Coulomb Crystals and Ground State Cooling of Single Ca + Ions in a Penning T rap

Imperial College London

Coulomb Crystals and Ground State Cooling of Single Ca+ Ions in a Penning Trap

Danny Segal1People involved in the workRichard Thompson(Alex Retzker, Martin Plenio)Dan CrickShailen BharadiaSean DonnellanSandeep MavadiaStephen RardinJoe GoodwinPosterGraham Stutter

Shamim PatelStefan ZeemanSarah WoodrowJuvid AryamanSupport: EPSRC, PICC (EU STREP)

Talk OutlinePenning Trap and Laser CoolingMotivation Quantum dynamics of small ion Coulomb crystals

Recent Trap ModificationsCoulomb CrystalsMotional Sideband Spectroscopy of a Single Ion In a Penning TrapGround state coolingHeating rate measurement

Ideal Trap Electrode Structure

Penning Trap: DC Potential +Axial B-FieldJoe GoodwinMotion in a Penning Trap

AxialMod. CyclotronMagnetron

Laser cooling in the Penning trapIn the Penning trap the ions are in an orbit around the trap centreMagnetron motion has negative total energyTo cool both cyclotron and magnetron motions the laser must be offset from trap centreTo the side where the ions go away from the laserMagnetron motion is always cooled less effectively than cyclotron

Tight localisation is difficult Axialisation, Rotating Wall require segmented ring electrode

Radial potential

ICCs in Penning Traps

NIST group (Bollinger, Biercuk)

Imperial Group

7Motivation : Degeneracy of zig-zag statesIf we keep y>x there are two degenerate statesMirror images of each otherDescribed by double-well potentialDepth and width of well adjustableIntrinsic well (no extra electrodes)Would like to look for evidence of tunnelingPenning Trap AdvantageIon-ion separations not affected by micromotionBig trap so heating rate should be very low

Double Well Potentials and Quantum Phase Transitions in Ion Traps, A. Retzker, R.C. Thompson, D.M.S and M.B. Plenio, PRL 101, 260504 (2008)8Quantum Information and SimulationQS - Exploit naturally occurring triangular lattice to study Hamiltonians of relevance to condensed matter systems (frustration) Biercuk, Bollinger

We concentrate on small to moderate sized ion Coulomb crystals

QI - Potential to use dipole force beams to generate exotic quantum states efficiently and/or demonstrate protocols of wider interest making use of natural geometry.Trap Modified to include vertical laser beams

In principle 1 skew laser beam would cool all motionsIn practice optical access means two beams are needed, axial and radialSuperconducting Magnet PT

21.2mmOriginally designed for use at GSI Darmstadt in an experiment with highly charged ionsB = 1.8T (up to 2.5T)Typical trap frequencies

~200 kHz~700 kHz~50kHz11Lasers2 x Violet Diode Lasers, Doppler Cooling

1 x 866nm diode laser for repumping (with rf sidebands)

1 x 854nm laser diode for quenching/repumping (J-state mixing)

1 x ultra-stable 729nm diode laser for spectroscopy, sideband cooling, manipulation

Trap Modification

Linear Chains

50m1429 Ion Chain

50mBSimulationsMatlab codeChoose a set of trap parametersInitialise ions in random positionsCalculate forces on each ionMove each ion in direction of forceIterateKeep going until a stable configuration is reachedRotate around magnetic field, convolve with a point spread function and project into a plane.

15 Ion ChainIncrease Trap Potential ExperimentSimulation

15 Ion ChainIncrease Trap Potential ExperimentSimulation

15 Ion ChainIncrease Trap Potential ExperimentSimulationSimulation gives zig-zagProjected image looks blurredMotion in a rotating frameIn lab frame x and y motions are coupled by vxBAxial motion harmonicRadial motion appears simpler in a frame rotating at c/2 In this frame the magnetic force is cancelled by the Coriolis forceRadial co-ordinates decouple

The ion appears to move in a 2D harmonic well in the radial planeCurvature of well is the same in both dimensions

Rotating frameLab frameTypical motion

At z=c /6 trap is sphericalLarger Ion Coulomb Crystalsr is the rotation frequency of the crystal in the lab frame.

r is the rotation frequency in the rotating frame

The number density of ions in the trap is given by

This has a maximum value when r = c/2

i.e. when the crystal is stationary in the rotating frame (r=0)

This can be achieved by using a rotating wall - but you can get close with good Doppler cooling

Rotation frequency of Coulomb crystalsThe stiffness of the effective potential in the radial plane is affected by the rotation of the ion crystal in that frame

The effective radial potential in the rotating frame is characterised by T

We can measure the radial size of a crystal and use this to infer the rotation frequency

T and r are related through

( )Linear zig-zag transitionsWe measure the axial voltage at which the linear to zig zag transition occurs

Comparison to the predicted transitions assuming r=0 shows that the density is not maximal for zig-zag chains

Zoo of crystal shapes

100 mFlatter crystals cool betterCompare crystal shape to simulationInfer a value of TPlot T against zCircles of different diameter correspond to different values of rTight axial confinement gives flat crystals that nearly rotate at c/2Weak axial confinement gives strings that dont rotate so fast

Controlling the shape of the Ion Coulomb Crystal

Stills from movie

Larger crystalsBest match is for 174 ions at

50 m

ExperimentSimulationSpectroscopy on the 729nm transtionAllows good measurement of temperature and heating rate

Provides a starting point for sub-Doppler sideband cooling

Sideband cooling to motional ground state in turn allows coherent manipulation of S-D qubit

Cooling 3D Ion Coulomb Crystal to motional GS would be a starting point for study of macroscopic quantum effects

Spectroscopy on the 729nm transitionLoad single ionWait for a start pulse triggered by mains cycleDoppler coolPrepare ion in one S1/2 sublevelInterrogate with 729nm pulseLook to see if ion is dark or brightRepeat 100 timesStep to new frequency

Axial SpectrumTemperature = 1.1 mK, n=130 near Doppler limit-Trap frequencies quite low so not in the Lamb-Dicke regimeBackground due to J-mixingRadial Spectrum (Trap voltage 5 V)

Temperature = 73 mK, n=200 -Zoom of one Cyclotron sideband at higher trap voltage (25V)

Temperature = 426 K, n=3000 -Axial Spectrum with Axialisation and High Trap Voltage

z

zPark laser on red sideband and pump ion down the ladder until it is in the ground motional state

|g>|e>Sideband Cooling35

z

zPark laser on red sideband and pump ion down the ladder until it is in the ground motional state

|g>|e>Sideband CoolingWhen the ion gets to the ground state the interaction switches off36Sideband coolingMotional ground state >99%

37Heating RateHeating rate < 0.3 phonon/s very low as expected (hoped!)Not surprising since ion-electrode distance is large

Scan of Carrier

Rabi Oscillations

(s)What next ?Sideband cool radial motion

Attempt sideband cooling for a small planar Ion Coulomb Crystal (ICC) - challenging for larger crystals

Control rotation of our ICCs new trap, rotating wall, stroboscopic imaging, single ion addressing

Multi-species crystals

Quantum crossovers/ Quantum information protocols

The team

42Effect of J-state MixingSwitch off the 854 repumper

Some ions get shelved in the D5/2 state by magnetic field J-mixing

These ions are not pushed by the laser beam.

Bright ions accumulate at one end of the trap

Trap Frequencies

B=1.85T

Trap frequencies measured by applying weak rf drive and seeing image of 3 ion crystal blur at COM freq.

Spectroscopy on the 729nm transtionAllows good measurement of temperature and heating rate

Provides a starting point for sub-Doppler sideband cooling

Sideband cooling to motional ground state in turn allows coherent manipulation of S-D qubit

Cooling 3D Ion Coulomb Crystal to motional GS would be a starting point for study of macroscopic quantum effects

Spectroscopy on the 729nm transtionLoad single ionWait for a start pulse triggered by mains cycleDoppler coolPrepare ion in one S1/2 sublevelInterrogate with 729nm pulseLook to see if ion is dark or brightRepeat 100 timesStep to new frequency

Laser cooling in the Penning trapIn the Penning trap the ions are in an orbit around the trap centreMagnetron motion has negative total energyTo cool both cyclotron and magnetron motions the laser must be offset from trap centreTo the side where the ions go away from the laserMagnetron motion is always cooled less effectively than cyclotron

Tight localisation is difficult Axialisation, Rotating Wall

Radial potential

Increase Trap Potential ExperimentSimulation






Increase Trap Potential ExperimentSimulationSingle Ions - Quantum JumpsIon cycles between states 1 and 2 high fluorescence rate

Occasionally ion makes quantum jump into state 3 (metastable state). Fluorescence switches off.

