
3.05569
−1.51171
5.01457


−1.61936
−0.52829
5.01457
2.67662
−1.2386
5.01457


−1.24266
−0.84382
5.01457
2.29654
−0.96702
5.01457


−0.85683
−1.14903
5.01457
1.91426
−0.69831
5.01457


−0.46255
−1.44478
5.01457
1.52979
−0.43298
5.01457


−0.05983
−1.73107
5.01457
1.14345
−0.17018
5.01457


0.35203
−2.00654
5.01457
0.75729
0.09295
5.01457


0.77115
−2.26714
5.01457
0.37281
0.35862
5.01457


1.19737
−2.51117
5.01457
−0.00896
0.628
5.01457


1.63017
−2.74
5.01457
−0.38836
0.9006
5.01457


2.06873
−2.95513
5.01457
−0.76523
1.17692
5.01457


2.51235
−3.15844
5.01457
−1.13957
1.45644
5.01457


2.9455
−3.34485
5.01457
−1.49852
1.73022
5.01457


3.36749
−3.51605
5.01457
−1.84261
1.99809
5.01457


3.77766
−3.67355
5.01457
−2.17148
2.25987
5.01457


4.17531
−3.81856
5.01457
−2.48582
2.51506
5.01457


4.5603
−3.9524
5.01457
−2.78546
2.76366
5.01457


4.93193
−4.0756
5.01457
−3.0709
3.00499
5.01457


5.29004
−4.18934
5.01457
−3.34248
3.23872
5.01457


5.63429
−4.29429
5.01457
−3.58888
3.45385
5.01457


5.94846
−4.38656
5.01457
−3.81095
3.64956
5.01457


6.23221
−4.46718
5.01457
−4.00936
3.82498
5.01457


6.48504
−4.53714
5.01457
−4.18461
3.97944
5.01457


6.72248
−4.60103
5.01457
−4.33722
4.11245
5.01457


6.92866
−4.65511
5.01457
−4.46752
4.22399
5.01457


7.08752
−4.696
5.01457
−4.5799
4.31778
5.01457


7.21461
−4.72811
5.01457
−4.67572
4.39485
5.01457


7.31111
−4.74518
5.01457
−4.75634
4.45619
5.01457


7.38108
−4.7222
5.01457
−4.82242
4.50284
5.01457


7.41217
−4.69516
5.01457
−4.87497
4.53647
5.01457


7.42772
−4.67386
5.01457
−4.91655
4.55759
5.01457


7.43414
−4.66203
5.01457
−4.95356
4.56925
5.01457


7.43685
−4.65595
5.01457
−4.98466
4.57044
5.01457


−4.99767
4.67589
6.19757
7.50208
−4.40853
6.19757


−5.01508
4.65798
6.19757
7.50309
−4.40566
6.19757


−5.02657
4.62671
6.19757
7.50512
−4.39975
6.19757


−5.03029
4.58514
6.19757
7.50833
−4.38792
6.19757


−5.02707
4.53528
6.19757
7.51171
−4.36358
6.19757


−5.0166
4.46988
6.19757
7.5085
−4.32522
6.19757


−4.99834
4.38555
6.19757
7.47774
−4.2637
6.19757


−4.97046
4.28162
6.19757
7.40254
−4.21013
6.19757


−4.93142
4.15706
6.19757
7.29607
−4.14608
6.19757


−4.88055
4.01037
6.19757
7.16307
−4.06563
6.19757


−4.81481
3.84086
6.19757
6.99052
−3.96068
6.19757


−4.7293
3.64364
6.19757
6.79194
−3.83867
6.19757


−4.62418
3.42005
6.19757
6.58086
−3.70718
6.19757


−4.49709
3.17162
6.19757
6.34443
−3.55779
6.19757


−4.34279
2.90156
6.19757
6.08282
−3.39014
6.19757


−4.16315
2.60902
6.19757
5.79636
−3.20373
6.19757


−3.95612
2.29502
6.19757
5.49842
−3.00685
6.19757


−3.7273
1.97544
6.19757
5.18881
−2.79898
6.19757


−3.4765
1.65029
6.19757
4.86788
−2.58046
6.19757


−3.20407
1.32006
6.19757
4.53545
−2.35096
6.19757


−2.91103
0.98814
6.19757
4.19154
−2.11098
6.19757


−2.59736
0.65504
6.19757
3.83562
−1.86069
6.19757


−2.26291
0.3211
6.19757
3.46771
−1.6006
6.19757


−1.90666
−0.01284
6.19757
3.08746
−1.33104
6.19757


−1.54077
−0.33563
6.19757
2.70704
−1.06166
6.19757


−1.16576
−0.64795
6.19757
2.32578
−0.79362
6.19757


−0.78179
−0.94995
6.19757
1.94266
−0.52813
6.19757


−0.38988
−1.24283
6.19757
1.5575
−0.26567
6.19757


0.01031
−1.52641
6.19757
1.171
−0.00507
6.19757


0.41946
−1.79951
6.19757
0.78517
0.25654
6.19757


0.83723
−2.0591
6.19757
0.40138
0.52086
6.19757


1.26192
−2.30246
6.19757
0.01994
0.78889
6.19757


1.69355
−2.53027
6.19757
−0.35896
1.06014
6.19757


2.13092
−2.74439
6.19757
−0.73583
1.33476
6.19757


2.5737
−2.94635
6.19757
−1.10999
1.6126
6.19757


3.00651
−3.13089
6.19757
−1.46929
1.88435
6.19757


3.42817
−3.29989
6.19757
−1.81337
2.15019
6.19757


3.8385
−3.4547
6.19757
−2.14275
2.40977
6.19757


4.23649
−3.59683
6.19757
−2.4576
2.66276
6.19757


4.62181
−3.72746
6.19757
−2.75842
2.90866
6.19757


4.99412
−3.84779
6.19757
−3.04521
3.14712
6.19757


5.35274
−3.95849
6.19757
−3.31865
3.3773
6.19757


5.6975
−4.06023
6.19757
−3.56725
3.58855
6.19757


6.01167
−4.14946
6.19757
−3.79152
3.7807
6.19757


6.29525
−4.22737
6.19757
−3.99212
3.95257
6.19757


6.54791
−4.29463
6.19757
−4.1694
4.104
6.19757


6.78501
−4.35614
6.19757
−4.32387
4.23413
6.19757


6.99102
−4.4082
6.19757
−4.45569
4.34296
6.19757


7.14955
−4.4474
6.19757
−4.56925
4.4349
6.19757


7.27663
−4.47833
6.19757
−4.66558
4.51078
6.19757


7.37246
−4.49726
6.19757
−4.7467
4.57111
6.19757


7.44394
−4.47749
6.19757
−4.81312
4.61691
6.19757


7.47588
−4.45095
6.19757
−4.86602
4.6497
6.19757


7.4916
−4.42949
6.19757
−4.90776
4.67032
6.19757


7.49802
−4.41783
6.19757
−4.9446
4.68215
6.19757


7.50073
−4.41158
6.19757
−4.9757
4.68367
6.19757


−4.96776
4.78084
7.38057
7.5009
−4.20607
7.38057


−4.98432
4.76242
7.38057
7.50191
−4.2032
7.38057


−4.99463
4.73099
7.38057
7.50394
−4.19728
7.38057


−4.99665
4.68958
7.38057
7.50698
−4.18545
7.38057


−4.99175
4.64057
7.38057
7.50985
−4.16112
7.38057


−4.97942
4.57601
7.38057
7.50546
−4.12326
7.38057


−4.95863
4.49303
7.38057
7.472
−4.06361
7.38057


−4.9277
4.39096
7.38057
7.39493
−4.01274
7.38057


−4.88545
4.2686
7.38057
7.28829
−3.95038
7.38057


−4.8312
4.12428
7.38057
7.15512
−3.87196
7.38057


−4.76191
3.95764
7.38057
6.9824
−3.76938
7.38057


−4.67302
3.76431
7.38057
6.78366
−3.65006
7.38057


−4.56435
3.54511
7.38057
6.57258
−3.52128
7.38057


−4.43355
3.30125
7.38057
6.33615
−3.37476
7.38057


−4.27621
3.03558
7.38057
6.07471
−3.21016
7.38057


−4.09352
2.74726
7.38057
5.78842
−3.02696
7.38057


−3.88345
2.43749
7.38057
5.49064
−2.83312
7.38057


−3.65192
2.12196
7.38057
5.18137
−2.62863
7.38057


−3.3996
1.80086
7.38057
4.86078
−2.41332
7.38057


−3.12785
1.47622
7.38057
4.52869
−2.1872
7.38057


−2.83616
1.14937
7.38057
4.18512
−1.95077
7.38057


−2.52418
0.8205
7.38057
3.82971
−1.70403
7.38057


−2.19159
0.4901
7.38057
3.4623
−1.44749
7.38057


−1.83771
0.15886
7.38057
3.08273
−1.18148
7.38057


−1.47419
−0.1619
7.38057
2.70299
−0.91564
7.38057


−1.10137
−0.47286
7.38057
2.32257
−0.65082
7.38057


−0.7196
−0.77402
7.38057
1.94046
−0.38819
7.38057


−0.32938
−1.06639
7.38057
1.55683
−0.1281
7.38057


0.06878
−1.34963
7.38057
1.17235
0.13081
7.38057


0.47337
−1.62139
7.38057
0.78906
0.39157
7.38057


0.88472
−1.87894
7.38057
0.40797
0.65555
7.38057


1.3035
−2.12112
7.38057
0.02941
0.92325
7.38057


1.72955
−2.34809
7.38057
−0.34662
1.19415
7.38057


2.16202
−2.56153
7.38057
−0.72045
1.46861
7.38057


2.6004
−2.76281
7.38057
−1.09157
1.74628
7.38057


3.02916
−2.94668
7.38057
−1.44799
2.01786
7.38057


3.44777
−3.11467
7.38057
−1.78937
2.28353
7.38057


3.8554
−3.26846
7.38057
−2.11639
2.54244
7.38057


4.25153
−3.40924
7.38057
−2.42921
2.79458
7.38057


4.63516
−3.53852
7.38057
−2.72851
3.03896
7.38057


5.00612
−3.65733
7.38057
−3.01412
3.27556
7.38057


5.36305
−3.76617
7.38057
−3.28705
3.50337
7.38057


5.70578
−3.86621
7.38057
−3.53548
3.71225
7.38057


6.01843
−3.95342
7.38057
−3.75974
3.9017
7.38057


6.30066
−4.0293
7.38057
−3.96068
4.07104
7.38057


6.55196
−4.0947
7.38057
−4.13847
4.21993
7.38057


6.78789
−4.15453
7.38057
−4.29345
4.34769
7.38057


6.99271
−4.20489
7.38057
−4.42577
4.4545
7.38057


7.15056
−4.24275
7.38057
−4.53968
4.54458
7.38057


7.27697
−4.27232
7.38057
−4.63635
4.61911
7.38057


7.37212
−4.29176
7.38057
−4.71747
4.67843
7.38057


7.4431
−4.27384
7.38057
−4.78405
4.72338
7.38057


7.47504
−4.24798
7.38057
−4.83695
4.75532
7.38057


7.49076
−4.22686
7.38057
−4.87852
4.7756
7.38057


7.49701
−4.2152
7.38057
−4.91537
4.78726
7.38057


7.49954
−4.20911
7.38057
−4.94612
4.78878
7.38057


−4.90151
4.94207
9.74657
7.40727
−3.87618
9.74657


−4.91722
4.92348
9.74657
7.40828
−3.87331
9.74657


−4.92635
4.89238
9.74657
7.40997
−3.86757
9.74657


−4.92686
4.85182
9.74657
7.41285
−3.85574
9.74657


−4.91976
4.80416
9.74657
7.41488
−3.83174
9.74657


−4.90354
4.74163
9.74657
7.40862
−3.79473
9.74657


−4.87819
4.6617
9.74657
7.37144
−3.73879
9.74657


−4.84337
4.563
9.74657
7.29286
−3.69248
9.74657


−4.79723
4.44453
9.74657
7.18656
−3.63299
9.74657


−4.73808
4.30511
9.74657
7.05389
−3.5583
9.74657


−4.66372
4.14422
9.74657
6.88202
−3.46028
9.74657


−4.56976
3.95764
9.74657
6.68429
−3.34569
9.74657


−4.45552
3.74589
9.74657
6.47439
−3.22215
9.74657


−4.31913
3.51064
9.74657
6.23948
−3.08121
9.74657


−4.15757
3.25359
9.74657
5.97973
−2.92252
9.74657


−3.97116
2.97457
9.74657
5.69564
−2.74557
9.74657


−3.75788
2.67493
9.74657
5.40006
−2.55782
9.74657


−3.525
2.36904
9.74657
5.09349
−2.35958
9.74657


−3.27235
2.05741
9.74657
4.7756
−2.15053
9.74657


−3.00127
1.74188
9.74657
4.44639
−1.93066
9.74657


−2.71177
1.42349
9.74657
4.10602
−1.70031
9.74657


−2.40335
1.10289
9.74657
3.75417
−1.45982
9.74657


−2.07583
0.78027
9.74657
3.39065
−1.20936
9.74657


−1.72836
0.45647
9.74657
3.0153
−0.94927
9.74657


−1.37262
0.14264
9.74657
2.64012
−0.68884
9.74657


−1.00876
−0.16207
9.74657
2.26443
−0.42926
9.74657


−0.63713
−0.45782
9.74657
1.88756
−0.17154
9.74657


−0.2584
−0.74512
9.74657
1.50985
0.08518
9.74657


0.12726
−1.02414
9.74657
1.1323
0.34206
9.74657


0.52069
−1.29454
9.74657
0.75678
0.60181
9.74657


0.92325
−1.55412
9.74657
0.38363