The absence of a large number of 1-2 photons accompanies the absorption of a single 1-3 photon

Use to read-out state of a single atom.Strong transitionWeak transition|1>|2>|3>59Quantum Jumps in a single Ca+ ion

Quantum jumps really happen, they are truly random, and they act as a measurement of the state of a single atom.|1>|2>|3>Quantum Jumps

z

zCarrierBlue SidebandRed Sideband

|g>|e>What if the ion is already in the motional ground state?Driving Carrier and Sideband TransitionsIf ion is in the motional ground state excitation on the red sideband does nothing!62Ion TrapsIon trap set of electrodes, apply electric potentials, attempt to trap an ion in 3DThis would be the equivalent of making a 3D potential bowl (a 2D one is shown)Impossible Earnshaws theoremLaplace Eq.Best you can do is make a 3D quadrupole

This is a 3D saddle point, (2D one shown ). Traps along z but not x and y

63Trap Loading

Photoionisation using pulsed 532nm YAG laser

Wait for required number of ions to come in then turn trap voltage off for 20sIons can continue to join the party for ~10 minutes. Most irritating

Or selectively eject ions one at a timeChart2-0.1648061688-0.16480616880.32845190.32845190.48978947240.48978947240.64769645820.64769645820.80108802030.80108802030.94892879680.94892879681.09024423971.09024423971.22413128381.22413128381.3497682291.3497682291.46642372551.46642372551.57346476451.57346476451.67036358531.67036358531.75670342381.75670342381.83218303761.83218303761.89661995941.89661995941.94995244191.94995244191.99224007311.99224007312.02366305542.02366305542.0445201562.0445201562.05522535142.05522535142.05630320342.05630320342.04838301652.04838301652.03219184262.03219184262.00854640812.00854640811.97834405411.97834405411.94255278891.94255278891.90220056161.90220056161.85836387611.85836387611.81215587041.81215587041.76471399261.76471399261.71718740891.71718740891.67072428331.67072428331.62645906821.62645906821.58549994611.58549994611.54891656131.54891656131.51772817581.51772817581.49289238111.49289238111.47529448821.47529448821.46573771591.46573771591.46493428141.46493428141.47349749571.47349749571.49193494671.49193494671.52064284861.52064284861.55990161731.55990161731.60987272251.60987272251.67059684921.67059684921.74199339071.74199339071.82386127771.82386127771.91588113441.91588113442.01761873822.01761873822.12852974482.12852974482.24796562612.24796562612.37518075672.37518075672.50934056972.50934056972.64953069282.64953069282.79476696352.79476696352.94400621362.94400621363.0961577043.0961577043.25009508363.25009508363.40466874093.40466874093.55871841253.55871841253.71108590893.71108590893.86062781783.86062781784.00622804534.00622804534.14681005644.14681005644.28134868034.28134868034.40888134974.40888134974.52851865224.52851865224.63945407484.63945407484.7409728374.7409728374.83245971294.83245971294.91340575754.91340575754.98341386344.98341386345.04220308455.04220308455.08961168245.08961168245.12559885895.12559885895.15024515745.15024515745.16375152785.16375152785.16643706645.16643706645.15873545355.15873545355.14119013085.14119013085.11444826935.11444826935.07925359555.07925359555.03643815435.03643815434.98691309994.98691309994.93165861524.93165861524.87171307254.87171307254.8081615524.8081615524.74212384814.74212384814.67474209264.67474209264.60716813314.60716813314.54055080414.54055080414.47602323294.47602323294.41469031784.41469031784.35761651884.35761651884.30581409374.30581409374.26023190994.26023190994.22174495454.22174495454.19114465994.19114465994.16913014894.16913014894.15630049784.15630049784.15314810254.15314810254.1600532194.1600532194.1772797414.1772797414.20497225864.20497225864.24315443274.24315443274.29172870134.29172870134.35047732184.35047732184.41906473754.41906473754.49704124334.49704124334.58384790754.58384790754.67882269924.67882269924.78120775084.78120775084.89015767684.89015767685.00474885775.00474885775.12398958585.12398958585.24683096155.24683096155.37217842055.37217842055.49890376465.49890376465.6258575635.6258575635.75188178915.75188178915.87582255115.87582255115.99654277965.99654277966.11293472866.11293472866.22393215556.22393215556.32852204366.32852204366.42575573996.42575573996.51475938386.51475938386.59474351286.59474351286.66501173936.66501173936.72496840276.72496840276.7741251136.7741251136.81210611266.81210611266.83865239916.83865239916.85362456216.85362456216.85700430376.85700430376.84889462476.84889462476.82951867696.82951867696.79921729136.79921729136.75844521116.75844521116.70776607076.70776607076.64784617626.64784617626.57944715486.57944715486.50341755576.50341755576.42068349416.42068349416.33223844086.33223844086.23913227156.23913227156.14245969476.14245969476.04334818686.04334818685.94294556695.94294556695.8424073485.8424073485.74288400415.74288400415.6455082945.6455082945.55138277995.55138277995.46156768025.46156768025.37706918875.37706918875.29882839035.29882839035.22771089355.22771089355.16449729555.16449729555.10987458475.10987458475.06442857425.06442857425.02863745095.02863745095.00286651045.00286651044.98736413624.98736413624.98225906784.98225906784.9875589864.9875589865.0031504345.0031504345.02880007225.02880007225.06415725445.06415725445.10875789755.10875789755.16202960015.16202960015.22329795625.22329795625.29179399195.29179399195.36666264535.36666264535.44697219495.44697219495.5317245335.5317245335.61986617125.61986617125.71029985635.71029985635.80189666925.80189666925.89350847315.89350847315.98398057365.98398057366.07216445286.07216445286.15693043456.15693043456.23718014396.23718014396.31185862216.31185862216.37996596386.37996596386.44056834846.44056834846.49280834486.49280834486.53591437476.53591437476.56920923066.56920923066.59211755626.59211755626.60417220416.60417220416.60501940326.60501940326.59442267756.59442267756.57226547326.57226547326.53855246646.53855246646.49340953536.49340953536.43708239796.43708239796.36993393126.36993393126.29244019956.29244019956.2051852376.2051852376.10885464196.10885464196.00422805186.00422805185.89217058485.89217058485.77362333855.77362333855.64959305345.64959305345.5211410545.5211410545.38937158865.38937158865.25541969725.25541969725.1204387415.1204387414.98558773054.98558773054.85201859164.85201859164.7208635114.7208635114.5932224994.5932224994.47015130754.47015130754.35264983614.35264983614.24165115414.24165115414.13801125844.13801125844.04249968214.04249968213.95579105513.95579105513.87845771083.87845771083.81096342043.81096342043.75365832313.75365832313.70677510893.70677510893.67042649543.67042649543.64460402643.64460402643.6291782063.6291782063.62389996643.62389996643.62840345353.62840345353.64221009863.64221009863.66473393313.66473393313.69528808623.69528808623.73309239433.73309239433.77728203913.77728203913.82691711823.82691711823.88099304333.88099304333.93845165113.93845165113.99819290593.99819290594.0590870624.0590870624.11998715584.11998715584.17974168674.17974168674.23720734854.23720734854.29126167184.29126167184.34081543684.34081543684.38482471984.38482471984.4223024424.4223024424.45232929264.45232929264.47406390494.47406390494.48675217534.48675217534.48973562124.48973562124.48245868584.48245868584.46447490974.46447490974.43545190144.43545190144.39517505164.39517505164.34354995044.34354995044.2806034814.2806034814.20648357824.20648357824.12145765274.12145765274.02590970124.02590970123.92033613153.92033613153.80534035063.80534035063.68162617393.68162617393.54999012913.54999012913.41131273963.41131273963.26654888163.26654888163.11671732483.11671732482.96288956732.96288956732.80617809152.80617809152.64772416862.64772416862.48868534572.48868534572.33022275472.33022275472.17348838162.17348838162.01961243652.01961243651.86969096481.86969096481.72477383361.72477383361.58585322791.58585322791.45385278251.45385278251.32961746851.32961746851.21390434741.21390434741.10737429271.10737429271.01058477261.01058477260.92398377050.92398377050.84790491250.84790491250.78256385490.78256385490.72805597060.72805597060.68435536110.68435536110.65131520460.65131520460.62866943590.62866943590.616035740.616035740.61291982660.61291982660.61872093790.61872093790.63273852920.63273852920.65418004940.65418004940.68216973430.68216973430.71575831720.71575831720.75393354870.75393354870.79563141130.79563141130.83974790330.83974790330.88515126390.88515126390.93069450410.93069450410.97522810480.97522810481.01761274411.01761274411.05673191131.05673191131.09150427011.09150427011.12089563441.12089563441.1439304251.1439304251.15970248041.15970248041.16738510371.16738510371.16624023351.16624023351.15562663911.15562663911.13500704871.13500704871.10395413331.10395413331.06215527841.06215527841.00941609371.00941609370.9456626190.9456626190.87094220490.87094220490.78542305650.78542305650.6893924460.6893924460.58325361410.58325361410.4675213940.4675213940.34281660530.34281660530.20985928210.20985928210.06946080630.0694608063-0.0774849635-0.0774849635-0.230011473-0.230011473-0.3870900535-0.3870900535-0.547641187-0.547641187-0.7105463323-0.7105463323-0.8746601804-0.8746601804-1.038823205-1.038823205-1.2018743698-1.2018743698-1.3626638527-1.3626638527-1.5200656457-1.5200656457-1.6729898938-1.6729898938-1.820394835-1.820394835-1.9612982109-1.9612982109-2.0947880221-2.0947880221-2.2200325096-2.2200325096-2.336289253-2.336289253-2.442913284-2.442913284-2.5393641274-2.5393641274-2.6252116908-2.6252116908-2.700140939-2.700140939-2.7639553008-2.7639553008-2.8165787714-2.8165787714-2.8580566869-2.8580566869-2.8885551625-2.8885551625-2.9083592004-2.9083592004-2.9178694883-2.9178694883-2.9175979243-2.9175979243-2.9081619165-2.9081619165-2.8902775211-2.8902775211-2.8647514935-2.8647514935-2.8324723415-2.8324723415-2.7944004776-2.7944004776-2.7515575795-2.7515575795-2.7050152765-2.7050152765-2.6558832856-2.6558832856-2.605297128-2.605297128-2.5544055628-2.5544055628-2.5043578737-2.5043578737-2.4562911513-2.4562911513-2.4113177096-2.4113177096-2.3705127754-2.3705127754-2.3349025873-2.3349025873-2.3054530338-2.3054530338-2.2830589567-2.2830589567-2.268534238-2.268534238-2.2626027777-2.2626027777-2.2658904643-2.2658904643-2.2789182243-2.2789182243-2.3020962289-2.3020962289-2.3357193202-2.3357193202-2.3799637088-2.3799637088-2.4348849784-2.4348849784-2.5004174187-2.5004174187-2.5763746959-2.5763746959-2.6624518511-2.6624518511-2.7582286065-2.7582286065-2.863173942-2.863173942-2.9766518914-2.9766518914-3.0979284961-3.0979284961-3.2261798377-3.2261798377-3.3605010621-3.3605010621-3.4999162957-3.4999162957-3.6433893441-3.6433893441-3.7898350557-3.7898350557-3.9381312251-3.9381312251-4.0871309048-4.0871309048-4.23567499-4.23567499-4.3826049381-4.3826049381-4.5267754818-4.5267754818-4.6670671969-4.6670671969-4.8023987858-4.8023987858-4.9317389414-4.9317389414-5.0541176607-5.0541176607-5.1686368843-5.1686368843-5.2744803428-5.2744803428-5.3709225039-5.3709225039-5.4573365198-5.4573365198-5.533201088-5.533201088-5.5981061512-5.5981061512-5.6517573703-5.6517573703-5.6939793256-5.6939793256-5.7247174065-5.7247174065-5.7440383728-5.7440383728-5.7521295781-5.7521295781-5.7492968667-5.7492968667-5.7359611648-5.7359611648-5.7126538055-5.7126538055-5.6800106374-5.6800106374-5.6387649831-5.6387649831-5.5897395244-5.5897395244-5.5338372037-5.5338372037-5.4720312417-5.4720312417-5.4053543821-5.4053543821-5.3348874806-5.3348874806-5.261747565-5.261747565-5.1870754968-5.1870754968-5.1120233717-5.1120233717-5.037741796-5.037741796-4.965367181-4.965367181-4.8960091932-4.8960091932-4.8307385003-4.8307385003-4.7705749477-4.7705749477-4.7164762944-4.7164762944-4.6693276341-4.6693276341-4.6299316172-4.6299316172-4.5989995814-4.5989995814-4.5771436884-4.5771436884-4.5648701539-4.5648701539-4.5625736456-4.5625736456-4.5705329095-4.5705329095-4.5889076744-4.5889076744-4.6177368678-4.6177368678-4.656938163-4.656938163-4.7063088624-4.7063088624-4.7655281071-4.7655281071-4.8341603891-4.8341603891-4.9116603266-4.9116603266-4.99737865-4.99737865-5.0905693335-5.0905693335-5.1903977922-5.1903977922-5.2959500564-5.2959500564-5.4062428196-5.4062428196-5.5202342519-5.5202342519-5.6368354585-5.6368354585-5.7549224566-5.7549224566-5.8733485405-5.8733485405-5.9909568963-5.9909568963-6.1065933301-6.1065933301-6.2191189663-6.2191189663-6.3274227795-6.3274227795-6.4304338189-6.4304338189-6.5271329928-6.5271329928-6.6165642821-6.6165642821-6.6978452597-6.6978452597-6.7701768004-6.7701768004-6.8328518732-6.8328518732-6.8852633202-6.8852633202-6.9269105364-6.9269105364-6.9574049758-6.9574049758-6.9764744242-6.9764744242-6.9839659913-6.9839659913-6.9798477892-6.9798477892-6.9642092784-6.9642092784-6.9372602778-6.9372602778-6.8993286504-6.8993286504-6.8508566881-6.8508566881-6.792396238-6.792396238-6.724602622-6.724602622-6.6482274172-6.6482274172-6.564110177-6.564110177-6.4731691835-6.4731691835-6.376391334-6.376391334-6.2748212714-6.2748212714-6.1695498802-6.1695498802-6.0617022731-6.0617022731-5.9524254012-5.9524254012-5.8428754254-5.8428754254-5.7342049851-5.7342049851-5.6275505082-5.6275505082-5.5240196995-5.5240196995-5.4246793458-5.4246793458-5.3305435728-5.3305435728-5.2425626831-5.2425626831-5.1616126968-5.1616126968-5.088485712-5.088485712-5.0238811897-5.0238811897-4.9683982598-4.9683982598-4.9225291334-4.9225291334-4.8866536926-4.8866536926-4.8610353189-4.8610353189-4.8458180054-4.8458180054-4.8410247844-4.8410247844-4.8465574879-4.8465574879-4.8621978445-4.8621978445-4.8876098992-4.8876098992-4.92234373-4.92234373-4.965840421-4.965840421-5.0174382365-5.0174382365-5.0763799279-5.0763799279-5.1418210938-5.1418210938-5.2128395004-5.2128395004-5.2884452602-5.2884452602-5.3675917556-5.3675917556-5.4491871894-5.4491871894-5.5321066323-5.5321066323-5.6152044369-5.6152044369-5.6973268794-5.6973268794-5.7773248925-5.7773248925-5.8540667457-5.8540667457-5.9264505371-5.9264505371-5.9934163557-5.9934163557-6.053957983-6.053957983-6.1071340027-6.1071340027-6.1520781981-6.1520781981-6.1880091214-6.1880091214-6.2142387296-6.2142387296-6.2301799928-6.2301799928-6.2353533898-6.2353533898-6.2293922206-6.2293922206-6.2120466763-6.2120466763-6.1831866223-6.1831866223-6.1428030639-6.1428030639-6.0910082782-6.0910082782-6.0280346104-6.0280346104-5.9542319483-5.9542319483-5.8700639031-5.8700639031-5.7761027373-5.7761027373-5.673023097-5.673023097-5.5615946167-5.5615946167-5.4426734786-5.4426734786-5.3171930188-5.3171930188-5.1861534843-5.1861534843-5.0506110541-5.0506110541-4.9116662436-4.9116662436-4.7704518221-4.7704518221-4.6281203753-4.6281203753-4.4858316501-4.4858316501-4.3447398204-4.3447398204-4.205980816-4.205980816-4.0706598521-4.0706598521-3.9398392974-3.9398392974-3.8145270156-3.8145270156-3.695665307-3.695665307-3.5841205728-3.5841205728-3.4806738164-3.4806738164-3.3860120854-3.3860120854-3.3007209489-3.3007209489-3.2252780936-3.2252780936-3.160048108-3.160048108-3.1052785133-3.1052785133-3.0610970841-3.0610970841-3.0275104884-3.0275104884-3.0044042623-3.0044042623-2.9915441191-2.9915441191-2.988578579-2.988578579-2.9950428898-2.9950428898-3.0103641957-3.0103641957-3.0338678978-3.0338678978-3.0647851347-3.0647851347-3.1022613031-3.1022613031-3.1453655221-3.1453655221-3.1931009386-3.1931009386-3.2444157597-3.2444157597-3.2982148909-3.2982148909-3.3533720512-3.3533720512-3.4087422324-3.4087422324-3.4631743648-3.4631743648-3.5155240505-3.5155240505-3.564666223-3.564666223-3.6095075947-3.6095075947-3.6489987545-3.6489987545-3.6821457822-3.6821457822-3.7080212529-3.7080212529-3.725774508-3.725774508-3.7346410822-3.7346410822-3.7339511806-3.7339511806-3.7231371136-3.7231371136-3.7017396079-3.7017396079-3.6694129223-3.6694129223-3.6259287152-3.6259287152-3.5711786172-3.5711786172-3.5051754844-3.5051754844-3.4280533151-3.4280533151-3.3400658334-3.3400658334-3.2415837542-3.2415837542-3.1330907595-3.1330907595

Sheet1LorentzianxL(x)L(x)L(x)-40.05882352940.07547169810.0470588235-3.950.06023189280.07750435960.0480711453-3.90.06169031460.07961783440.0491159136-3.850.06320113760.08181632240.0501945037-3.80.06476683940.08410428930.0513083633-3.750.06639004150.08648648650.0524590164-3.70.06807351940.08896797150.0536480687-3.650.0698202130.09155413140.0548772122-3.60.07163323780.09425070690.0561482313-3.550.07351589780.09706381950.0574630082-3.50.07547169810.10.0588235294-3.450.07750435960.103066220.0602318928-3.40.07961783440.10626992560.0616903146-3.350.08181632240.10961907370.0632011376-3.30.08410428930.11312217190.0647668394-3.250.08648648650.11678832120.0663900415-3.20.08896797150.12062726180.0680735194-3.150.09155413140.12464942350.069820213-3.10.09425070690.12886597940.0716332378-3.050.09706381950.13328890370.0735158978-30.10.13793103450.0754716981-2.950.103066220.14280614070.0775043596-2.90.10626992560.14792899410.0796178344-2.850.10961907370.15331544650.0818163224-2.80.11312217190.15898251190.0841042893-2.750.11678832120.16494845360.0864864865-2.70.12062726180.17123287670.0889679715-2.650.12464942350.17785682530.0915541314-2.60.12886597940.18484288350.0942507069-2.550.13328890370.19221528110.0970638195-2.50.13793103450.20.1-2.450.14280614070.20822488290.10306622-2.40.14792899410.21691973970.1062699256-2.350.15331544650.226116450.1096190737-2.30.15898251190.23584905660.1131221719-2.250.16494845360.24615384620.1167883212-2.20.17123287670.25706940870.1206272618-2.150.17785682530.26863666890.1246494235-2.10.18484288350.28089887640.1288659794-2.050.19221528110.2939015430.1332889037-20.20.30769230770.1379310345-1.950.20822488290.32232070910.1428061407-1.90.21691973970.33783783780.1479289941-1.850.226116450.3542958370.1533154465-1.80.23584905660.37174721190.1589825119-1.750.24615384620.39024390240.1649484536-1.70.25706940870.40983606560.1712328767-1.650.26863666890.43057050590.1778568253-1.60.28089887640.45248868780.1848428835-1.550.2939015430.47562425680.1922152811-1.50.30769230770.50.2-1.450.32232070910.52562417870.2082248829-1.40.33783783780.55248618780.2169197397-1.350.3542958370.58055152390.22611645-1.30.37174721190.60975609760.2358490566-1.250.39024390240.640.2461538462-1.20.40983606560.67114093960.2570694087-1.150.43057050590.70298769770.2686366689-1.10.45248868780.73529411760.2808988764-1.050.47562425680.76775431860.293901543-10.50.80.3076923077-0.950.52562417870.83160083160.3223207091-0.90.55248618780.86206896550.3378378378-0.850.58055152390.89086859690.354295837-0.80.60975609760.91743119270.3717472119-0.750.640.94117647060.3902439024-0.70.67114093960.96153846150.4098360656-0.650.70298769770.977995110.4305705059-0.60.73529411760.99009900990.4524886878-0.550.76775431860.99750623440.4756242568-0.50.810.5-0.450.83160083160.99750623440.5256241787-0.40.86206896550.99009900990.5524861878-0.350.89086859690.977995110.5805515239-0.30.91743119270.96153846150.6097560976-0.250.94117647060.94117647060.64-0.20.96153846150.91743119270.6711409396-0.150.977995110.89086859690.7029876977-0.10.99009900990.86206896550.7352941176-0.050.99750623440.83160083160.7677543186-010.80.80.050.99750623440.76775431860.83160083160.10.99009900990.73529411760.86206896550.150.977995110.70298769770.89086859690.20.96153846150.67114093960.91743119270.250.94117647060.640.94117647060.30.91743119270.60975609760.96153846150.350.89086859690.58055152390.977995110.40.86206896550.55248618780.99009900990.450.83160083160.52562417870.99750623440.50.80.510.550.76775431860.47562425680.99750623440.60.73529411760.45248868780.99009900990.650.70298769770.43057050590.977995110.70.67114093960.40983606560.96153846150.750.640.39024390240.94117647060.80.60975609760.37174721190.91743119270.850.58055152390.3542958370.89086859690.90.55248618780.33783783780.86206896550.950.52562417870.32232070910.831600831610.50.30769230770.81.050.47562425680.2939015430.76775431861.10.45248868780.28089887640.73529411761.150.43057050590.26863666890.70298769771.20.40983606560.25706940870.67114093961.250.39024390240.24615384620.641.30.37174721190.23584905660.60975609761.350.3542958370.226116450.58055152391.40.33783783780.21691973970.55248618781.450.32232070910.20822488290.52562417871.50.30769230770.20.51.550.2939015430.19221528110.47562425681.60.28089887640.18484288350.45248868781.650.26863666890.17785682530.43057050591.70.25706940870.17123287670.40983606561.750.24615384620.16494845360.39024390241.80.23584905660.15898251190.37174721191.850.226116450.15331544650.3542958371.90.21691973970.14792899410.33783783781.950.20822488290.14280614070.322320709120.20.13793103450.30769230772.050.19221528110.13328890370.2939015432.10.18484288350.12886597940.28089887642.150.17785682530.12464942350.26863666892.20.17123287670.12062726180.25706940872.250.16494845360.11678832120.24615384622.30.15898251190.11312217190.23584905662.350.15331544650.10961907370.226116452.40.14792899410.10626992560.21691973972.450.14280614070.103066220.20822488292.50.13793103450.10.22.550.13328890370.09706381950.19221528112.60.12886597940.09425070690.18484288352.650.12464942350.09155413140.17785682532.70.12062726180.08896797150.17123287672.750.11678832120.08648648650.16494845362.80.11312217190.08410428930.15898251192.850.10961907370.08181632240.15331544652.90.10626992560.07961783440.14792899412.950.103066220.07750435960.142806140730.10.07547169810.13793103453.050.09706381950.07351589780.13328890373.10.09425070690.07163323780.12886597943.150.09155413140.0698202130.12464942353.20.08896797150.06807351940.12062726183.250.08648648650.06639004150.11678832123.30.08410428930.06476683940.11312217193.350.08181632240.06320113760.10961907373.40.07961783440.06169031460.10626992563.450.07750435960.06023189280.103066223.50.07547169810.05882352940.13.550.07351589780.05746300820.09706381953.60.07163323780.05614823130.09425070693.650.0698202130.05487721220.09155413143.70.06807351940.05364806870.08896797153.750.06639004150.05245901640.08648648653.80.06476683940.05130836330.08410428933.850.06320113760.05019450370.08181632243.90.06169031460.04911591360.07961783443.950.06023189280.04807114530.077504359640.05882352940.04705882350.0754716981