0.86511
9.74657


1.33561
−1.8007
9.74657
0.01318
1.13213
9.74657


1.75456
−2.03206
9.74657
−0.35524
1.40236
9.74657


2.17926
−2.24871
9.74657
−0.72112
1.6758
9.74657


2.60902
−2.45219
9.74657
−1.08481
1.95212
9.74657


3.02916
−2.63725
9.74657
−1.43413
2.22201
9.74657


3.43864
−2.80557
9.74657
−1.76926
2.48548
9.74657


3.83731
−2.95902
9.74657
−2.09002
2.74236
9.74657


4.22416
−3.09878
9.74657
−2.39727
2.99215
9.74657


4.59883
−3.22638
9.74657
−2.69116
3.23415
9.74657


4.96083
−3.34299
9.74657
−2.97203
3.46788
9.74657


5.30981
−3.44946
9.74657
−3.24024
3.69299
9.74657


5.64528
−3.5468
9.74657
−3.48478
3.89917
9.74657


5.95184
−3.63164
9.74657
−3.70583
4.08591
9.74657


6.22883
−3.70499
9.74657
−3.90424
4.25221
9.74657


6.47591
−3.76802
9.74657
−4.08
4.39806
9.74657


6.70829
−3.82515
9.74657
−4.23345
4.52312
9.74657


6.9099
−3.87314
9.74657
−4.36459
4.62722
9.74657


7.06521
−3.90897
9.74657
−4.47799
4.71476
9.74657


7.18977
−3.93702
9.74657
−4.57432
4.78676
9.74657


7.28339
−3.95646
9.74657
−4.65477
4.84439
9.74657


7.35184
−3.94108
9.74657
−4.72017
4.889
9.74657


7.38277
−3.91658
9.74657
−4.77239
4.92044
9.74657


7.39781
−3.89613
9.74657
−4.81363
4.93987
9.74657


7.40355
−3.88497
9.74657
−4.85013
4.95035
9.74657


7.40609
−3.87923
9.74657
−4.88038
4.95069
9.74657


−4.83729
4.98195
12.11257
7.22086
−3.63536
12.11257


−4.85216
4.9637
12.11257
7.22188
−3.63266
12.11257


−4.86027
4.93328
12.11257
7.22357
−3.62691
12.11257


−4.85976
4.8939
12.11257
7.22593
−3.61542
12.11257


−4.85148
4.84777
12.11257
7.22745
−3.59176
12.11257


−4.83357
4.78794
12.11257
7.21985
−3.55576
12.11257


−4.80518
4.71155
12.11257
7.1798
−3.50371
12.11257


−4.76749
4.61708
12.11257
7.10138
−3.46078
12.11257


−4.71882
4.50368
12.11257
6.99643
−3.40434
12.11257


−4.65696
4.37017
12.11257
6.86546
−3.33302
12.11257


−4.57956
4.21638
12.11257
6.69578
−3.23956
12.11257


−4.48306
4.03792
12.11257
6.50075
−3.13005
12.11257


−4.36612
3.83562
12.11257
6.29373
−3.01158
12.11257


−4.22737
3.61052
12.11257
6.06203
−2.87655
12.11257


−4.06462
3.36411
12.11257
5.806
−2.72394
12.11257


−3.87737
3.09676
12.11257
5.52613
−2.55342
12.11257


−3.6646
2.80929
12.11257
5.23511
−2.37225
12.11257


−3.43357
2.51506
12.11257
4.93328
−2.18061
12.11257


−3.1843
2.21559
12.11257
4.62063
−1.97815
12.11257


−2.91812
1.91224
12.11257
4.29699
−1.76487
12.11257


−2.63437
1.60533
12.11257
3.96254
−1.54128
12.11257


−2.33321
1.29555
12.11257
3.61694
−1.30738
12.11257


−2.0138
0.98307
12.11257
3.26018
−1.06352
12.11257


−1.67564
0.66907
12.11257
2.89176
−0.81002
12.11257


−1.32986
0.36369
12.11257
2.52368
−0.55618
12.11257


−0.97682
0.06692
12.11257
2.15526
−0.30302
12.11257


−0.61685
−0.2219
12.11257
1.78599
−0.05104
12.11257


−0.25029
−0.50294
12.11257
1.41639
0.2006
12.11257


0.12253
−0.77656
12.11257
1.04797
0.45393
12.11257


0.5021
−1.04273
12.11257
0.68192
0.71065
12.11257


0.88945
−1.29944
12.11257
0.31857
0.97124
12.11257


1.28643
−1.545
12.11257
−0.04225
1.23522
12.11257


1.69169
−1.7772
12.11257
−0.4007
1.50224
12.11257


2.10388
−1.99555
12.11257
−0.75712
1.7723
12.11257


2.52249
−2.20123
12.11257
−1.11134
2.0449
12.11257


2.93316
−2.38848
12.11257
−1.45171
2.31091
12.11257


3.33437
−2.55917
12.11257
−1.77839
2.57049
12.11257


3.7251
−2.71431
12.11257
−2.09138
2.82331
12.11257


4.1045
−2.85559
12.11257
−2.39101
3.06904
12.11257


4.47208
−2.98437
12.11257
−2.67781
3.30716
12.11257


4.82715
−3.10149
12.11257
−2.95192
3.537
12.11257


5.16903
−3.20813
12.11257
−3.2137
3.75839
12.11257


5.49774
−3.3053
12.11257
−3.45216
3.96119
12.11257


5.79771
−3.38946
12.11257
−3.66781
4.14473
12.11257


6.06862
−3.46213
12.11257
−3.86148
4.30815
12.11257


6.30995
−3.52433
12.11257
−4.03319
4.45129
12.11257


6.53675
−3.58043
12.11257
−4.18326
4.57399
12.11257


6.73381
−3.62725
12.11257
−4.3117
4.67589
12.11257


6.88557
−3.6624
12.11257
−4.42273
4.76124
12.11257


7.00725
−3.68978
12.11257
−4.5172
4.83154
12.11257


7.09851
−3.70955
12.11257
−4.59579
4.88833
12.11257


7.16611
−3.69823
12.11257
−4.65967
4.93227
12.11257


7.19687
−3.67491
12.11257
−4.71071
4.96302
12.11257


7.21174
−3.65513
12.11257
−4.75127
4.98161
12.11257


7.21731
−3.64415
12.11257
−4.78726
4.99125
12.11257


7.21985
−3.6384
12.11257
−4.81684
4.99091
12.11257


−4.77138
4.92618
14.47857
7.02482
−3.4716
14.47857


−4.78507
4.90759
14.47857
7.02584
−3.46889
14.47857


−4.79098
4.87768
14.47857
7.02736
−3.46332
14.47857


−4.78845
4.83948
14.47857
7.02972
−3.45199
14.47857


−4.77831
4.79504
14.47857
7.03057
−3.42884
14.47857


−4.7587
4.73724
14.47857
7.02195
−3.39386
14.47857


−4.72845
4.66423
14.47857
6.97987
−3.34569
14.47857


−4.68772
4.57415
14.47857
6.90213
−3.30564
14.47857


−4.63567
4.46599
14.47857
6.79853
−3.25207
14.47857


−4.5701
4.33891
14.47857
6.66942
−3.18447
14.47857


−4.48949
4.19221
14.47857
6.50211
−3.09574
14.47857


−4.38961
4.0222
14.47857
6.30995
−2.99164
14.47857


−4.26945
3.82954
14.47857
6.10597
−2.87892
14.47857


−4.12766
3.61474
14.47857
5.87765
−2.75014
14.47857


−3.96305
3.37932
14.47857
5.6255
−2.60446
14.47857


−3.77445
3.12346
14.47857
5.34986
−2.44121
14.47857


−3.56066
2.84833
14.47857
5.06341
−2.26781
14.47857


−3.32998
2.5666
14.47857
4.76631
−2.0836
14.47857


−3.08324
2.28032
14.47857
4.45873
−1.88891
14.47857


−2.82027
1.98964
14.47857
4.1405
−1.68358
14.47857


−2.54108
1.69524
14.47857
3.81163
−1.46777
14.47857


−2.245
1.39712
14.47857
3.47227
−1.24181
14.47857


−1.93201
1.09597
14.47857
3.12194
−1.00589
14.47857


−1.60111
0.79227
14.47857
2.76062
−0.76033
14.47857


−1.26361
0.49652
14.47857
2.39963
−0.5141
14.47857


−0.91953
0.20838
14.47857
2.03865
−0.26803
14.47857


−0.56902
−0.0725
14.47857
1.67716
−0.02265
14.47857


−0.2126
−0.34645
14.47857
1.31617
0.22342
14.47857


0.1499
−0.61347
14.47857
0.95688
0.47185
14.47857


0.51815
−0.87373
14.47857
0.59995
0.72417
14.47857


0.89367
−1.12554
14.47857
0.2459
0.98003
14.47857


1.27781
−1.36755
14.47857
−0.10529
1.23962
14.47857


1.66955
−1.59705
14.47857
−0.45427
1.50224
14.47857


2.06805
−1.81388
14.47857
−0.80089
1.76774
14.47857


2.47281
−2.01837
14.47857
−1.14548
2.03611
14.47857


2.86979
−2.20528
14.47857
−1.47638
2.29823
14.47857


3.25798
−2.37614
14.47857
−1.7941
2.55376
14.47857


3.63587
−2.53179
14.47857
−2.09864
2.80253
14.47857


4.00293
−2.67392
14.47857
−2.39017
3.0442
14.47857


4.35868
−2.80354
14.47857
−2.66936
3.27792
14.47857


4.70243
−2.92167
14.47857
−2.93621
3.50354
14.47857


5.03367
−3.02966
14.47857
−3.19123
3.7207
14.47857


5.35206
−3.12802
14.47857
−3.42377
3.91962
14.47857


5.64257
−3.21354
14.47857
−3.63401
4.09943
14.47857


5.90503
−3.28722
14.47857
−3.82261
4.25981
14.47857


6.13909
−3.35043
14.47857
−3.98992
4.40042
14.47857


6.35896
−3.40738
14.47857
−4.13594
4.52092
14.47857


6.5501
−3.45521
14.47857
−4.26066
4.62131
14.47857


6.6973
−3.49086
14.47857
−4.36848
4.70581
14.47857


6.81526
−3.51875
14.47857
−4.46008
4.77543
14.47857


6.90382
−3.5392
14.47857
−4.5363
4.83154
14.47857


6.97041
−3.53193
14.47857
−4.59849
4.87481
14.47857


7.00116
−3.51013
14.47857
−4.64835
4.90506
14.47857


7.01587
−3.49103
14.47857
−4.68772
4.92365
14.47857


7.02144
−3.48022
14.47857
−4.72254
4.93396
14.47857


7.02381
−3.47447
14.47857
−4.75144
4.93463
14.47857


−4.70462
4.83019
16.84457
6.8663
−3.37476
16.84457


−4.71662
4.8116
16.84457
6.86715
−3.37206
16.84457


−4.72
4.78186
16.84457
6.86884
−3.36648
16.84457


−4.71476
4.74501
16.84457
6.87086
−3.3555
16.84457


−4.70243
4.70226
16.84457
6.8712
−3.33268
16.84457


−4.68079
4.64682
16.84457
6.86157
−3.29871
16.84457


−4.64818
4.5772
16.84457
6.81729
−3.25443
16.84457


−4.60424
4.49151
16.84457
6.7404
−3.21658
16.84457


−4.54864
4.38859
16.84457
6.63798
−3.16588
16.84457


−4.47918
4.26776
16.84457
6.51039
−3.10166
16.84457


−4.39485
4.12867
16.84457
6.34511
−3.01733
16.84457


−4.29125
3.96694
16.84457
6.15515
−2.91829
16.84457


−4.16737
3.7834
16.84457
5.95353
−2.81081
16.84457


−4.0222
3.57874
16.84457
5.72809
−2.68795
16.84457


−3.85489
3.35364
16.84457
5.47881
−2.54886
16.84457


−3.66426
3.10892
16.84457
5.20638
−2.39287
16.84457


−3.44895
2.84579
16.84457
4.92331
−2.22691
16.84457


−3.21861
2.57725
16.84457
4.62959
−2.05048
16.84457


−2.97322
2.30398
16.84457
4.32556
−1.86373
16.84457


−2.71245
2.0258
16.84457
4.01122
−1.66651
16.84457


−2.4363
1.74324
16.84457
3.68657
−1.45898
16.84457


−2.14427
1.45661
16.84457
3.35144
−1.24114
16.84457


−1.83585
1.16644
16.84457
3.00617
−1.01332
16.84457


−1.51086
0.87322
16.84457
2.64992
−0.77571
16.84457


−1.18013
0.5866
16.84457
2.29468
−0.53691
16.84457


−0.84365
0.30657
16.84457
1.93961
−0.29761
16.84457


−0.50125
0.03312
16.84457
1.58488
−0.05797
16.84457


−0.15328
−0.2339
16.84457
1.23117
0.18303
16.84457


0.2001
−0.49483
16.84457
0.87914
0.42689
16.84457


0.55905
−0.74935
16.84457
0.53015
0.67465
16.84457


0.92443
−0.99642
16.84457
0.18404
0.92612
16.84457


1.29741
−1.23455
16.84457
−0.15954
1.18114
16.84457


1.67699
−1.46134
16.84457
−0.50041
1.43954
16.84457


2.06298
−1.67648
16.84457
−0.83892
1.70115
16.84457


2.45489
−1.88063
16.84457
−1.17489
1.96581
16.84457


2.8392
−2.06788
16.84457
−1.49768
2.22455
16.84457


3.21489
−2.23976
16.84457
−1.80746
2.4767
16.84457


3.58077
−2.39727
16.84457
−2.10456
2.72208
16.84457


3.93601
−2.54142
16.84457
−2.38898
2.9602
16.84457


4.28043
−2.67358
16.84457
−2.66124
3.19089
16.84457


4.61319
−2.79458
16.84457
−2.9215
3.41329
16.84457


4.93396
−2.90545
16.84457
−3.17044
3.62725
16.84457


5.24221
−3.00702
16.84457
−3.39724
3.82295
16.84457


5.52377
−3.09557
16.84457
−3.60224
4.0004
16.84457


5.77811
−3.17213
16.84457
−3.78594
4.15892
16.84457


6.00491
−3.2377
16.84457
−3.94835
4.29818
16.84457


6.21819
−3.29719
16.84457
−4.08997
4.418
16.84457


6.40341
−3.34705
16.84457
−4.21064
4.51838
16.84457


6.54622
−3.38439
16.84457
−4.31491
4.60288
16.84457


6.66063
−3.41363
16.84457
−4.4033
4.67268
16.84457


6.74648
−3.43509
16.84457
−4.47681
4.7293
16.84457


6.81171
−3.43239
16.84457
−4.53681
4.7729
16.84457


6.84264
−3.41211
16.84457
−4.58497
4.80366
16.84457


6.85734
−3.39352
16.84457
−4.62283
4.82343
16.84457


6.86292
−3.38304
16.84457
−4.65646
4.83526
16.84457


6.86529
−3.37747
16.84457
−4.68468
4.83796
16.84457


−4.63601
4.68147
19.21057
6.72806
−3.33741
19.21057


−4.64699
4.66271
19.21057
6.7289
−3.33488
19.21057


−4.64835
4.63347
19.21057
6.73043
−3.32947
19.21057


−4.64159
4.59798
19.21057
6.73245
−3.31848
19.21057


−4.6279
4.55658
19.21057
6.73228
−3.29618
19.21057


−4.60474
4.50351
19.21057
6.7213
−3.26322
19.21057


−4.57044
4.43676
19.21057
6.67466
−3.22283
19.21057


−4.52413
4.35513
19.21057
6.59877
−3.187
19.21057


−4.46566
4.25711
19.21057
6.49788
−3.1385
19.21057


−4.39349
4.14219
19.21057
6.37198
−3.07732
19.21057


−4.30612
4.00969
19.21057
6.20889
−2.99654
19.21057


−4.19982
3.85557
19.21057
6.02164
−2.90173
19.21057


−4.07324
3.68048
19.21057
5.82273
−2.79898
19.21057


−3.92553
3.48512
19.21057
5.60032
−2.68102
19.21057


−3.75636
3.26998
19.21057
5.35443
−2.54751
19.21057


−3.56421
3.03592
19.21057
5.08572
−2.3976
19.21057


−3.34857
2.78461
19.21057
4.80653
−2.2379
19.21057


−3.11856
2.52773
19.21057
4.51669
−2.06822
19.21057


−2.87435
2.26561
19.21057
4.21672
−1.88824
19.21057


−2.61561
1.99826
19.21057
3.9066
−1.69811
19.21057


−2.34217
1.72617
19.21057
3.58635
−1.49785
19.21057


−2.05352
1.44951
19.21057
3.25595
−1.28744
19.21057


−1.74915
1.16914
19.21057
2.91525
−1.06707
19.21057


−1.42906
0.88505
19.21057
2.56424
−0.83689
19.21057


−1.10374
0.60705
19.21057
2.21424
−0.60519
19.21057


−0.77301
0.33496
19.21057
1.86508
−0.37248
19.21057


−0.43687
0.06895
19.21057
1.51661
−0.13858
19.21057


−0.09565
−0.19131
19.21057
1.16948
0.09718
19.21057


0.25063
−0.44582
19.21057
0.82438
0.33597
19.21057


0.60215
−0.69425
19.21057
0.48216
0.57883
19.21057


0.95958
−0.93592
19.21057
0.14264
0.82573
19.21057


1.32276
−1.1688
19.21057
−0.19401
1.07636
19.21057


1.69169
−1.39138
19.21057
−0.52829
1.33071
19.21057


2.0667
−1.60381
19.21057
−0.86004
1.58826
19.21057


2.44729
−1.80627
19.21057
−1.18908
1.84886
19.21057


2.82044
−1.99302
19.21057
−1.50495
2.10371
19.21057


3.18464
−2.16506
19.21057
−1.80796
2.35214
19.21057


3.5392
−2.32358
19.21057
−2.09864
2.59364
19.21057


3.88362
−2.4696
19.21057
−2.37699
2.82805
19.21057


4.2174
−2.60395
19.21057
−2.6435
3.05484
19.21057


4.53985
−2.72766
19.21057
−2.89835
3.2737
19.21057


4.85064
−2.84123
19.21057
−3.14188
3.48427
19.21057


5.1496
−2.94584
19.21057
−3.36378
3.6771
19.21057


5.42253
−3.03727
19.21057
−3.56438
3.85185
19.21057


5.66911
−3.11653
19.21057
−3.74369
4.00817
19.21057


5.88914
−3.18464
19.21057
−3.90221
4.14591
19.21057


6.09583
−3.24649
19.21057
−4.04011
4.26472
19.21057


6.27565
−3.29837
19.21057
−4.1574
4.36443
19.21057


6.41423
−3.33724
19.21057
−4.25846
4.44876
19.21057


6.52526
−3.36766
19.21057
−4.34398
4.51872
19.21057


6.60875
−3.39014
19.21057
−4.41529
4.57551
19.21057


6.67263
−3.39234
19.21057
−4.47343
4.61928
19.21057


6.70406
−3.37392
19.21057
−4.51991
4.65054
19.21057


6.7191
−3.356
19.21057
−4.55641
4.67099
19.21057


6.72468
−3.34569
19.21057
−4.58886
4.684
19.21057


6.72705
−3.34029
19.21057
−4.6164
4.68823
19.21057


−4.56604
4.52278
21.57657
6.59438
−3.3462
21.57657


−4.57618
4.50402
21.57657
6.59523
−3.3435
21.57657


−4.57669
4.47546
21.57657
6.59658
−3.33826
21.57657


−4.56892
4.44064
21.57657
6.59844
−3.32744
21.57657


−4.55438
4.40059
21.57657
6.59759
−3.30547
21.57657


−4.53038
4.34905
21.57657
6.58542
−3.2737
21.57657


−4.49489
4.28466
21.57657
6.53692
−3.23703
21.57657


−4.4469
4.20641
21.57657
6.46188
−3.20255
21.57657


−4.38623
4.11245
21.57657
6.36234
−3.15608
21.57657


−4.3117
4.00226
21.57657
6.23813
−3.09726
21.57657


−4.22196
3.87517
21.57657
6.07707
−3.01969
21.57657


−4.11346
3.72713
21.57657
5.89219
−2.92843
21.57657


−3.98451
3.55897
21.57657
5.69598
−2.8294
21.57657


−3.83495
3.37121
21.57657
5.47645
−2.71566
21.57657


−3.66443
3.16402
21.57657
5.23393
−2.58671
21.57657


−3.47109
2.93857
21.57657
4.9686
−2.44188
21.57657


−3.25511
2.6964
21.57657
4.69313
−2.28725
21.57657


−3.02561
2.4483
21.57657
4.40735
−2.12247
21.57657


−2.78242
2.1943
21.57657
4.11177
−1.94773
21.57657


−2.5252
1.93522
21.57657
3.80605
−1.76267
21.57657


−2.25378
1.6709
21.57657
3.49053
−1.56764
21.57657


−1.96767
1.40186
21.57657
3.1652
−1.36231
21.57657


−1.66668
1.12858
21.57657
2.82991
−1.147
21.57657


−1.35031
0.85142
21.57657
2.48464
−0.92173
21.57657


−1.02904
0.57984
21.57657
2.14072
−0.69476
21.57657


−0.70287
0.31366
21.57657
1.79765
−0.46627
21.57657


−0.37163
0.05324
21.57657
1.45577
−0.23643
21.57657


−0.03566
−0.20196
21.57657
1.11523
−0.00423
21.57657


0.30488
−0.45191
21.57657
0.77706
0.23136
21.57657


0.65048
−0.69611
21.57657
0.44177
0.47083
21.57657


1.00014
−0.93322
21.57657
0.10917
0.71453
21.57657


1.3542
−1.16154
21.57657
−0.22071
0.96195
21.57657


1.71315
−1.38022
21.57657
−0.5479
1.21291
21.57657


2.07667
−1.58945
21.57657
−0.87255
1.46692
21.57657


2.44492
−1.78937
21.57657
−1.19466
1.72414
21.57657


2.80506
−1.97426
21.57657
−1.50393
1.97544
21.57657


3.15641
−2.14546
21.57657
−1.80053
2.22049
21.57657


3.49847
−2.30398
21.57657
−2.08512
2.45878
21.57657


3.83072
−2.45067
21.57657
−2.35755
2.6898
21.57657


4.15301
−2.58621
21.57657
−2.61849
2.91356
21.57657


4.46498
−2.71161
21.57657
−2.86793
3.12954
21.57657


4.76597
−2.82737
21.57657
−3.10622
3.33724
21.57657


5.0558
−2.93401
21.57657
−3.32322
3.52754
21.57657


5.32097
−3.02764
21.57657
−3.51943
3.69992
21.57657


5.56111
−3.10926
21.57657
−3.69485
3.85438
21.57657


5.77524
−3.17923
21.57657
−3.84982
3.99026
21.57657


5.97685
−3.24311
21.57657
−3.98468
4.10771
21.57657


6.15194
−3.29668
21.57657
−4.0991
4.20624
21.57657


6.28697
−3.33691
21.57657
−4.19779
4.2899
21.57657


6.39513
−3.36834
21.57657
−4.28128
4.35936
21.57657


6.47642
−3.39166
21.57657
−4.35057
4.41563
21.57657


6.53895
−3.39791
21.57657
−4.40718
4.45923
21.57657


6.57038
−3.38135
21.57657
−4.45247
4.49033
21.57657


6.58542
−3.36428
21.57657
−4.4883
4.51095
21.57657


6.591
−3.35414
21.57657
−4.51991
4.5243
21.57657


6.59337
−3.3489
21.57657
−4.54678
4.52903
21.57657


−4.49489
4.34905
23.94257
6.44177
−3.39808
23.94257


−4.5047
4.33063
23.94257
6.44262
−3.39555
23.94257


−4.50486
4.30274
23.94257
6.44397
−3.39031
23.94257


−4.49692
4.26894
23.94257
6.44566
−3.37966
23.94257


−4.48222
4.2299
23.94257
6.44431
−3.3582
23.94257


−4.45822
4.18005
23.94257
6.43079
−3.32761
23.94257


−4.42256
4.11785
23.94257
6.38127
−3.29415
23.94257


−4.37423
4.04231
23.94257
6.30742
−3.26069
23.94257


−4.31254
3.9524
23.94257
6.2094
−3.21573
23.94257


−4.23734
3.84661
23.94257
6.08704
−3.15878
23.94257


−4.14726
3.72476
23.94257
5.92835
−3.08374
23.94257


−4.03826
3.58246
23.94257
5.74634
−2.99536
23.94257


−3.90948
3.42073
23.94257
5.553
−2.89953
23.94257


−3.76042
3.2399
23.94257
5.33668
−2.78935
23.94257


−3.59091
3.03997
23.94257
5.09772
−2.66429
23.94257


−3.39977
2.82247
23.94257
4.83644
−2.52368
23.94257


−3.1865
2.58857
23.94257
4.56503
−2.37327
23.94257


−2.96054
2.34809
23.94257
4.28364
−2.21306
23.94257


−2.72158
2.10152
23.94257
3.99263
−2.0427
23.94257


−2.46909
1.84954
23.94257
3.69197
−1.86204
23.94257


−2.20308
1.59198
23.94257
3.38186
−1.67124
23.94257


−1.92322
1.32952
23.94257
3.06211
−1.46996
23.94257


−1.62899
1.0625
23.94257
2.73307
−1.25821
23.94257


−1.32006
0.79109
23.94257
2.39456
−1.03648
23.94257


−1.00673
0.52475
23.94257
2.05774
−0.81255
23.94257


−0.68868
0.26347
23.94257
1.72194
−0.58677
23.94257


−0.36605
0.00744
23.94257
1.38749
−0.35913
23.94257


−0.03904
−0.24387
23.94257
1.05456
−0.12912
23.94257


0.29254
−0.48993
23.94257
0.72417
0.10427
23.94257


0.62834
−0.73076
23.94257
0.39631
0.34172
23.94257


0.96854
−0.96482
23.94257
0.07132
0.58305
23.94257


1.31347
−1.19128
23.94257
−0.25063
0.82827
23.94257


1.66397
−1.40895
23.94257
−0.57004
1.0767