Sheet1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

Lorentzian L(x)

Sheet20.05882352940.07547169810.04705882350.06023189280.07750435960.04807114530.06169031460.07961783440.04911591360.06320113760.08181632240.05019450370.06476683940.08410428930.05130836330.06639004150.08648648650.05245901640.06807351940.08896797150.05364806870.0698202130.09155413140.05487721220.07163323780.09425070690.05614823130.07351589780.09706381950.05746300820.07547169810.10.05882352940.07750435960.103066220.06023189280.07961783440.10626992560.06169031460.08181632240.10961907370.06320113760.08410428930.11312217190.06476683940.08648648650.11678832120.06639004150.08896797150.12062726180.06807351940.09155413140.12464942350.0698202130.09425070690.12886597940.07163323780.09706381950.13328890370.07351589780.10.13793103450.07547169810.103066220.14280614070.07750435960.10626992560.14792899410.07961783440.10961907370.15331544650.08181632240.11312217190.15898251190.08410428930.11678832120.16494845360.08648648650.12062726180.17123287670.08896797150.12464942350.17785682530.09155413140.12886597940.18484288350.09425070690.13328890370.19221528110.09706381950.13793103450.20.10.14280614070.20822488290.103066220.14792899410.21691973970.10626992560.15331544650.226116450.10961907370.15898251190.23584905660.11312217190.16494845360.24615384620.11678832120.17123287670.25706940870.12062726180.17785682530.26863666890.12464942350.18484288350.28089887640.12886597940.19221528110.2939015430.13328890370.20.30769230770.13793103450.20822488290.32232070910.14280614070.21691973970.33783783780.14792899410.226116450.3542958370.15331544650.23584905660.37174721190.15898251190.24615384620.39024390240.16494845360.25706940870.40983606560.17123287670.26863666890.43057050590.17785682530.28089887640.45248868780.18484288350.2939015430.47562425680.19221528110.30769230770.50.20.32232070910.52562417870.20822488290.33783783780.55248618780.21691973970.3542958370.58055152390.226116450.37174721190.60975609760.23584905660.39024390240.640.24615384620.40983606560.67114093960.25706940870.43057050590.70298769770.26863666890.45248868780.73529411760.28089887640.47562425680.76775431860.2939015430.50.80.30769230770.52562417870.83160083160.32232070910.55248618780.86206896550.33783783780.58055152390.89086859690.3542958370.60975609760.91743119270.37174721190.640.94117647060.39024390240.67114093960.96153846150.40983606560.70298769770.977995110.43057050590.73529411760.99009900990.45248868780.76775431860.99750623440.47562425680.810.50.83160083160.99750623440.52562417870.86206896550.99009900990.55248618780.89086859690.977995110.58055152390.91743119270.96153846150.60975609760.94117647060.94117647060.640.96153846150.91743119270.67114093960.977995110.89086859690.70298769770.99009900990.86206896550.73529411760.99750623440.83160083160.767754318610.80.80.99750623440.76775431860.83160083160.99009900990.73529411760.86206896550.977995110.70298769770.89086859690.96153846150.67114093960.91743119270.94117647060.640.94117647060.91743119270.60975609760.96153846150.89086859690.58055152390.977995110.86206896550.55248618780.99009900990.83160083160.52562417870.99750623440.80.510.76775431860.47562425680.99750623440.73529411760.45248868780.99009900990.70298769770.43057050590.977995110.67114093960.40983606560.96153846150.640.39024390240.94117647060.60975609760.37174721190.91743119270.58055152390.3542958370.89086859690.55248618780.33783783780.86206896550.52562417870.32232070910.83160083160.50.30769230770.80.47562425680.2939015430.76775431860.45248868780.28089887640.73529411760.43057050590.26863666890.70298769770.40983606560.25706940870.67114093960.39024390240.24615384620.640.37174721190.23584905660.60975609760.3542958370.226116450.58055152390.33783783780.21691973970.55248618780.32232070910.20822488290.52562417870.30769230770.20.50.2939015430.19221528110.47562425680.28089887640.18484288350.45248868780.26863666890.17785682530.43057050590.25706940870.17123287670.40983606560.24615384620.16494845360.39024390240.23584905660.15898251190.37174721190.226116450.15331544650.3542958370.21691973970.14792899410.33783783780.20822488290.14280614070.32232070910.20.13793103450.30769230770.19221528110.13328890370.2939015430.18484288350.12886597940.28089887640.17785682530.12464942350.26863666890.17123287670.12062726180.25706940870.16494845360.11678832120.24615384620.15898251190.11312217190.23584905660.15331544650.10961907370.226116450.14792899410.10626992560.21691973970.14280614070.103066220.20822488290.13793103450.10.20.13328890370.09706381950.19221528110.12886597940.09425070690.18484288350.12464942350.09155413140.17785682530.12062726180.08896797150.17123287670.11678832120.08648648650.16494845360.11312217190.08410428930.15898251190.10961907370.08181632240.15331544650.10626992560.07961783440.14792899410.103066220.07750435960.14280614070.10.07547169810.13793103450.09706381950.07351589780.13328890370.09425070690.07163323780.12886597940.09155413140.0698202130.12464942350.08896797150.06807351940.12062726180.08648648650.06639004150.11678832120.08410428930.06476683940.11312217190.08181632240.06320113760.10961907370.07961783440.06169031460.10626992560.07750435960.06023189280.103066220.07547169810.05882352940.10.07351589780.05746300820.09706381950.07163323780.05614823130.09425070690.0698202130.05487721220.09155413140.06807351940.05364806870.08896797150.06639004150.05245901640.08648648650.06476683940.05130836330.08410428930.06320113760.05019450370.08181632240.06169031460.04911591360.07961783440.06023189280.04807114530.07750435960.05882352940.04705882350.0754716981