23.94257


2.02006
−1.61818
23.94257
−0.88674
1.32851
23.94257


2.38138
−1.81895
23.94257
−1.20108
1.58319
23.94257


2.73493
−2.00502
23.94257
−1.50292
1.83196
23.94257


3.08003
−2.1774
23.94257
−1.79241
2.07448
23.94257


3.41583
−2.33727
23.94257
−2.07008
2.31023
23.94257


3.74217
−2.48548
23.94257
−2.33609
2.53889
23.94257


4.0582
−2.62237
23.94257
−2.59077
2.76011
23.94257


4.36375
−2.74912
23.94257
−2.83447
2.97339
23.94257


4.65849
−2.86607
23.94257
−3.06718
3.17872
23.94257


4.94173
−2.97389
23.94257
−3.27928
3.36648
23.94257


5.20064
−3.0687
23.94257
−3.47092
3.53666
23.94257


5.4347
−3.15101
23.94257
−3.64263
3.68893
23.94257


5.64359
−3.22199
23.94257
−3.79405
3.82312
23.94257


5.83996
−3.28671
23.94257
−3.92587
3.93888
23.94257


6.01065
−3.34113
23.94257
−4.03792
4.03623
23.94257


6.14231
−3.38203
23.94257
−4.13442
4.11853
23.94257


6.24776
−3.41414
23.94257
−4.21604
4.18714
23.94257


6.32702
−3.4378
23.94257
−4.28381
4.24275
23.94257


6.38752
−3.44659
23.94257
−4.33924
4.28584
23.94257


6.41845
−3.43171
23.94257
−4.38369
4.31643
23.94257


6.43315
−3.41549
23.94257
−4.41867
4.33688
23.94257


6.43856
−3.40586
23.94257
−4.4496
4.35006
23.94257


6.44076
−3.40079
23.94257
−4.47597
4.35513
23.94257


−4.4229
4.11498
26.30857
6.29238
−3.48748
26.30857


−4.43219
4.0969
26.30857
6.29322
−3.48478
26.30857


−4.43219
4.06952
26.30857
6.29457
−3.47971
26.30857


−4.42425
4.03657
26.30857
6.2961
−3.46923
26.30857


−4.40955
3.99854
26.30857
6.29424
−3.44811
26.30857


−4.38555
3.9497
26.30857
6.27936
−3.4187
26.30857


−4.35023
3.88903
26.30857
6.229
−3.38828
26.30857


−4.30206
3.81585
26.30857
6.15633
−3.356
26.30857


−4.24055
3.72865
26.30857
6.05983
−3.31257
26.30857


−4.16534
3.6264
26.30857
5.93934
−3.25764
26.30857


−4.0756
3.50793
26.30857
5.78318
−3.18531
26.30857


−3.96728
3.37003
26.30857
5.6037
−3.10031
26.30857


−3.83951
3.21303
26.30857
5.41324
−3.0082
26.30857


−3.69214
3.03744
26.30857
5.19996
−2.90224
26.30857


−3.52517
2.84309
26.30857
4.96421
−2.78208
26.30857


−3.33707
2.63116
26.30857
4.70648
−2.64688
26.30857


−3.12735
2.4025
26.30857
4.43862
−2.50221
26.30857


−2.90528
2.16692
26.30857
4.16095
−2.34792
26.30857


−2.67105
1.92525
26.30857
3.87382
−2.18382
26.30857


−2.42414
1.678
26.30857
3.57722
−2.00941
26.30857


−2.16438
1.42518
26.30857
3.2715
−1.82469
26.30857


−1.89162
1.16745
26.30857
2.95649
−1.6295
26.30857


−1.60516
0.905
26.30857
2.63234
−1.42399
26.30857


−1.30485
0.63848
26.30857
2.29941
−1.20801
26.30857


−1.00031
0.37704
26.30857
1.96834
−0.98916
26.30857


−0.69155
0.12067
26.30857
1.63896
−0.76811
26.30857


−0.37856
−0.13047
26.30857
1.31093
−0.54469
26.30857


−0.06118
−0.37636
26.30857
0.98493
−0.3184
26.30857


0.2606
−0.61685
26.30857
0.66147
−0.08856
26.30857


0.58677
−0.85176
26.30857
0.34087
0.14585
26.30857


0.91835
−1.08042
26.30857
0.02366
0.38448
26.30857


1.25584
−1.30181
26.30857
−0.29034
0.62699
26.30857


1.59992
−1.51509
26.30857
−0.6013
0.87322
26.30857


1.95026
−1.72025
26.30857
−0.90956
1.12301
26.30857


2.3055
−1.91714
26.30857
−1.21528
1.37583
26.30857


2.65296
−2.09949
26.30857
−1.50866
1.62291
26.30857


2.99198
−2.26883
26.30857
−1.79005
1.86373
26.30857


3.32203
−2.42616
26.30857
−2.05994
2.09763
26.30857


3.64246
−2.57201
26.30857
−2.31868
2.32443
26.30857


3.95274
−2.70721
26.30857
−2.56643
2.54362
26.30857


4.25255
−2.83244
26.30857
−2.80354
2.75487
26.30857


4.54171
−2.94854
26.30857
−3.03017
2.95801
26.30857


4.81971
−3.05569
26.30857
−3.23669
3.14391
26.30857


5.07355
−3.14982
26.30857
−3.4236
3.31206
26.30857


5.30305
−3.23213
26.30857
−3.59091
3.46247
26.30857


5.50788
−3.30311
26.30857
−3.73862
3.59497
26.30857


5.70037
−3.368
26.30857
−3.86723
3.70921
26.30857


5.86768
−3.42293
26.30857
−3.97657
3.8052
26.30857


5.99663
−3.46416
26.30857
−4.0707
3.88649
26.30857


6.10006
−3.49678
26.30857
−4.15047
3.95409
26.30857


6.17763
−3.52078
26.30857
−4.21655
4.00919
26.30857


6.23695
−3.53278
26.30857
−4.2708
4.05144
26.30857


6.26855
−3.52027
26.30857
−4.31423
4.08169
26.30857


6.28376
−3.50455
26.30857
−4.34837
4.10197
26.30857


6.28934
−3.49509
26.30857
−4.37862
4.11532
26.30857


6.29153
−3.49002
26.30857
−4.40448
4.12073
26.30857


−4.38673
3.96356
27.49157
6.20484
−3.54545
27.49157


−4.39586
3.94564
27.49157
6.20551
−3.54292
27.49157


−4.39535
3.9186
27.49157
6.20686
−3.53785
27.49157


−4.38724
3.88599
27.49157
6.20822
−3.52754
27.49157


−4.37254
3.84864
27.49157
6.20602
−3.50658
27.49157


−4.34871
3.80064
27.49157
6.19081
−3.47785
27.49157


−4.31356
3.74082
27.49157
6.14011
−3.44878
27.49157


−4.26573
3.66865
27.49157
6.06828
−3.41701
27.49157


−4.20455
3.5828
27.49157
5.97263
−3.37442
27.49157


−4.12968
3.48208
27.49157
5.85348
−3.32068
27.49157


−4.04045
3.36564
27.49157
5.69868
−3.2497
27.49157


−3.93297
3.22976
27.49157
5.52106
−3.16655
27.49157


−3.80639
3.07512
27.49157
5.33212
−3.07631
27.49157


−3.66037
2.9019
27.49157
5.12053
−2.97305
27.49157


−3.49526
2.70992
27.49157
4.88664
−2.85576
27.49157


−3.30953
2.50052
27.49157
4.63077
−2.72394
27.49157


−3.10233
2.2744
27.49157
4.36493
−2.583
27.49157


−2.88365
2.04152
27.49157
4.08929
−2.43259
27.49157


−2.65279
1.80239
27.49157
3.80402
−2.27271
27.49157


−2.40943
1.55734
27.49157
3.50945
−2.1027
27.49157


−2.15357
1.30671
27.49157
3.20559
−1.92238
27.49157


−1.88486
1.05084
27.49157
2.89277
−1.73174
27.49157


−1.60263
0.79008
27.49157
2.571
−1.5308
27.49157


−1.30654
0.52525
27.49157
2.2406
−1.31921
27.49157


−1.00606
0.26533
27.49157
1.91224
−1.10442
27.49157


−0.70135
0.01048
27.49157
1.5859
−0.88708
27.49157


−0.39191
−0.23914
27.49157
1.26108
−0.66704
27.49157


−0.07808
−0.48334
27.49157
0.93846
−0.44363
27.49157


0.24066
−0.72197
27.49157
0.61854
−0.21632
27.49157


0.56463
−0.95468
27.49157
0.302
0.01589
27.49157


0.89418
−1.18063
27.49157
−0.01082
0.25249
27.49157


1.23015
−1.39898
27.49157
−0.32009
0.49365
27.49157


1.5717
−1.60837
27.49157
−0.62631
0.73853
27.49157


1.91832
−1.80881
27.49157
−0.92967
0.98713
27.49157


2.26967
−2.00079
27.49157
−1.23032
1.23877
27.49157


2.61342
−2.17892
27.49157
−1.5188
1.48483
27.49157


2.94888
−2.34437
27.49157
−1.79546
1.72448
27.49157


3.27522
−2.49799
27.49157
−2.06096
1.95753
27.49157


3.59193
−2.64079
27.49157
−2.3153
2.18314
27.49157


3.89849
−2.77329
27.49157
−2.559
2.40132
27.49157


4.19458
−2.89615
27.49157
−2.79205
2.61139
27.49157


4.48002
−3.01006
27.49157
−3.01513
2.81334
27.49157


4.75448
−3.11552
27.49157
−3.21844
2.99806
27.49157


5.00494
−3.20847
27.49157
−3.40231
3.1652
27.49157


5.2314
−3.28975
27.49157
−3.56691
3.3146
27.49157


5.43318
−3.36006
27.49157
−3.71259
3.44625
27.49157


5.62297
−3.42462
27.49157
−3.83917
3.55965
27.49157


5.78791
−3.4792
27.49157
−3.94683
3.65513
27.49157


5.915
−3.52027
27.49157
−4.03961
3.73591
27.49157


6.01691
−3.55272
27.49157
−4.11802
3.80301
27.49157


6.09346
−3.57689
27.49157
−4.18326
3.85759
27.49157


6.1516
−3.58905
27.49157
−4.23683
3.89951
27.49157


6.18185
−3.57705
27.49157
−4.27959
3.92976
27.49157


6.19655
−3.56201
27.49157
−4.31322
3.94987
27.49157


6.20179
−3.55289
27.49157
−4.34296
3.96339
27.49157


6.20382
−3.54799
27.49157
−4.36848
3.96897
27.49157


−4.35074
3.80199
28.67457
6.10141
−3.61356
28.67457


−4.35952
3.78425
28.67457
6.10225
−3.61119
28.67457


−4.35868
3.75755
28.67457
6.10344
−3.60612
28.67457


−4.35023
3.72561
28.67457
6.10462
−3.59581
28.67457


−4.33553
3.68876
28.67457
6.10225
−3.5752
28.67457


−4.3117
3.64144
28.67457
6.08654
−3.54714
28.67457


−4.27671
3.58263
28.67457
6.036
−3.51926
28.67457


−4.22939
3.51165
28.67457
5.96486
−3.48799
28.67457


−4.16855
3.42732
28.67457
5.87038
−3.44625
28.67457


−4.09436
3.32829
28.67457
5.75242
−3.39352
28.67457


−4.00598
3.21354
28.67457
5.59931
−3.32406
28.67457


−3.89951
3.07986
28.67457
5.42338
−3.24277
28.67457


−3.77445
2.92725
28.67457
5.2363
−3.15472
28.67457


−3.63029
2.75622
28.67457
5.02657
−3.054
28.67457


−3.46754
2.5666
28.67457
4.7947
−2.94009
28.67457


−3.28452
2.35958
28.67457
4.54069
−2.81199
28.67457


−3.08087
2.13582
28.67457
4.27671
−2.67544
28.67457


−2.86607
1.90514
28.67457
4.00293
−2.52976
28.67457


−2.63961
1.66786
28.67457
3.71935
−2.37479
28.67457


−2.40098
1.4245
28.67457
3.42664
−2.21001
28.67457


−2.15002
1.17523
28.67457
3.12464
−2.03527
28.67457


−1.88655
0.92037
28.67457
2.81368
−1.85021
28.67457


−1.60989
0.66079
28.67457
2.4941
−1.65451
28.67457


−1.31972
0.39664
28.67457
2.16624
−1.44799
28.67457


−1.02532
0.1374
28.67457
1.84075
−1.23793
28.67457


−0.72636
−0.11661
28.67457
1.51762
−1.02448
28.67457


−0.42267
−0.36538
28.67457
1.19652
−0.80765
28.67457


−0.11391
−0.60857
28.67457
0.87796
−0.58711
28.67457


0.2001
−0.84568
28.67457
0.5626
−0.36166
28.67457


0.51984
−1.07636
28.67457
0.25097
−0.13098
28.67457


0.84601
−1.29978
28.67457
−0.05645
0.10478
28.67457


1.17844
−1.51441
28.67457
−0.36014
0.34527
28.67457


1.51644
−1.71941
28.67457
−0.66011
0.58998
28.67457


1.85968
−1.91511
28.67457