Lorentzian L(x)

Sheet3orbitom1=10.5om 2=1decay 10.2r1=1r2=6decay 20.1txyxy0.016.9941925652-0.16480616886.9862088666-0.1645367950.026.97683095470.32845196.9609410344-0.32737998170.036.94809658140.48978947246.9244439436-0.48739702920.046.90828958030.64769645826.877081105-0.64348956110.056.8578255040.80108802036.8193276607-0.79460523470.066.79723074790.94892879686.7517647347-0.93974906790.076.72713675491.09024423976.6750726421-1.07799408950.086.64827306371.22413128386.5900230345-1.20849119930.096.56145927711.3497682296.4974700733-1.33047813390.16.46759603961.46642372556.3983407315-1.44328744020.116.36765512191.57346476456.2936243338-1.54635337710.126.26266872351.67036358536.1843614537-1.63921766910.136.15371811011.75670342386.0716322919-1.72153405730.146.04192171071.83218303765.9565446655-1.79307159960.155.92842280681.89661995945.8402217426-1.85371669040.165.8143769481.94995244195.7237896571-1.90347378250.175.70093923321.99224007315.6083651414-1.94246480710.185.58925159742.02366305545.4950433118-1.97092730610.195.48043024422.0445201565.3848857416-1.98921129970.25.37555336242.05522535145.2789089504-1.99777493010.215.27564926222.05630320345.1780734366-1.99717893460.225.18168506042.04838301655.0832733689-1.98808001210.235.0945560422.03219184264.9953270497-1.97122316180.245.0150758122.00854640814.9149682513-1.94743308140.254.94396734881.97834405414.8428385169-1.91760472380.264.88185505551.94255278894.7794805063-1.88269311920.274.82925789821.90220056164.7253324575-1.84370257770.284.78658370631.85836387614.6807238178-1.80167539330.294.75412469741.81215587044.6458720902-1.75768017580.34.73205427631.76471399264.6208809233-1.71279994040.314.72042514321.71718740894.605739462-1.66812008620.324.71916873281.67072428334.6003229598-1.62471639810.334.72809598861.62645906824.6043946422-1.58364320140.344.74689946581.58549994614.6176087946-1.54592180120.354.7751567391.54891656134.6395150367-1.51252933070.364.81233507641.51772817584.6695637312-1.48438813050.374.85779732981.49289238114.7071124628-1.46235577370.384.91080897571.47529448824.7514335122-1.44721584240.394.97054622941.46573771594.801722239-1.43966955670.45.03610514271.46493428144.8571062769-1.44032834160.415.10651158541.47349749574.9166554381-1.44970741270.425.18073200061.49193494674.9793922139-1.46822044570.435.25768481461.52064284865.0443027546-1.49617538380.445.33625237731.55990161735.1103482054-1.53377142540.455.41529329951.60987272255.1764762728-1.58109722030.465.49365505271.67059684925.2416328927-1.63813028910.475.57018669291.74199339075.3047738715-1.7047376670.485.64375156591.82386127775.3648763738-1.78067776120.495.71323985781.91588113445.4209501284-1.86560339580.55.77758084862.01761873825.4720482328-1.95906600580.515.83575473692.12852974485.5172774376-2.06052092970.525.88680390432.24796562615.5558078004-2.16933373920.535.92984349432.37518075675.5868816053-2.28478752980.545.96407119212.50934056975.6098214531-2.40609109130.555.98877609422.64953069285.624037436-2.53238786180.566.00334657252.79476696355.6290333224-2.66276556680.576.00727704522.94400621365.6244116866-2.79626643110.586.00017358023.0961577045.6098779327-2.93189785280.595.98175826963.25009508365.5852431708-3.06864341640.65.95187232583.40466874095.550425921-3.20547412560.615.91047786743.55871841255.5054526287-3.34135972940.625.85765837273.71108590895.450456992-3.47528001780.635.79361779753.86062781785.3856781121-3.60623596220.645.71867836644.00622804535.3114574931-3.73326057890.655.6332770624.14681005645.2282349269-3.85542939760.665.53796085034.28134868035.1365433154-3.97187042110.675.43338069514.40888134975.0370024886-4.08177346840.685.32028442814.52851865224.9303120918-4.18439880180.695.19950855154.63945407484.8172436251-4.27908494510.75.07196906544.7409728374.6986317226-4.36525561050.714.93865141934.83245971294.575364775-4.44242566160.724.80059969964.91340575754.4483749962-4.51020605140.734.65890517154.98341386344.31862805-4.56830768290.744.51469430195.04220308454.1871123494-4.61654415760.754.36911639475.08961168244.0548281494-4.65483338310.764.22333097555.12559885893.9227765526-4.68319802760.774.07849506375.15024515743.7919485509-4.70176482240.783.93575047355.16375152783.6633142206-4.71076272150.793.79621128155.16643706643.537812193-4.71051994710.83.6609516025.15873545353.4163395109-4.70145995370.813.53099380125.14119013083.2997419852-4.68409636360.823.40729728355.11444826933.1888051519-4.65902692990.833.29074797055.07925359553.0842459294-4.62692660050.843.18214859025.03643815432.9867050634-4.58853976010.853.08220988384.98691309992.8967404399-4.54467174140.862.99154282494.93165861522.8148213364-4.49617969950.872.91065193894.87171307252.7413236705-4.44396295430.882.83992979544.8081615522.6765262946-4.38895290730.892.77965273354.74212384812.6206083727-4.33210264770.92.72997786844.67474209262.5736478641-4.27437636140.912.69094141154.60716813312.5356211266-4.21673866020.922.66245832284.54055080412.5064036384-4.1601439510.932.64432329874.47602323292.4857718269-4.10552595910.942.63621308564.41469031782.4734059793-4.05378752140.952.63769009284.35761651882.4688941994-4.00579076140.962.64820726514.30581409372.4717373618-3.96234775080.972.66711416174.26023190992.4813550067-3.92421176020.982.69366417394.22174495452.4970921048-3.8920691910.992.72702280334.19114465992.5182266157-3.866532276512.76627690724.16913014892.5439777532-3.84813262741.012.81044481214.15630049782.573514864-3.83731569131.022.85848718094.15314810252.6059668188-3.83443618131.032.90931851674.1600532192.6404318114-3.83975452171.042.96181917544.1772797412.6759874567-3.8534343461.053.01484775354.20497225862.7117010738-3.87554106881.063.06725371774.24315443272.7466400421-3.9060415451.073.11789013414.29172870132.779882115-3.94480481391.083.16562635864.35047732182.8105255789-3.99160391761.093.20936054814.41906473752.8376991455-4.04611876771.13.24803185464.49704124332.8605714702-4.10794002561.113.28063216864.58384790752.8783601934-4.17657394891.123.30621728114.67882269922.8903404069-4.25144814821.133.32391734274.78120775082.8958524551-4.33191818541.143.33294650364.89015767682.8943089869-4.41727493891.153.33261162875.00474885772.8852011853-4.50675265181.163.3223199925.12398958582.8681041074-4.59953757031.173.30158586455.24683096152.8426810816-4.69477707731.183.27003592515.37217842052.8086871162-4.79158921651.193.22741343225.49890376462.7659712865-4.88907250211.23.17358111245.6258575632.7144780774-4.98631590471.213.10852273325.75188178912.6542476716-5.08240890311.223.03234334275.87582255112.5854151852-5.17645149051.232.94526817385.99654277962.5082088605-5.26756402581.242.84764022436.11293472862.4229472437-5.35489682281.252.73991654086.22393215552.3300353798-5.43763937151.262.62266324616.32852204362.2299600716-5.51502909291.272.49654936556.42575573992.1232842588-5.5863595321.282.36233951976.51475938382.0106405818-5.6509879021.292.22088556526.59474351281.8927242049-5.7083418981.32.07311727376.66501173931.7702849805-5.75792570991.311.92003215386.72496840271.6441190432-5.79932517021.321.76268452656.7741251131.5150599283-5.83221198371.331.6021739756.81210611261.3839693141-5.85634699741.341.43963329666.83865239911.2517274924-5.87158247721.351.27621608846.85362456211.1192236716-5.87786337041.361.11308410436.85700430370.9873462204-5.87522754511.370.95139452216.84889462470.8569729597-5.86380500721.380.79228726186.82951867690.7289616095-5.84381610791.390.63687249296.79921729130.6041404941-5.81556876521.40.48621847086.75844521110.4832996085-5.77945473441.410.34133983436.70776607070.3671821407-5.73594497181.420.20318649416.64784617620.2564765435-5.6855841471.430.07263323376.57944715480.1518092395-5.62898436651.44-0.04952986076.50341755570.0537380363-5.56681818141.45-0.16260603886.4206834941-0.0372536761-5.49981095951.46-0.26599949566.3322384408-0.1207618876-5.42873270691.47-0.35922186916.2391322715-0.1964660378-5.35438943191.48-0.44189755486.1424596947-0.2641321507-5.27761414881.49-0.51376777756.0433481868-0.323615007-5.19925762021.5-0.57469337675.9429455669-0.3748593298