−0.95722
0.83824
28.67457


2.20799
−2.10219
28.67457
−1.25178
1.08988
28.67457


2.54886
−2.27542
28.67457
−1.53418
1.33561
28.67457


2.88128
−2.4363
28.67457
−1.80543
1.57491
28.67457


3.20475
−2.58536
28.67457
−2.06535
1.80729
28.67457


3.51841
−2.72377
28.67457
−2.31479
2.03223
28.67457


3.8221
−2.85255
28.67457
−2.55376
2.24939
28.67457


4.11532
−2.9722
28.67457
−2.78259
2.45861
28.67457


4.39755
−3.08324
28.67457
−3.00144
2.65955
28.67457


4.66896
−3.1865
28.67457
−3.2012
2.84309
28.67457


4.91655
−3.27759
28.67457
−3.38186
3.00905
28.67457


5.14014
−3.35769
28.67457
−3.54376
3.15743
28.67457


5.33939
−3.42715
28.67457
−3.6869
3.28806
28.67457


5.52681
−3.49086
28.67457
−3.81163
3.40062
28.67457


5.68955
−3.54511
28.67457
−3.91759
3.49526
28.67457


5.81495
−3.58601
28.67457
−4.00885
3.57536
28.67457


5.91534
−3.61846
28.67457
−4.08608
3.64195
28.67457


5.99088
−3.64246
28.67457
−4.1503
3.69603
28.67457


6.04817
−3.65564
28.67457
−4.20303
3.73777
28.67457


6.07842
−3.64465
28.67457
−4.24511
3.76752
28.67457


6.09313
−3.62995
28.67457
−4.27824
3.78763
28.67457


6.09837
−3.62083
28.67457
−4.30747
3.80115
28.67457


6.10056
−3.61609
28.67457
−4.33265
3.80706
28.67457


−4.31491
3.63958
29.85757
5.98142
−3.69282
29.85757


−4.32319
3.62201
29.85757
5.98209
−3.69028
29.85757


−4.32201
3.59581
29.85757
5.98328
−3.68538
29.85757


−4.31322
3.56438
29.85757
5.98446
−3.67507
29.85757


−4.29835
3.52821
29.85757
5.98192
−3.65479
29.85757


−4.27469
3.48174
29.85757
5.96587
−3.62742
29.85757


−4.24004
3.42394
29.85757
5.91551
−3.60038
29.85757


−4.19323
3.35381
29.85757
5.84537
−3.56979
29.85757


−4.13306
3.27083
29.85757
5.75192
−3.52855
29.85757


−4.05972
3.17331
29.85757
5.63531
−3.47684
29.85757


−3.97251
3.06042
29.85757
5.48405
−3.40856
29.85757


−3.86757
2.92843
29.85757
5.30998
−3.32896
29.85757


−3.74453
2.77785
29.85757
5.12476
−3.24294
29.85757


−3.60308
2.60868
29.85757
4.91722
−3.14458
29.85757


−3.44354
2.42109
29.85757
4.68738
−3.03372
29.85757


−3.2644
2.21576
29.85757
4.43574
−2.9095
29.85757


−3.06549
1.99352
29.85757
4.17362
−2.77718
29.85757


−2.85559
1.76402
29.85757
3.90153
−2.63657
29.85757


−2.63471
1.52759
29.85757
3.61981
−2.48684
29.85757


−2.40217
1.28491
29.85757
3.32862
−2.32798
29.85757


−2.15779
1.03614
29.85757
3.02814
−2.15931
29.85757


−1.90142
0.78163
29.85757
2.71887
−1.98051
29.85757


−1.6322
0.52204
29.85757
2.40132
−1.79106
29.85757


−1.3498
0.25806
29.85757
2.07566
−1.59046
29.85757


−1.06318
−0.00118
29.85757
1.75287
−1.38563
29.85757


−0.77165
−0.25485
29.85757
1.43261
−1.17641
29.85757


−0.47506
−0.50278
29.85757
1.11523
−0.96313
29.85757


−0.17323
−0.74461
29.85757
0.80089
−0.74512
29.85757


0.13452
−0.97986
29.85757
0.49027
−0.52137
29.85757


0.44853
−1.20784
29.85757
0.18404
−0.29186
29.85757


0.76963
−1.42771
29.85757
−0.11729
−0.05645
29.85757


1.09867
−1.63896
29.85757
−0.41422
0.18421
29.85757


1.43447
−1.84024
29.85757
−0.70727
0.42943
29.85757


1.77551
−2.03138
29.85757
−0.99693
0.67854
29.85757


2.12163
−2.21339
29.85757
−1.28389
0.93102
29.85757


2.46047
−2.38138
29.85757
−1.55919
1.17759
29.85757


2.79104
−2.53703
29.85757
−1.82334
1.41774
29.85757


3.11247
−2.68135
29.85757
−2.07684
1.65045
29.85757


3.42411
−2.81537
29.85757
−2.32003
1.87573
29.85757


3.72561
−2.94026
29.85757
−2.55325
2.09307
29.85757


4.01645
−3.05653
29.85757
−2.77684
2.30195
29.85757


4.29649
−3.16503
29.85757
−2.99079
2.50255
29.85757


4.5652
−3.26609
29.85757
−3.18616
2.68558
29.85757


4.81025
−3.356
29.85757
−3.36327
2.85086
29.85757


5.03147
−3.43509
29.85757
−3.52196
2.9984
29.85757


5.22852
−3.50405
29.85757
−3.6624
3.12836
29.85757


5.41375
−3.56759
29.85757
−3.78476
3.24007
29.85757


5.57463
−3.62167
29.85757
−3.88886
3.33403
29.85757


5.69851
−3.66274
29.85757
−3.97843
3.41363
29.85757


5.79771
−3.69519
29.85757
−4.05431
3.47988
29.85757


5.87224
−3.71935
29.85757
−4.11752
3.53345
29.85757


5.92869
−3.73338
29.85757
−4.1694
3.57486
29.85757


5.95877
−3.72324
29.85757
−4.2108
3.60443
29.85757


5.97331
−3.70887
29.85757
−4.24342
3.62454
29.85757


5.97854
−3.69992
29.85757
−4.27215
3.63823
29.85757


5.98057
−3.69519
29.85757
−4.29683
3.64449
29.85757


−4.27773
3.46619
31.04057
5.77946
−3.78188
31.04057


−4.2855
3.44895
31.04057
5.78031
−3.77935
31.04057


−4.28381
3.42326
31.04057
5.78132
−3.77462
31.04057


−4.27486
3.39251
31.04057
5.78234
−3.76464
31.04057


−4.25998
3.35719
31.04057
5.7798
−3.74487
31.04057


−4.23632
3.31189
31.04057
5.76425
−3.71817
31.04057


−4.20235
3.25528
31.04057
5.71507
−3.69164
31.04057


−4.15639
3.18666
31.04057
5.64629
−3.66139
31.04057


−4.09757
3.10521
31.04057
5.55452
−3.62116
31.04057


−4.02558
3.00955
31.04057
5.44011
−3.57029
31.04057


−3.94024
2.89869
31.04057
5.29156
−3.50371
31.04057


−3.83765
2.76907
31.04057
5.1207
−3.42597
31.04057


−3.71766
2.62085
31.04057
4.93886
−3.34214
31.04057


−3.57993
2.45422
31.04057
4.7347
−3.24649
31.04057


−3.42479
2.26899
31.04057
4.50875
−3.13867
31.04057


−3.25122
2.06603
31.04057
4.26117
−3.01817
31.04057


−3.05856
1.84582
31.04057
4.00327
−2.8899
31.04057


−2.85576
1.61818
31.04057
3.73558
−2.75369
31.04057


−2.64232
1.38327
31.04057
3.45842
−2.60885
31.04057


−2.41788
1.14176
31.04057
3.17196
−2.45506
31.04057


−2.18213
0.89384
31.04057
2.87638
−2.29164
31.04057


−1.93488
0.64017
31.04057
2.57218
−2.11808
31.04057


−1.67513
0.38126
31.04057
2.2597
−1.93387
31.04057


−1.40253
0.11796
31.04057
1.93928
−1.738
31.04057


−1.12554
−0.14027
31.04057
1.62189
−1.53706
31.04057


−0.84348
−0.39309
31.04057
1.30806
−1.33121
31.04057


−0.55601
−0.63967
31.04057
0.99744
−1.12081
31.04057


−0.2628
−0.87981
31.04057
0.69053
−0.90516
31.04057


0.0365
−1.1132
31.04057
0.38786
−0.68377
31.04057


0.34273
−1.33882
31.04057
0.08991
−0.45562
31.04057


0.65623
−1.55615
31.04057
−0.20314
−0.22105
31.04057


0.978
−1.76419
31.04057
−0.49196
0.01977
31.04057


1.30789
−1.9626
31.04057
−0.77639
0.26516
31.04057


1.64336
−2.15069
31.04057
−1.0571
0.51477
31.04057


1.98389
−2.32899
31.04057
−1.33476
0.7676
31.04057


2.3175
−2.49326
31.04057
−1.60094
1.01451
31.04057


2.64282
−2.64519
31.04057
−1.8563
1.25483
31.04057


2.95936
−2.78613
31.04057
−2.10135
1.48771
31.04057


3.26626
−2.91694
31.04057
−2.33676
1.71265
31.04057


3.56286
−3.03879
31.04057
−2.56255
1.92947
31.04057


3.84898
−3.1527
31.04057
−2.77921
2.13785
31.04057


4.12428
−3.25883
31.04057
−2.98691
2.33744
31.04057


4.38859
−3.3582
31.04057
−3.17669
2.51945
31.04057


4.62959
−3.44659
31.04057
−3.3489
2.68372
31.04057


4.84692
−3.52466
31.04057
−3.50337
2.83024
31.04057


5.04059
−3.59294
31.04057
−3.64009
2.95902
31.04057


5.22244
−3.65581
31.04057
−3.75941
3.06972
31.04057


5.38045
−3.70955
31.04057
−3.86114
3.16267
31.04057


5.50196
−3.75045
31.04057
−3.94869
3.24125
31.04057


5.59948
−3.7829
31.04057
−4.02305
3.30665
31.04057


5.67249
−3.80706
31.04057
−4.08473
3.35972
31.04057


5.72792
−3.8216
31.04057
−4.1356
3.40045
31.04057


5.75749
−3.8118
31.04057
−4.17616
3.42986
31.04057


5.77169
−3.79777
31.04057
−4.20793
3.4498
31.04057


5.77676
−3.78898
31.04057
−4.23582
3.46382
31.04057


5.77879
−3.78425
31.04057
−4.25998
3.47058
31.04057


−4.24308
3.31139
32.22357
5.45566
−3.87838
32.22357


−4.25052
3.29432
32.22357
5.45633
−3.87602
32.22357


−4.24832
3.26931
32.22357
5.45735
−3.87128
32.22357


−4.2392
3.23956
32.22357
5.45819
−3.86165
32.22357


−4.22432
3.20525
32.22357
5.45566
−3.84272
32.22357


−4.20117
3.16115
32.22357
5.44112
−3.81653
32.22357


−4.16788
3.10605
32.22357
5.39397
−3.78999
32.22357


−4.12309
3.03913
32.22357
5.32688
−3.76042
32.22357


−4.06597
2.95953
32.22357
5.23765
−3.72087
32.22357


−3.99584
2.86624
32.22357
5.12611
−3.67119
32.22357


−3.91269
2.75808
32.22357
4.98144
−3.60629
32.22357


−3.81281
2.63133
32.22357
4.81464
−3.53058
32.22357


−3.69637
2.48633
32.22357
4.63736
−3.44895
32.22357


−3.56303
2.32291
32.22357
4.43828
−3.356
32.22357


−3.41312
2.14089
32.22357
4.21773
−3.25156
32.22357


−3.24565
1.9413
32.22357
3.97589
−3.13461
32.22357


−3.06042
1.72448
32.22357
3.72442
−3.01006
32.22357


−2.86573
1.49954
32.22357
3.46349
−2.87706
32.22357


−2.66124
1.26699
32.22357
3.19359
−2.73543
32.22357


−2.44644
1.02735
32.22357
2.91491
−2.58452
32.22357


−2.22117
0.78061
32.22357
2.62778
−2.4238
32.22357


−1.98474
0.52762
32.22357
2.33254
−2.25243
32.22357


−1.73648
0.26871
32.22357
2.02969
−2.06974
32.22357


−1.47588
0.0049
32.22357
1.71974
−1.87455
32.22357


−1.21072
−0.25451
32.22357
1.41402
−1.67327
32.22357


−0.94032
−0.50869
32.22357
1.11236
−1.46641
32.22357


−0.66417
−0.75712
32.22357
0.81475
−1.25415
32.22357


−0.38194
−0.99947
32.22357
0.52137
−1.03614
32.22357


−0.09329
−1.23522
32.22357
0.23238
−0.81221
32.22357


0.20229
−1.46388
32.22357
−0.05205
−0.58204
32.22357


0.50396
−1.68307
32.22357
−0.33192
−0.34561
32.22357


0.81221
−1.89145
32.22357
−0.60705
−0.10394
32.22357


1.1274
−2.08901
32.22357
−0.87796
0.14213
32.22357


1.44918