-5.12017894231.51-0.6246562745.842407348-0.4178999777-5.04123607641.52-0.66375960725.7428840041-0.4528611465-4.96327643141.53-0.69222652865.645508294-0.4799545905-4.88712760031.54-0.71039768185.5513827799-0.4994768897-4.81358835231.55-0.7187273845.4615676802-0.5118057942-4.7434199781.56-0.71777855665.3770691887-0.5173956913-4.67733808261.57-0.70821645885.2988283903-0.5167722481-4.61600491381.58-0.69080129485.2277108935-0.5105262915-4.56002230861.59-0.66637977435.1644972955-0.4993069968-4.50992533221.6-0.63587572125.1098745847-0.4838144621-4.46617667791.61-0.60027983175.0644285742-0.4647917514-4.42916188521.62-0.56063869685.0286374509-0.4430164991-4.3991854261.63-0.51804320875.0028665104-0.4192921666-4.3764676991.64-0.47361647944.9873641362-0.3944390503-4.36114296031.65-0.42850140424.9822590678-0.3692851415-4.35325821071.66-0.38384800764.987558986-0.3446569371-4.35277304721.67-0.34080071075.003150434-0.3213703048-4.35956047691.68-0.30048566015.0288000722-0.300221501-4.37340868021.69-0.26399825865.0641572544-0.2819784414-4.39402370061.7-0.23239103415.1087578975-0.2673723175-4.4210330271.71-0.2066619815.1620296001-0.2570896512-4.45399002661.72-0.18774350285.2232979562-0.2517648728-4.49237917551.73-0.17649207675.2917939919-0.2519735011-4.53562202621.74-0.17367875465.3666626453-0.2582259995-4.58308384391.75-0.17998060585.4469721949-0.2709623716-4.63408083611.76-0.19597319415.531724533-0.2905475547-4.68788789321.77-0.22212417375.6198661712-0.3172676562-4.7437467521.78-0.25878807385.7102998563-0.3513270727-4.80087449351.79-0.30620232935.8018966692-0.3928465202-4.85847227691.8-0.36448460095.8935084731-0.4418619911-4.91573421471.81-0.43363141565.9839805736-0.498324649-4.97185629081.82-0.51351814096.0721644528-0.5621016563-5.02604522191.83-0.60390029386.1569304345-0.6329779224-5.07752716721.84-0.70441617046.2371801439-0.7106587504-5.12555618861.85-0.81459076666.3118586221-0.7947733482-5.1694223721.86-0.93384094686.3799659638-0.8848791639-5.20845951971.87-1.06148180446.4405683484-0.9804669918-5.24205233151.88-1.19673414276.4928083448-1.0809667929-5.26964299921.89-1.33873299516.5359143747-1.1857541605-5.29073714151.9-1.48653709056.5692092306-1.2941573582-5.30490901861.91-1.63913915826.5921175562-1.4054648517-5.31180597221.92-1.79547696176.6041722041-1.5189332471-5.31115204381.93-1.95444493656.6050194032-1.6337955493-5.30275073541.94-2.11490630666.5944226775-1.7492696468-5.28648688661.95-2.2757055446.5722654732-1.8645669296-5.26232764931.96-2.43568103636.5385524664-1.9789009442-5.23032255421.97-2.59367781996.4934095353-2.0914959909-5.19060267131.98-2.74856024156.4370823979-2.2015955689-5.14337887781.99-2.89922440696.3699339312-2.3084705769-5.08893925522-3.04461027956.2924401995-2.4114271802-5.02764564842.01-3.1837132976.205185237-2.5098142585-4.95992942772.02-3.31559537676.1088546419-2.6030303555-4.8862865042.03-3.43939518886.0042280518-2.690530054-4.80727165362.04-3.55433758495.8921705848-2.7718297104-4.72349221932.05-3.65974207715.7736233385-2.8465124873-4.63560125912.06-3.75503027545.6495930534-2.9142326317-4.54429021912.07-3.83973219965.521141054-2.9747189543-4.45028121512.08-3.91349139895.3893715886-3.0277774765-4.35431900642.09-3.97606881975.2554196972-3.0732932173-4.25716275482.1-4.02734538235.120438741-3.1112311047-4.15957765722.11-4.06732323464.9855877305-3.1416360061-4.06232654572.12-4.09612567264.8520185916-3.1646318785-3.96616154822.13-4.11399572534.720863511-3.1804200541-3.87181589982.14-4.12129342214.593222499-3.1892766817-3.77999599512.15-4.11849177124.4701513075-3.1915493558-3.69137376772.16-4.10617149444.3526498361-3.1876529744-3.60657947932.17-4.08501457534.2416511541-3.1780648734-3.52619499662.18-4.0557966934.1380112584-3.1633192942-3.45074762652.19-4.01937862334.0424996821-3.1440012483-3.38070457782.2-3.9766967043.9557910551-3.1207398481-3.31646810432.21-3.92875246753.8784577108-3.0942011803-3.25837138382.22-3.87660155613.8109634204-3.0650808014-3.20667517152.23-3.82134204113.7536583231-3.0340959392-3.16156526522.24-3.76410227563.7067751089-3.0019774884-3.12315080432.25-3.70602841393.6704264954-2.9694618873-3.09146341842.26-3.6482717353.6446040264-2.9372829674-3.06645723342.27-3.59197591033.629178206-2.9061638639-3.04800972852.28-3.53826435583.6238999664-2.876809077-3.03592343432.29-3.48822780673.6284034535-2.8498967703-3.02992844712.3-3.44291225413.6422100986-2.8260713899-3.02968573172.31-3.40330737343.6647339331-2.8059366841-3.03479116962.32-3.37033557433.6952880862-2.7900491993-3.04478030862.33-3.34484179193.7330923943-2.7789123215-3.05913375652.34-3.32758413213.7772820391-2.7729709258-3.07728315692.35-3.31922547263.8269171182-2.7726066926-3.09861768152.36-3.32032611483.8809930433-2.7781341364-3.12249096212.37-3.33133756523.9384516511-2.7897973909-3.14822838692.38-3.35259751553.9981929059-2.8077677804-3.17513467822.39-3.38432607724.059087062-2.8321422025-3.20250166742.4-3.42662331194.1199871558-2.8629423363-3.22961618082.41-3.47946808364.1797416867-2.9001146811-3.2557679492.42-3.54271824784.2372073485-2.9435314226-3.28025745342.43-3.61611217264.2912616718-2.9929921127-3.30240362322.44-3.69927157734.3408154368-3.0482261424-3.32155129822.45-3.79170565624.3848247198-3.108895977-3.33707837852.46-3.89281644174.422302442-3.1746011142-3.3484025812.47-4.00190534984.4523292926-3.2448827196-3.35498773172.48-4.11818083224.4740639049-3.3192288864-3.3563495262.49-4.24076705534.4867521753-3.3970804568-3.35206069592.5-4.36871350584.4897356212-3.4778373417-3.34175552882.51-4.50100542164.4824586858-3.5608652648-3.32513369272.52-4.63657492874.4644749097-3.645502857-3.30196332562.53-4.77431276574.4354519014-3.73106902-3.27208336172.54-4.91308046324.3951750516-3.8168704787-3.2354050682.55-5.05172284644.3435499504-3.902209438-3.1919127812.56-5.18908072164.280603481-3.9863912584-3.14166383592.57-5.32400360784.2064835782-4.0687320674-3.08478769392.58-5.45536237324.1214576527-4.1485662229-3.02148428052.59-5.58206163624.0259097012-4.2252535456-2.95202155422.6-5.70305179613.9203361315-4.2981862446-2.87673233822.61-5.81734055973.8053403506-4.3667954585-2.7960104512.62-5.92400383723.6816261739-4.4305573437-2.71030618172.63-6.02219588733.5499901291-4.4889986426-2.62012116252.64-6.11115860033.4113127396-4.5417016752-2.52600269722.65-6.19022981613.2665488816-4.5883086996-2.42853760992.66-6.25885058593.1167173248-4.6285255955-2.32834568422.67-6.3165712982.9628895673-4.6621248358-2.22607276592.68-6.36305659942.8061780915-4.6889477126-2.12238360652.69-6.39808905982.6477241686-4.7089057992-2.01795452752.7-6.4215715372.4886853457-4.7219816337-1.91346598722.71-6.43352821792.3302227547-4.7282286197-1.80959513142.72-6.43410432422.1734883816-4.7277701487-1.70700840982.73-6.42356448452.0196124365-4.7207979572-1.60635434042.74-6.40228979321.8696909648-4.7075697386-1.50825649972.75-6.37077358531.7247738336-4.6884060409-1.41330681482.76-6.32961597731.5858532279-4.6636864847-1.32205923052.77-6.27951723121.4538527825-4.6338453485-1.23502381992.78-6.22127001691.3296174685-4.59936657-1.15266140022.79-6.15575065661.2139043474-4.5607782228-1.07537871182.8-6.08390944881.1073742927-4.5186465294-1.0035242122.81-6.00676017821.0105847726-4.4735694793-0.93738452542.82-5.92536892680.9239837705-4.4261701244-0.8771815892.83-5.84084230910.8479049125-4.3770896252-0.82307052022.84-5.75431526240.7825638549-4.3269801262-0.77513822732.85-5.66693852470.7280559706-4.2764975405-0.73340277642.86-5.57986594010.6843553611-4.2262943208-0.69781351752.87-5.494241730.6513152046-4.1770122985-0.66825196572.88-5.41118787140.6286694359-4.1292756694-0.64453342472.89-5.33179172010.61603574-4.0836842001-0.62640933212.9-5.25709401670.6129198266-4.0408067326-0.61357029772.91-5.18807740650.6187209379-4.0011750538-0.60564979792.92-5.12565559940.6327385292-3.9652781985-0.60222848422.93-5.07066329030.6541800494-3.9335572453-0.60283905522.94-5.02384695050.6821697343-3.9064006614-0.60697163632.95-4.98585659130.7157583172-3.8841402444-0.61407960572.96-4.95723859030.7539335487-3.867047705-0.62358580182.97-4.93842966120.7956314113-3.8553319237-0.63488904132.98-4.92975203040.8397479033-3.8491369104-0.6473708752.99-4.93140987690.8851512639-3.8485404858-0.66040250663-4.9434870720.9306945041-3.8535536963-0.67335179813.01-4.96594624560.9752281048-3.8641209662-0.68559028283.02-4.99862918771.0176127441-3.8801209826-0.69650011093.03-5.0412585831.0567319113-3.9013682996-0.70548084983.04-5.09344105651.0915042701-3.9276156423-0.71195606553.05-5.1546714991.1208956344-3.958556882-0.71537961433.06-5.22433862421.143930425-3.9938306466-0.71524157593.07-5.30173169521.1597024804-4.0330245256-0.71107376383.08-5.38604834781.1673851037-4.0756798191-0.70245475543.09-5.47640342331.1662402335-4.1212967776-0.68901438713.1-5.57183871391.1556266391-4.1693402733-0.67043766783.11-5.6713335141.1350070487-4.2192458373-0.64646806993.12-5.77381585971.1039541333-4.2704259969-0.61691016383.13-5.87817433391.0621552784-4.3222768401-0.58163157053.14-5.98327030711.0094160937-4.3741847356-0.5405642123.15-6.08795047770.945662619-4.4255331334-0.493704853.16-6.19105957530.8709422049-4.4757093705-0.44111490913.17-6.29145308610.7854230565-4.5241114072-0.38291958953.18-6.38800986030.689392446-4.5701544202-0.31930628143.19-6.47964446320.5832536141-4.6132771808-0.25052230213.2-6.5653191330.467521394-4.6529481478-0.17687198243.21-6.64405521460.3428166053-4.6886712109-0.0987131383.22-6.71494394290.2098592821-4.7199910218-0.01645296623.23-6.77715645710.0694608063-4.74649785540.0694565843.24-6.8299529346-0.0774849635-4.76783195160.1585239163.25-6.8726907464-0.230011473-4.78368728970.25022330523.26-6.9048315411-0.3870900535-4.79381475770.3440007723.27-6.9259471815-0.547641187-4.79802468360.43928024323.28-6.9357244684-0.7105463323-4.79618870280.53546993063.29-6.9339685979-0.8746601804-4.78824094510.63196885833.3-6.9206053163-1.038823205-4.77417852930.72817346483.31-6.8956817472-1.2018743698-4.75406136430.82348420763.32-6.8593658823-1.3626638527-4.72801126040.91731209693.33-6.811944742-1.5200656457-4.6962103641.00908508853.34-6.7538212249-1.6729898938-4.65889893571.0982542643.35-6.6855096817-1.820394835-4.61637249791.18429973293.36-6.607630263-1.9612982109-4.56897838711.26673619213.37-6.5209021008-2.0947880221-4.51711175081.34511808323.38-6.4261354018-2.2200325096-4.46121103381.41904429163.39-6.3242225373-2.336289253-4.40175300841.48816234013.4-6.2161282292-2.442913284-4.33924740181.55217202943.41-6.1028789392-2.5393641274-4.27423118411.61082849013.42-5.9855515792-2.6252116908-4.20726257931.66394461513.43-5.8652616661-2.700140939-4.13891486681.71139284633.44-5.7431510522-2.7639553008-4.06977004281.75310629983.45-5.6203753661-2.8165787714-4.00041241151.78907922043.46-5.4980913029-2.8580566869-3.93142217651.81936676183.47-5.3774439025-2.8885551625-3.86336910341.84408409773.48-5.2595539575-2.9083592004-3.79680632331.86340487793.49-5.1455056885-2.9178694883-3.73226434331.8775590473.5-5.0363348232-2.9175979243-3.67024533131.88683005323.51-4.9330172099-2.9081619165-3.61121773471.89155148013.52-4.8364580912-2.8902775211-3.5556112921.89210314143.53-4.7474821565-2.8647514935-3.50381249031.88890668243.54-4.6668244815-2.8324723415-3.45616051721.88242074023.55-4.5951224567-2.7944004776-3.41294374891.87313571583.56-4.5329087907-2.7515575795-3.37439681181.86156821933.57-4.4806056693-2.7050152765-3.34069824691.84825524813.58-4.4385201306-2.6558832856-3.31196880051.83374816533.59-4.4068407104-2.605297128-3.28827035861.81860654433.6-4.3856353929-2.5544055628-3.26960553181.80339194843.61-4.3748508898-2.5043578737-3.25591789461.78866171243.62-4.3743132563-2.4562911513-3.24709287381.77496279793.63-4.3837298359-2.4113177096-3.24295927211.76282578573.64-4.4026925142-2.3705127754-3.24329140931.75275907353.65-4.4306822446-2.3349025873-3.2478118541.74524334153.66-4.4670747962-2.3054530338-3.25619471441.74072634413.67-4.5111476619-2.2830589567-3.26806944811.73961808583.68-4.5620880483-2.268534238-3.28302514931.74228643163.69-4.6190018612-2.2626027777-3.30061526181.74905319863.7-4.680923588-2.2658904643-3.32036266631.76019076973.71-4.7468269656-2.2789182243-3.34176508381.77591926573.72-4.8156363196-2.3020962289-3.36430073341.79640430233.73-4.8862384475-2.3357193202-3.38743418371.82175535763.74-4.957494916-2.3799637088-3.410622331.85202476243.75-5.0282546368-2.4348849784-3.43332043291.88720732393.76-5.0973665824-2.5004174187-3.45498815071.92724058423.77-5.1636925015-2.5763746959-3.47509551.9720057073.78-5.2261194944-2.6624518511-3.49312867862.02132898223.79-5.2835723101-2.7582286065-3.50859568692.07498392743.8-5.3350252282-2.863173942-3.52103168892.13269396243.81-5.3795133968-2.9766518914-3.53000405132.19413562383.82-5.4161434998-3.0979284961-3.53511701022.25894228323.83-5.4441036371-3.2261798377-3.53601591312.32670832553.84-5.4626723086-3.3605010621-3.53239099262.3969937393.85-5.4712264023-3.4999162957-3.52398063082.46932906743.86-5.4692481002-3.6433893441-3.51057408272.54322066423.87-5.456330624-3.7898350557-3.49201362812.61815619443.88-5.4321827586-3.9381312251-3.46819613322.69361031893.89-5.3966321035-4.0871309048-3.43907400492.76905049993.9-5.3496270149-4.23567499-3.40465553152.84394286363.91-5.2912372198-4.3826049381-3.36500460722.91775805313.92-5.221653092-4.5267754818-3.32023984662.98997700983.93-5.1411836006-4.6670671969-3.27053310113.06009661843.94-5.0502529529-4.8023987858-3.21610739613.12763515463.95-4.9493959676-4.9317389414-3.15723431353.19213747643.96-4.8392522305-5.0541176607-3.09423085153.25317990223.97-4.7205590971-5.1686368843-3.02745579683.31037472463.98-4.5941436177-5.2744803428-2.95730565253.36337431043.99-4.4609134762-5.3709225039-2.88421016783.41187474464-4.3218470402-5.4573365198-2.80862751943.45561897874.01-4.1779826332-5.533201088-2.73103920023.4943994524.02-4.0304071473-5.5981061512-2.65194467193.52806015894.03-3.8802441207-5.6517573703-2.57185584213.55649814074.04-3.7286414125-5.6939793256-2.49129142533.57966438914.05-3.5767586096-5.7247174065-2.41077125343.59756415294.06-3.4257543052-5.7440383728-2.33081059553.61025664754.07-3.2767733881-5.7521295781-2.25191455133.61785417254.08-3.1309344844-5.7492968667-2.17457257853.62052064924.09-2.9893176875-5.7359611648-2.09925321443.61846959694.1-2.8529527141-5.7126538055-2.02639904863.61196157264.11-2.7228076149-5.6800106374-1.95642200123.60130110344.12-2.599778165-5.6387649831-1.88969895743.58683314854.13-2.4846780508-5.5897395244-1.82656780473.56893913144.14-2.3782299616-5.5338372037-1.76732391483.54803258644.15-2.2810576836-5.4720312417-1.71221710763.52455447094.16-2.193679284-5.4053543821-1.66144912773.49896819484.17-2.11650146-5.3348874806-1.61517166013.47175442294.18-2.049815114-5.261747565-1.57348490473.44340570944.19-1.9937922059-5.1870754968-1.53643672163.41442102334.2-1.948483915-5.1120233717-1.50402235733.3853002254.21-1.9138201327-5.037741796-1.47618474843.35653855674.22-1.8896102921-4.965367181-1.45281540143.32862120474.23-1.8755455238-4.8960091932-1.43375583333.30201799554.24-1.8712021159-4.8307385003-1.41879955673.2771782824.25-1.876046239-4.7705749477-1.40769458533.25452607534.26-1.8894398842-4.7164762944-1.40014642863.23445547614.27-1.9106479495-4.6693276341-1.39582154343.21732645224.28-1.9388463954-4.6299316172-1.39435120063.20346101044.29-1.9731313805-4.5989995814-1.39533572263.19313984.3-2.012529277-4.5771436884-1.39834904563.18659918584.31-2.0560074539-4.5648701539-1.40294355323.18402882054.32-2.1024857122-4.5625736456-1.40865512713.18556974034.33-2.1508482424-4.5705329095-1.41500836033.19131300364.34-2.1999559756-4.5889076744-1.42152187263.20129888494.35-2.2486591913-4.6177368678-1.42771367163.21551663074.36-2.2958102417-4.656938163-1.43310649763.23390477864.37-2.3402762544-4.7063088624-1.43723309683.25635203274.38-2.3809516719-4.7655281071-1.43964136183.28269868354.39-2.4167704912-4.8341603891-1.43989928623.31273855634.4-2.4467180669-4.9116603266-1.43759967783.34622146144.41-2.4698423499-4.99737865-1.432364583.38285612114.42-2.4852644362-5.0905693335-1.42384935413.42231353524.43-2.49218831