−2.27575
32.22357
−1.14548
0.39191
32.22357


1.77704
−2.45287
32.22357
−1.41014
0.64457
32.22357


2.09915
−2.61544
32.22357
−1.66397
0.89097
32.22357


2.41383
−2.76552
32.22357
−1.90784
1.13027
32.22357


2.72006
−2.9041
32.22357
−2.14224
1.3618
32.22357


3.01716
−3.03287
32.22357
−2.36769
1.58505
32.22357


3.30463
−3.15236
32.22357
−2.58435
1.79968
32.22357


3.58196
−3.26373
32.22357
−2.79256
2.00569
32.22357


3.84898
−3.36733
32.22357
−2.99248
2.20258
32.22357


4.10535
−3.46399
32.22357
−3.17568
2.38189
32.22357


4.33908
−3.55001
32.22357
−3.34214
2.54328
32.22357


4.54999
−3.62606
32.22357
−3.49154
2.6871
32.22357


4.73792
−3.69248
32.22357
−3.62387
2.81351
32.22357


4.91435
−3.754
32.22357
−3.73946
2.92218
32.22357


5.06747
−3.80673
32.22357
−3.83816
3.0131
32.22357


5.18526
−3.84695
32.22357
−3.92334
3.09
32.22357


5.27973
−3.87889
32.22357
−3.99567
3.15371
32.22357


5.35054
−3.90272
32.22357
−4.05583
3.20542
32.22357


5.40411
−3.91776
32.22357
−4.10518
3.24514
32.22357


5.43386
−3.90863
32.22357
−4.14456
3.27404
32.22357


5.44805
−3.89444
32.22357
−4.17548
3.29381
32.22357


5.45312
−3.88548
32.22357
−4.20252
3.30784
32.22357


5.45498
−3.88075
32.22357
−4.22585
3.31494
32.22357


−4.21756
3.25764
32.98407
5.13794
−3.95054
32.98407


−4.22483
3.24091
32.98407
5.13861
−3.94818
32.98407


−4.22247
3.21641
32.98407
5.13963
−3.94362
32.98407


−4.21351
3.18734
32.98407
5.14047
−3.93415
32.98407


−4.19864
3.15354
32.98407
5.13794
−3.91556
32.98407


−4.17582
3.11045
32.98407
5.12391
−3.8897
32.98407


−4.14304
3.05637
32.98407
5.07811
−3.86334
32.98407


−4.09893
2.99079
32.98407
5.01237
−3.83478
32.98407


−4.04265
2.91255
32.98407
4.92483
−3.79659
32.98407


−3.97387
2.82095
32.98407
4.81532
−3.74859
32.98407


−3.89207
2.71482
32.98407
4.67353
−3.68555
32.98407


−3.79388
2.59026
32.98407
4.51027
−3.61187
32.98407


−3.67964
2.4478
32.98407
4.33654
−3.5321
32.98407


−3.54883
2.28691
32.98407
4.14185
−3.44101
32.98407


−3.40214
2.10794
32.98407
3.92655
−3.33792
32.98407


−3.23855
1.91105
32.98407
3.69096
−3.22148
32.98407


−3.05806
1.69693
32.98407
3.44659
−3.09591
32.98407


−2.86844
1.47453
32.98407
3.19393
−2.96088
32.98407


−2.66952
1.24401
32.98407
2.933
−2.81605
32.98407


−2.46098
1.00606
32.98407
2.66395
−2.66107
32.98407


−2.24246
0.76067
32.98407
2.38696
−2.49579
32.98407


−2.01364
0.50818
32.98407
2.10287
−2.32003
32.98407


−1.77399
0.24928
32.98407
1.81219
−2.13278
32.98407


−1.52269
−0.01538
32.98407
1.51559
−1.93319
32.98407


−1.2675
−0.27665
32.98407
1.22322
−1.72735
32.98407


−1.00809
−0.53387
32.98407
0.93525
−1.51542
32.98407


−0.7436
−0.78653
32.98407
0.65166
−1.29708
32.98407


−0.47405
−1.03411
32.98407
0.37265
−1.07231
32.98407


−0.19959
−1.27494
32.98407
0.0987
−0.84162
32.98407


0.07994
−1.50782
32.98407
−0.17018
−0.60536
32.98407


0.36555
−1.73107
32.98407
−0.43484
−0.36436
32.98407


0.65792
−1.94367
32.98407
−0.69577
−0.11965
32.98407


0.95739
−2.14495
32.98407
−0.95384
0.12827
32.98407


1.26378
−2.33541
32.98407
−1.2097
0.37873
32.98407


1.57643
−2.51573
32.98407
−1.46388
0.63088
32.98407


1.88401
−2.68186
32.98407
−1.70842
0.87593
32.98407


2.18517
−2.83565
32.98407
−1.94367
1.11337
32.98407


2.47906
−2.97846
32.98407
−2.1703
1.34237
32.98407


2.76501
−3.11129
32.98407
−2.38865
1.56308
32.98407


3.04268
−3.23466
32.98407
−2.59888
1.77484
32.98407


3.31139
−3.34874
32.98407
−2.80118
1.97764
32.98407


3.57063
−3.45402
32.98407
−2.99553
2.17148
32.98407


3.82025
−3.55069
32.98407
−3.17399
2.34741
32.98407


4.0484
−3.63553
32.98407
−3.3364
2.50593
32.98407


4.25424
−3.70989
32.98407
−3.48208
2.64705
32.98407


4.43794
−3.77462
32.98407
−3.61153
2.77092
32.98407


4.61049
−3.8341
32.98407
−3.72442
2.87706
32.98407


4.76039
−3.8848
32.98407
−3.82109
2.96612
32.98407


4.87565
−3.9235
32.98407
−3.90441
3.04132
32.98407


4.96809
−3.95409
32.98407
−3.97522
3.10352
32.98407


5.03738
−3.97691
32.98407
−4.0342
3.15388
32.98407


5.09011
−3.98992
32.98407
−4.0827
3.19275
32.98407


5.11783
−3.97978
32.98407
−4.12123
3.2208
32.98407


5.13101
−3.96575
32.98407
−4.15132
3.24007
32.98407


5.13557
−3.9573
32.98407
−4.17785
3.25393
32.98407


5.13726
−3.95274
32.98407
−4.2005
3.26102
32.98407


−4.17058
3.25426
33.66007
4.8263
−4.01747
33.66007


−4.17768
3.23787
33.66007
4.82698
−4.01527
33.66007


−4.17548
3.21387
33.66007
4.82782
−4.01054
33.66007


−4.1667
3.18531
33.66007
4.82884
−4.00141
33.66007


−4.15216
3.15236
33.66007
4.8263
−3.98282
33.66007


−4.12985
3.11011
33.66007
4.81261
−3.9573
33.66007


−4.09774
3.05704
33.66007
4.76749
−3.93128
33.66007


−4.05482
2.99265
33.66007
4.70276
−3.90407
33.66007


−3.99989
2.91593
33.66007
4.61657
−3.86773
33.66007


−3.93263
2.82619
33.66007
4.50875
−3.82194
33.66007


−3.85269
2.72191
33.66007
4.36916
−3.7616
33.66007


−3.75704
2.59973
33.66007
4.20861
−3.69062
33.66007


−3.64584
2.45946
33.66007
4.03792
−3.61356
33.66007


−3.51858
2.30144
33.66007
3.84695
−3.52517
33.66007


−3.37611
2.12501
33.66007
3.63587
−3.42411
33.66007


−3.21759
1.93083
33.66007
3.40586
−3.30885
33.66007


−3.04285
1.71924
33.66007
3.16807
−3.18261
33.66007


−2.85965
1.4992
33.66007
2.92319
−3.04487
33.66007


−2.66783
1.27088
33.66007
2.67172
−2.89548
33.66007


−2.46723
1.03428
33.66007
2.41366
−2.73476
33.66007


−2.25767
0.78991
33.66007
2.14884
−2.56255
33.66007


−2.03865
0.53793
33.66007
1.87759
−2.37868
33.66007


−1.80965
0.27868
33.66007
1.60077
−2.18297
33.66007


−1.57052
0.01268
33.66007
1.31905
−1.97477
33.66007


−1.32834
−0.2508
33.66007
1.04189
−1.76098
33.66007


−1.08261
−0.51106
33.66007
0.76946
−1.54128
33.66007


−0.833
−0.76794
33.66007
0.50193
−1.3155
33.66007


−0.57899
−1.02076
33.66007
0.23914
−1.08363
33.66007


−0.32042
−1.26767
33.66007
−0.01876
−0.84585
33.66007


−0.05678
−1.50731
33.66007
−0.27243
−0.60299
33.66007


0.21277
−1.7385
33.66007
−0.52221
−0.35642
33.66007


0.48926
−1.95956
33.66007
−0.76929
−0.10715
33.66007


0.77301
−2.16996
33.66007
−1.01434
0.14416
33.66007


1.06419
−2.36972
33.66007
−1.25804
0.39681
33.66007


1.36248
−2.55951
33.66007
−1.50072
0.65031
33.66007


1.65637
−2.73459
33.66007
−1.73495
0.8957
33.66007


1.94485
−2.89683
33.66007
−1.96125
1.13264
33.66007


2.22691
−3.04775
33.66007
−2.17959
1.36096
33.66007


2.50205
−3.18785
33.66007
−2.39034
1.58015
33.66007


2.77059
−3.31713
33.66007
−2.59381
1.79039
33.66007


3.03152
−3.43509
33.66007
−2.78985
1.9915
33.66007


3.28435
−3.54156
33.66007
−2.97846
2.18331
33.66007


3.52872
−3.63756
33.66007
−3.15185
2.35738
33.66007


3.75248
−3.72054
33.66007
−3.3097
2.51388
33.66007


3.95511
−3.79219
33.66007
−3.45166
2.6533
33.66007


4.13577
−3.85421
33.66007
−3.57773
2.77532
33.66007


4.30578
−3.91083
33.66007
−3.68809
2.87993
33.66007


4.45332
−3.95883
33.66007
−3.78239
2.96764
33.66007


4.56706
−3.99516
33.66007
−3.86385
3.04149
33.66007


4.65815
−4.02389
33.66007
−3.93297
3.10284
33.66007


4.72642
−4.04552
33.66007
−3.99077
3.15219
33.66007


4.77848
−4.05718
33.66007
−4.03826
3.19021
33.66007


4.80619
−4.04654
33.66007
−4.07611
3.21776
33.66007


4.8192
−4.03268
33.66007
−4.10569
3.23669
33.66007


4.82377
−4.02423
33.66007
−4.13154
3.25021
33.66007


4.82546
−4.01983
33.66007
−4.15385
3.25731
33.66007


−4.04873
3.25764
34.3817
4.49287
−4.08845
34.3817


−4.056
3.24193
34.3817
4.49354
−4.08625
34.3817


−4.05431
3.21844
34.3817
4.49439
−4.08169
34.3817


−4.04603
3.19055
34.3817
4.4954
−4.07256
34.3817


−4.03234
3.1581
34.3817
4.49287
−4.05414
34.3817


−4.01122
3.1167
34.3817
4.47884
−4.02913
34.3817


−3.9808
3.06465
34.3817
4.43439
−4.00412
34.3817


−3.9399
3.0011
34.3817
4.37085
−3.97877
34.3817


−3.88768
2.92556
34.3817
4.28601
−3.9448
34.3817


−3.82363
2.837
34.3817
4.18022
−3.9017
34.3817


−3.74741
2.73425
34.3817
4.04316
−3.84458
34.3817


−3.65615
2.61359
34.3817
3.88599
−3.77715
34.3817


−3.55018
2.47517
34.3817
3.71901
−3.70296
34.3817


−3.42918
2.31868
34.3817
3.53244
−3.61728
34.3817


−3.29381
2.1441
34.3817
3.32693
−3.51841
34.3817


−3.1434
1.95161
34.3817
3.10335
−3.40434
34.3817


−2.97795
1.74155
34.3817
2.873
−3.27792
34.3817


−2.80489
1.52252
34.3817
2.63725
−3.1385
34.3817


−2.62406
1.29505
34.3817
2.39659
−2.98572
34.3817


−2.43512
1.05912
34.3817
2.15103
−2.81977
34.3817


−2.23807
0.81475
34.3817
1.90007
−2.64079
34.3817


−2.03239
0.56243
34.3817
1.64471
−2.44881
34.3817


−1.81793
0.30234
34.3817
1.38546
−2.24398
34.3817


−1.59401
0.03515
34.3817
1.1225
−2.02631
34.3817


−1.36755
−0.23018
34.3817
0.86427
−1.80289
34.3817


−1.13822
−0.49297
34.3817
0.61094
−1.57424
34.3817


−0.9055
−0.75306
34.3817
0.36251
−1.33983
34.3817


−0.66907
−1.00994
34.3817
0.11881
−1.10019
34.3817


−0.42875
−1.26209
34.3817
−0.12067
−0.85565
34.3817


−0.1837
−1.50849
34.3817
−0.35642
−0.60739
34.3817


0.06676
−1.74746
34.3817
−0.58913
−0.35659
34.3817


0.3238
−1.97798
34.3817
−0.81999
−0.10394
34.3817


0.58846
−2.19886
34.3817
−1.04949
0.1499
34.3817


0.86089
−2.4096
34.3817
−1.27815
0.40442
34.3817


1.14109
−2.61037
34.3817
−1.50647
0.65944
34.3817


1.41842
−2.79594
34.3817
−1.72718
0.90567
34.3817


1.69186
−2.96798
34.3817
−1.94063
1.14329
34.3817


1.96023
−3.12768
34.3817
−2.14731
1.3716
34.3817


2.22353
−3.27522
34.3817
−2.34707
1.5908
34.3817


2.4821
−3.41008
34.3817
−2.54007
1.8007
34.3817


2.73476
−3.53109
34.3817
−2.72648
2.0013
34.3817


2.98065
−3.6384
34.3817
−2.90612
2.19227
34.3817


3.21911
−3.73338
34.3817
−3.07158
2.36566
34.3817


3.43831
−3.81416
34.3817
−3.22232
2.52131
34.3817


3.63688
−3.88294
34.3817
−3.35803
2.65989
34.3817


3.81433
−3.94176
34.3817
−3.4787
2.78106
34.3817


3.98147
−3.99499
34.3817
−3.58449
2.885
34.3817


4.12664
−4.03961
34.3817
−3.67491
2.97203
34.3817


4.23852
−4.07307
34.3817
−3.75298
3.04555
34.3817


4.32826
−4.0996
34.3817
−3.8194
3.10639
34.3817


4.39552
−4.11921
34.3817
−3.875
3.15557
34.3817


4.44673
−4.1285
34.3817
−3.9208
3.19326
34.3817


4.47343
−4.11718
34.3817
−3.95714
3.22063
34.3817


4.48594
−4.10332
34.3817
−3.9857
3.23956
34.3817


4.4905
−4.09504
34.3817
−4.01088
3.25308
34.3817


4.49219
−4.09065
34.3817
−4.03234
3.26035
34.3817


−3.81957
3.24835
35.22839
4.10197
−4.17109
35.22839


−3.82734
3.23348
35.22839
4.10264
−4.16889
35.22839


−3.8265
3.21083
35.22839
4.10349
−4.1645
35.22839


−3.81974
3.18345
35.22839
4.10433
−4.15554
35.22839


−3.80808
3.15168
35.22839
4.10163
−4.13797
35.22839


−3.78932
3.11095
35.22839
4.08777
−4.1138
35.22839


−3.76228
3.05941
35.22839
4.04451
−4.09031
35.22839


−3.72544
2.99654
35.22839
3.98232
−4.06749
35.22839


−3.67795
2.9215
35.22839
3.89951
−4.03673
35.22839


−3.61964
2.83362
35.22839
3.79642
−3.99753
35.22839


−3.55018
2.73138
35.22839
3.66291
−3.9448
35.22839


−3.4672
2.61156
35.22839
3.50996
−3.88142
35.22839


−3.37054
2.47365
35.22839
3.34823
−3.81112
35.22839


−3.26018
2.318
35.22839
3.16807
−3.72865
35.22839


−3.13664
2.1441
35.22839
2.97068
−3.63215
35.22839


−2.99975
1.95229
35.22839
2.7569
−3.51943
35.22839


−2.849
1.74273
35.22839
2.53787
−3.39335
35.22839


−2.69133
1.52438
35.22839
2.31429
−3.25241
35.22839


−2.52672
1.29724
35.22839
2.08664
−3.09608
35.22839


−2.35485
1.06149
35.22839
1.8563
−2.92539
35.22839


−2.17571
0.81712
35.22839
1.62358
−2.74084
35.22839


−1.98862
0.5648
35.22839
1.3885
−2.54193
35.22839


−1.79343
0.30437
35.22839
1.15157
−2.32882
35.22839


−1.58961
0.0365
35.22839
0.91226
−2.10168
35.22839


−1.38343
−0.22967
35.22839
0.67803
−1.86863
35.22839


−1.17472
−0.49382
35.22839
0.4487
−1.63001
35.22839


−0.96313
−0.75594
35.22839
0.22477
−1.38681
35.22839


−0.74867
−1.01552
35.22839
0.00541
−1.13974
35.22839


−0.531
−1.27173
35.22839
−0.21041
−0.88962
35.22839


−0.30944
−1.52354
35.22839
−0.42351
−0.63713
35.22839


−0.08298
−1.76994
35.22839
−0.63476
−0.38312
35.22839


0.1499
−2.00958
35.22839
−0.845
−0.12827
35.22839


0.39022
−2.24128
35.22839
−1.05456
0.12709
35.22839


0.63899
−2.46368
35.22839
−1.26378
0.38295
35.22839


0.89638
−2.67679
35.22839
−1.473
0.63865
35.22839


1.15292
−2.87452
35.22839
−1.6753
0.88573
35.22839


1.40743
−3.05806
35.22839
−1.87134
1.12385
35.22839


1.65924
−3.2279
35.22839
−2.06096
1.35285
35.22839


1.90869
−3.38372
35.22839
−2.24466
1.57271
35.22839


2.15407
−3.52348
35.22839
−2.42228
1.78295
35.22839


2.39507
−3.64685
35.22839
−2.59398
1.98389
35.22839


2.63116
−3.75467
35.22839
−2.75977
2.17554
35.22839


2.86168
−3.84847
35.22839
−2.91238
2.34927
35.22839


3.07411
−3.92688
35.22839
−3.05163
2.50543
35.22839


3.26728
−3.99229
35.22839
−3.17703
2.64451
35.22839


3.44
−4.04687
35.22839
−3.28857
2.76636
35.22839


3.60291
−4.09555
35.22839
−3.38642
2.8708
35.22839


3.74453
−4.1356
35.22839
−3.47025
2.95835
35.22839


3.85388
−4.16517
35.22839
−3.54258
3.03237
35.22839


3.94159
−4.18833
35.22839
−3.60426
3.09388
35.22839


4.00733
−4.2054
35.22839
−3.65581
3.14357
35.22839


4.05752
−4.21182
35.22839
−3.69857
3.18176
35.22839


4.08321
−4.19948
35.22839
−3.7327
3.20948
35.22839


4.09538
−4.18562
35.22839
−3.75941
3.22875
35.22839


4.0996
−4.17751
35.22839
−3.78323
3.24277
35.22839


4.10129
−4.17329
35.22839
−3.80368
3.25055
35.22839


−3.61085
3.2377
35.94157
3.77293
−4.24021
35.94157


−3.6188
3.22334
35.94157
3.77343
−4.23818
35.94157


−3.61897
3.20137
35.94157
3.77428
−4.23396
35.94157


−3.61356
3.17467
35.94157
3.77495
−4.22534
35.94157


−3.60359
3.14323
35.94157
3.77225
−4.20827
35.94157


−3.58719
3.10284
35.94157
3.75839
−4.18512
35.94157


−3.56303
3.05163
35.94157
3.71597
−4.16298
35.94157


−3.5299
2.9891
35.94157
3.65496
−4.14253
35.94157


−3.48715
2.91441
35.94157
3.57401
−4.11464
35.94157


−3.43391
2.82669
35.94157
3.47312
−4.07848
35.94157


−3.37087
2.72479
35.94157
3.34265
−4.02964
35.94157


−3.2955
2.6048
35.94157
3.19359
−3.97015
35.94157


−3.20813
2.46656
35.94157
3.03625
−3.90322
35.94157


−3.10757
2.31091
35.94157
2.86151
−3.82329
35.94157


−2.99451
2.13734
35.94157
2.67037
−3.72831
35.94157


−2.86928
1.9457
35.94157
2.46419
−3.61576
35.94157


−2.73155
1.73614
35.94157
2.25328
−3.48833
35.94157


−2.58756
1.51779
35.94157
2.03966
−3.34536
35.94157


−2.43698
1.29065
35.94157
1.82469
−3.18683
35.94157


−2.27981
1.0549
35.94157
1.6082
−3.01259
35.94157


−2.11554
0.81052
35.94157
1.39003
−2.82264
35.94157


−1.94435
0.55804
35.94157
1.17168
−2.61781
35.94157


−1.76554
0.29744
35.94157
0.95316
−2.39828
35.94157


−1.57863
0.02907
35.94157
0.73447
−2.16472
35.94157


−1.38952
−0.23761
35.94157
0.5217
−1.92559
35.94157


−1.19804
−0.50278
35.94157
0.31434
−1.68138
35.94157


−1.00437
−0.76642
35.94157
0.11205
−1.43278
35.94157


−0.80799
−1.02803
35.94157
−0.08619
−1.18047
35.94157


−0.60925
−1.28727
35.94157
−0.28139
−0.92595
35.94157


−0.40712
−1.54331
35.94157
−0.47489
−0.67009
35.94157


−0.20077
−1.79495
35.94157
−0.66755
−0.41354
35.94157


0.01149
−2.04101
35.94157
−0.85987
−0.15666
35.94157


0.23052
−2.28015
35.94157
−1.05203
0.10005
35.94157


0.45782
−2.51134
35.94157
−1.24452
0.35693
35.94157


0.69391
−2.73374
35.94157
−1.43718
0.61347
35.94157


0.93035
−2.9406
35.94157
−1.62375
0.86106
35.94157


1.16661
−3.13275
35.94157
−1.80458
1.09985
35.94157


1.40236
−3.30987
35.94157
−1.97967
1.32935
35.94157


1.63846
−3.47177
35.94157
−2.14934
1.54956
35.94157


1.8737
−3.61626
35.94157
−2.31361
1.76047
35.94157


2.10591
−3.74251
35.94157
−2.47264
1.96209
35.94157


2.3344
−3.85134
35.94157
−2.62592
2.15424
35.94157


2.55832
−3.94497
35.94157
−2.76738
2.32882
35.94157


2.76569
−4.02169
35.94157
−2.89632
2.48582
35.94157


2.95463
−4.08439
35.94157
−3.01243
2.62575
35.94157


3.12397
−4.13577
35.94157
−3.11552
2.74862
35.94157


3.28384
−4.18022
35.94157
−3.20593
2.85424
35.94157


3.42293
−4.21638
35.94157
−3.2835
2.94263
35.94157


3.53041
−4.24291
35.94157
−3.35059
3.0175
35.94157


3.6166
−4.26319
35.94157
−3.40789
3.07969
35.94157


3.68133
−4.2779
35.94157
−3.45588
3.12988
35.94157


3.73051
−4.28145
35.94157
−3.49577
3.16858
35.94157


3.75501
−4.26826
35.94157
−3.52788
3.19697
35.94157


3.76667
−4.25474
35.94157
−3.55323
3.21658
35.94157


3.77073
−4.24663
35.94157
−3.5757
3.23111
35.94157


3.77225
−4.24241
35.94157
−3.59531
3.23922
35.94157









It is noted that the first column of TABLE I lists X coordinate values of the pressure side at each respective Z coordinate value of the third column, the second column lists Y coordinate values of the pressure side at each respective Z coordinate value of the third column, the fourth column lists X coordinate values of the suction side at each respective Z coordinate value of the sixth column, and the fifth column lists Y coordinate values of the suction side at each respective Z coordinate value of the sixth column. The Z coordinate values of the third column and the sixth column are equal to each other for each respective row. As set forth in TABLE I, at each respective Z coordinate value, the airfoil shape 110 of the airfoil 82 (e.g., a cross-sectional profile taken through line 6-6 of FIGS. 3, 4, and 5) is defined by multiple sets of Cartesian coordinate values of X, Y, and Z for both the suction side 62 (e.g., suction side profile 112) and the pressure side 64 (e.g., pressure side profile 114). For example, at each respective Z coordinate value, the suction side profile 112 of the suction side 62 may be defined by at least equal to or greater than 10, 15, 20, 25, 30, 35, 40, 45, 50, or 55 (e.g., 56) sets of Cartesian coordinate values of X, Y, and Z. Similarly, at each respective Z coordinate value, the pressure side profile 114 of the pressure side 64 may be defined by at least equal to or greater than 10, 15, 20, 25, 30, 35, 40, 45, 50, or 55 (e.g., 56) sets of Cartesian coordinate values of X, Y, and Z. Furthermore, in the Z direction along the Z axis 74, the airfoil profile of the airfoil 82 may be defined by multiple sets of Cartesian coordinate values of X, Y, and Z at multiple Cartesian coordinate values of Z, such as at least equal to or greater than 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, or more Cartesian coordinate values of Z.


As noted above, the Cartesian coordinate values of X, Y, and Z as set forth in TABLE I may be non-dimensional values convertible to dimensional distances. For example, the Cartesian coordinate values of X, Y, and Z may be multiplied by a scale factor F (e.g., F equal to 1, greater than 1, or less than 1) to obtain the desired dimensional distances. In certain embodiments, a nominal airfoil profile of the airfoil 82 may be partially or entirely (e.g., all or part of the suction side 62, all or part of the pressure side 64, or a combination thereof) defined by the Cartesian coordinate values of X, Y, and Z as set forth in TABLE I. The nominal airfoil profile of the airfoil 82 also may be covered by the coating 120, which increases the X and Y values as set forth in TABLE I.


For example, the airfoil 82 may include a first suction portion (e.g., 80) of the nominal airfoil profile substantially in accordance with Cartesian coordinate values of X, Y, and Z of the suction side 62 as set forth in TABLE I, wherein the X and Y values of the suction side 62 are coordinate values that couple together (e.g., in a smooth continuous and/or curved manner) to define suction side sections of the first suction portion (e.g., 80) of the nominal airfoil profile at each Z coordinate value, and the suction side sections of the first suction portion (e.g., 80) of the nominal airfoil profile are coupled together (e.g., in a smooth continuous and/or curved manner) to define the first suction portion (e.g., 80). In such an embodiment, the airfoil 82 has an airfoil length L along the Z axis 74, and the first suction portion (e.g., 80) comprises a first portion length l along the Z axis as illustrated and described above with reference to FIG. 4. The first portion length l is less than or equal to the airfoil length L. The first portion length l may include greater than or equal to 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, or more Cartesian coordinate values of Z (e.g., consecutive values of Z) in TABLE I. The first portion length l may be equal to or greater than approximately 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 99, or 100 percent of the airfoil length L.


By further example, the airfoil 82 may include a second suction portion (e.g., 80) of the nominal airfoil profile substantially in accordance with the Cartesian coordinate values of X, Y, and Z of the suction side 62 as set forth in TABLE I, wherein the X and Y values of the suction side 62 are coordinate values that couple together (e.g., in a smooth continuous and/or curved manner) to define suction side sections of the second suction portion (e.g., 80) of the nominal airfoil profile at each Z coordinate value, the suction side sections of the second suction portion (e.g., 80) of the nominal airfoil profile are coupled together (e.g., in a smooth continuous and/or curved manner) to define the second suction portion (e.g., 80). In such an embodiment, the second suction portion (e.g., 80) has a second portion length l along the Z axis, the second portion length l is less than or equal to the airfoil length L, and the first and second suction portions (e.g., 80, 102, 104, 106) are offset from one another along the Z axis as illustrated and described above with reference to FIGS. 4 and 5. Again, the second portion length l may include greater than or equal to 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, or more Cartesian coordinate values of Z (e.g., consecutive values of Z) in TABLE I. The second portion length l may be equal to or greater than approximately 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 99, or 100 percent of the airfoil length L. Furthermore, the first and second suction portions (e.g., 80, 102, 104, 106) may be separated by an offset distance of equal to or greater than approximately 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, or 90 percent of the airfoil length L.


By further example, the airfoil 82 may include a first pressure portion (e.g., 80) of the nominal airfoil profile substantially in accordance with the Cartesian coordinate values of X, Y, and Z of the pressure side 64 as set forth in TABLE I, wherein the X and Y values of the pressure side 64 are coordinate values that couple together (e.g., in a smooth continuous and/or curved manner) to define pressure side sections of the first pressure portion (e.g., 80) of the nominal airfoil profile at each Z coordinate value, the pressure side sections of the first pressure portion (e.g., 80) of the nominal airfoil profile are coupled together (e.g., in a smooth continuous and/or curved manner) to define the first pressure portion (e.g., 80). In such an embodiment, the first pressure portion (e.g., 80) comprises a second portion length l along the Z axis, and the second portion length l is less than or equal to the airfoil length L as illustrated and described above with reference to FIG. 4. Similar to the first suction portion (e.g., 80), the second portion length l of the first pressure portion (e.g., 80) may include greater than or equal to 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, or more Cartesian coordinate values of Z (e.g., consecutive values of Z) in TABLE I. The second portion length l of the first pressure portion (e.g., 80) may be equal to or greater than approximately 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 99, or 100 percent of the airfoil length L. In certain embodiments, the first suction portion (e.g., 80) and the first pressure portion (e.g., 80) at least partially overlap with one another along the Z axis.


For example, in certain embodiments, the first and second portion lengths l may be substantially the same, and the first and second portion lengths l may start at a common distance d relative to the base 60 of the airfoil 82 and extend toward the tip 68 of the airfoil 82. However, in some embodiments, the first and second portion lengths l may be different from one another, the first and second portion lengths l may start at different distances d relative to the base 60 of the airfoil 82, or a combination thereof. Additionally, the airfoil 82 may include a second pressure portion (e.g., 80) of the nominal airfoil profile substantially in accordance with the Cartesian coordinate values of X, Y, and Z of the pressure side 64 as set forth in TABLE I, wherein the first and second pressure portions (e.g., 80, 102, 104, 106) are offset from one another along the Z axis 74.


Technical effects of the disclosed embodiments include an airfoil having a first suction portion of a nominal airfoil profile substantially in accordance with Cartesian coordinate values of X, Y, and Z of a suction side as set forth in TABLE I, wherein the X and Y values of the suction side are coordinate values that couple together to define suction side sections of the first suction portion of the nominal airfoil profile at each Z coordinate value, the suction side sections of the first suction portion of the nominal airfoil profile are coupled together to define the first suction portion, the airfoil includes an airfoil length along a Z axis, the first suction portion comprises a first portion length along the Z axis, the first portion length is less than or equal to the airfoil length, and the Cartesian coordinate values of X, Y, and Z are non-dimensional values convertible to dimensional distances (e.g., instances in inches or mm).


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

Claims
  • 1. A system comprising: an airfoil comprising a first suction portion of a nominal airfoil profile substantially in accordance with Cartesian coordinate values of X, Y, and Z of a suction side as set forth in TABLE I to a maximum of three decimal places, wherein the X and Y values of the suction side are coordinate values that couple together to define suction side sections of the first suction portion of the nominal airfoil profile at each Z coordinate value, the suction side sections of the first suction portion of the nominal airfoil profile are coupled together to define the first suction portion, the airfoil comprises an airfoil length along a Z axis, the first suction portion comprises a first portion length along the Z axis, the first portion length is less than or equal to the airfoil length, and the Cartesian coordinate values of X, Y, and Z are non-dimensional values convertible to dimensional distances.
  • 2. The system of claim 1, wherein the airfoil comprises a second suction portion of the nominal airfoil profile substantially in accordance with the Cartesian coordinate values of X, Y, and Z of the suction side as set forth in TABLE I to the maximum of three decimal places, wherein the X and Y values of the suction side are coordinate values that couple together to define suction side sections of the second suction portion of the nominal airfoil profile at each Z coordinate value, the suction side sections of the second suction portion of the nominal airfoil profile are coupled together to define the second suction portion, the second suction portion comprises a second portion length along the Z axis, the second portion length is less than or equal to the airfoil length, and the first and second suction portions are offset from one another along the Z axis.
  • 3. The system of claim 1, wherein the airfoil comprises a first pressure portion of the nominal airfoil profile substantially in accordance with the Cartesian coordinate values of X, Y, and Z of a pressure side as set forth in TABLE I to the maximum of three decimal places, wherein the X and Y values of the pressure side are coordinate values that couple together to define pressure side sections of the first pressure portion of the nominal airfoil profile at each Z coordinate value, the pressure side sections of the first pressure portion of the nominal airfoil profile are coupled together to define the first pressure portion, the first pressure portion comprises a second portion length along the Z axis, and the second portion length is less than or equal to the airfoil length.
  • 4. The system of claim 3, wherein the first suction portion and the first pressure portion at least partially overlap with one another along the Z axis.
  • 5. The system of claim 4, wherein the first and second portion lengths are substantially the same, and the first and second portion lengths start at a common distance relative to a base of the airfoil and extend toward a tip of the airfoil.
  • 6. The system of claim 1, wherein the first portion length of the first suction portion starts at a distance relative to a base of the airfoil and extends toward a tip of the airfoil.
  • 7. The system of claim 1, wherein the first portion length includes greater than or equal to two consecutive Cartesian coordinate values of Z in TABLE I.
  • 8. The system of claim 1, wherein the first portion length is equal to or greater than approximately 10 percent of the airfoil length.
  • 9. The system of claim 1, wherein the first portion length is equal to or greater than approximately 25 percent of the airfoil length.
  • 10. The system of claim 1, wherein the first portion length is equal to or greater than approximately 50 percent of the airfoil length.
  • 11. The system of claim 1, wherein the first portion length is equal to or greater than approximately 75 percent of the airfoil length.
  • 12. The system of claim 1, wherein the first portion length is equal to approximately 100 percent of the airfoil length.
  • 13. The system of claim 1, wherein the airfoil comprises the nominal airfoil profile substantially in accordance with Cartesian coordinate values of X, Y, and Z as set forth in TABLE I to the maximum of three decimal places along an entirety of both the suction side and a pressure side of the airfoil.
  • 14. The system of claim 1, wherein the airfoil comprises a coating disposed over the first suction portion of the nominal airfoil profile substantially in accordance with the Cartesian coordinate values of X, Y, and Z of the suction side as set forth in TABLE I to the maximum of three decimal places.
  • 15. The system of claim 14, wherein the coating increases the X and Y values of the suction side in TABLE I to the maximum of three decimal places by no greater than approximately 3.5 mm along the first suction portion.
  • 16. The system of claim 1, comprising a plurality of compressor airfoils of a compressor stage, wherein each of the plurality of compressor airfoils comprises the airfoil having the first suction portion of the nominal airfoil profile substantially in accordance with the Cartesian coordinate values of X, Y, and Z of the suction side as set forth in TABLE I to the maximum of three decimal places.
  • 17. The system of claim 1, comprising a compressor having the airfoil.
  • 18. The system of claim 17, comprising a gas turbine engine having the compressor, a combustor, and a turbine.
  • 19. The system of claim 1, wherein the airfoil is a first stage compressor airfoil.
  • 20. The system of claim 19, wherein the airfoil is a compressor stator vane.
  • 21. The system of claim 1, wherein the airfoil comprises the first suction portion of the nominal airfoil profile substantially in accordance with Cartesian coordinate values of X, Y, and Z of the suction side as set forth in TABLE I to a maximum of four decimal places.
  • 22. The system of claim 1, wherein the airfoil comprises the first suction portion of the nominal airfoil profile substantially in accordance with Cartesian coordinate values of X, Y, and Z of the suction side as set forth in TABLE I to a maximum of five decimal places.
  • 23. A system comprising: an airfoil comprising a suction side of a nominal airfoil profile substantially in accordance with Cartesian coordinate values of X, Y, and Z of the suction side as set forth in TABLE I to a maximum of three decimal places, wherein the X and Y values of the suction side are coordinate values that couple together to define suction side sections of the suction side of the nominal airfoil profile at each Z coordinate value, the suction side sections of the suction side of the nominal airfoil profile are coupled together to define the suction side, and the Cartesian coordinate values of X, Y, and Z are non-dimensional values convertible to dimensional distances.
  • 24. A system comprising: an airfoil comprising a nominal airfoil profile substantially in accordance with Cartesian coordinate values of X, Y, and Z as set forth in TABLE I to a maximum of three decimal places, wherein the X and Y values are coordinate values that couple together to define airfoil sections of the nominal airfoil profile at each Z coordinate value, the airfoil sections of the nominal airfoil profile are coupled together to define an entirety of the airfoil, and the Cartesian coordinate values of X, Y, and Z are non-dimensional values convertible to dimensional distances.