-5.1903977922-1.41174637943.46423074984.44-2.4899096748-5.2959500564-1.39578833053.50821498414.45-2.4778237738-5.4062428196-1.37575099893.55384806974.46-2.4554321138-5.5202342519-1.35145562913.60069115124.47-2.42234802-5.6368354585-1.32277074563.6482895964.48-2.3783009576-5.7549224566-1.2896134523.69617805954.49-2.323139576-5.8733485405-1.25195019133.74388564664.5-2.256833439-5.9909568963-1.20979696043.79094111544.51-2.1794734241-6.1065933301-1.16321897853.83687806364.52-2.0912707855-6.2191189663-1.11232981553.88124004194.53-1.9925548909-6.3274227795-1.05728999223.92358553754.54-1.8837696585-6.4304338189-0.99830506973.96349277434.55-1.7654687306-6.5271329928-0.93562325124.0005642774.56-1.6383094407-6.6165642821-0.86953252384.03443115034.57-1.5030456371-6.6978452597-0.80035737464.06475702694.58-1.3605194442-6.7701768004-0.72845511844.0912416434.59-1.2116520514-6.8328518732-0.65421187874.11362400234.6-1.0574336311-6.8852633202-0.57803826814.13168509634.61-0.8989124972-6.9269105364-0.50036481634.14525015214.62-0.7371836229-6.9574049758-0.42163719754.1541903864.63-0.5733766448-6.9764744242-0.34231130964.15842424364.64-0.4086434856-6.9839659913-0.26284826154.15791811684.65-0.2441457305-6.9798477892-0.18370932194.15268653054.66-0.0810418985-6.9642092784-0.1053508874.14279180084.670.079525254-6.9372602778-0.02821952164.12834316754.680.2364412544-6.89932865040.0472528724.10949541644.690.3886321248-6.85085668810.12065370474.08644700534.70.535076146-6.7923962380.19159412084.05943771814.710.6748150463-6.7246026220.25971313924.02874587454.720.8069644912-6.64822741720.32468147213.99468512664.730.9307237587-6.5641101770.38620497993.95760088124.741.0453844936-6.47316918350.44402772583.91786638664.751.1503384448-6.3763913340.49793459873.87587852984.761.2450840993-6.27482127140.54775347683.83205339094.771.3292321409-6.16954988020.59335690913.78682160414.781.4025096731-6.06170227310.63466330023.74062357824.791.4647631598-5.95242540120.67163758633.69390462854.81.5159600506-5.84287542540.70429139563.64711007484.811.5561890747-5.73420498510.73268269663.60068035954.821.5856591978-5.62755050820.75691493733.55504623864.831.6046972554-5.52401969950.77713568793.51062409944.841.6137442873-5.42467934580.79353480443.46781145474.851.6133506149-5.33054357280.80634213443.42698266374.861.6041697145-5.24256268310.81582479273.38848492394.871.586950954-5.16161269680.82228403763.35263457914.881.5625312743-5.0884857120.82605178543.31971378114.891.5318259054-5.02388118970.82748680093.2899675414.91.4958182211-4.96839825980.82697060843.26360120194.911.4555488424-4.92252913340.82490316973.24077835734.921.4121041109-4.88665369260.82169837523.22161923754.931.3666040584-4.86103531890.8177794023.20619958054.941.3201900063-4.84581800540.81357398683.19454999534.951.2740119294-4.84102478440.80950966933.18665582634.961.2292157257-4.84655748790.80600905593.18245751494.971.1869305303-4.86219784450.80348515743.18185145444.981.148256215-4.88760989920.80233685083.18469132614.991.1142512099-4.922343730.80294451493.190789951.0859207811-4.9658404210.80566588743.19992127885.011.0642058956-5.01743823650.8108321873.21182355825.021.049972793-5.07637992790.81874454363.22620187275.031.044003382-5.14182109380.82967077343.24273179275.041.0469865645-5.21283950040.84384253393.26106303275.051.0595105859-5.28844526020.86145288773.28082342985.061.0820564928-5.36759175560.88265430093.30162314715.071.114992773-5.44918718940.90755709663.32305905475.081.1585712346-5.53210663230.93622837753.34471924045.091.2129241712-5.61520443690.96869142873.36618759845.11.2780628432-5.69732687941.00492560573.38704844655.111.3538772931-5.77732489251.0448667053.4068911215.121.4401374955-5.85406674571.08840781333.42531449715.131.5364958306-5.92645053711.13540062323.44193138795.141.6424908529-5.99341635571.18565719893.45637277235.151.7575523139-6.0539579831.23895217113.46829180625.161.8810073834-6.10713400271.29502533493.47736757495.172.0120880019-6.15207819811.35358462123.4833085455.182.1499392804-6.18800912141.41430940623.48585567985.192.293628859-6.21423872961.47685412243.48478518525.22.4421571176-6.23017999281.54085212993.47991085795.212.5944681284-6.23535338981.60591980443.47108600975.222.7494612288-6.22939222061.67166079513.45820495155.232.9060030874-6.21204667631.73767040693.44120401965.243.06294013-6.18318662231.80354005663.42006213655.253.2191111891-6.14280306391.86886175463.39480090125.263.3733602373-6.09100827821.93323256233.36548421025.273.5245490644-6.02803461041.99625897683.3322174155.283.6715697583-5.95423194832.05756119413.29514602755.293.813356853-5.87006390312.11677720583.25445398895.33.9488990092-5.77610273732.1735666833.21036152335.314.0772500991-5.6730230972.22761460763.16312260115.324.1975395728-5.56159461672.27863461053.11302204175.334.3089819934-5.44267347862.32637198223.06037228835.344.4108856343-5.31719301882.37060632283.00550989295.354.5026600452-5.18615348432.41115380522.94879174935.364.583822502-5.05061105412.44786902752.89059111875.374.654003272-4.91166624362.48064643472.83129349075.384.7129496333-4.77045182212.50942129822.77129232675.394.7605286069-4.62812037532.5341702422.71098473295.44.7967283694-4.48583165012.55491131252.65076711085.414.8216583327-4.34473982042.57170359292.59103083275.424.8355478872-4.2059808162.58464636842.53215799015.434.8387438253-4.07065985212.59387785242.47451726175.444.8317064714-3.93983929742.5995734912.41845994445.454.8150045617-3.81452701562.60194386412.36431619315.464.7893089309-3.6956653072.60123220962.31239150685.474.7553850739-3.58412057282.59771159872.26296350085.484.7140846661-3.48067381642.59168179392.21627899835.494.6663361345-3.38601208542.58346582782.17255147235.54.6131343836-3.30072094892.57340633842.1319588655.514.5555297898-3.22527809362.56186170532.09464180625.524.4946165854-3.1600481082.54920202762.06070224995.534.4315207597-3.10527851332.53580498942.03020254135.544.3673876106-3.06109708412.52205165932.00316492365.554.3033690848-3.02751048842.50832226931.97957148765.564.2406110443-3.00440426232.49499202031.95936456355.574.1802406007-2.99154411912.48242696011.9424475485.584.1233536571-2.9885785792.47097997861.92868615715.594.0710027933-2.99504288982.46098696441.91791008775.64.0241856295-3.01036419572.45276316391.90991506935.613.9838337952-3.03386789782.44659978211.90446528075.623.9508026263-3.06478513472.44276086221.90129610465.633.9258617021-3.10226130312.44148047611.90011718745.643.9096863283-3.14536552212.44296025681.90061577055.653.9028500582-3.19310093862.4473672971.90246025445.663.9058183358-3.24441575972.45483243661.90530395635.673.9189433298-3.29821489092.46544895651.90878901765.683.9424600163-3.35337205122.47927169041.91255042025.693.9764835523-3.40874223242.49631656321.91622006495.74.0210079698-3.46317436482.51656056051.91943086675.714.0759062051-3.51552405052.53994212561.92182082475.724.1409314616-3.5646662232.56636197971.92303701755.734.2157198926-3.60950759472.59568435431.92273948475.744.2997945741-3.64899875452.62773861961.92060494975.754.3925707226-3.68214578222.66232129091.91633034435.764.4933621031-3.70802125292.69919838781.9096360975.774.6013885538-3.7257745082.73810812091.90026914985.784.715784547-3.73464108222.77876387271.88800567195.794.8356086895-3.73395118062.82085744061.87265344075.84.959854061-3.72313711362.86406250511.85405386575.815.0874592732-3.70173960792.90803828281.8320836355.825.2173201307-3.66941292232.95243332511.80665596695.835.3483017629-3.62592871522.99688941881.77772145515.845.4792510953-3.57117861723.04104554661.74526849915.855.6090095214-3.50517548443.08454186191.70932331765.865.7364256361-3.42805331513.12702363641.66994954585.875.8603678905-3.34006583343.16814513541.62724742315.885.979737029-3.24158375423.20757337881.58135258085.896.0934781703-3.13309075953.24499174811.53243444655.96.2005924011-3.01517823073.28010339891.48069428235.916.3001477533-2.88853879523.31263444231.42636288115.926.3912894454-2.75395875783.34233686251.36969794795.936.4732492729-2.61230950013.36899113771.31098119425.946.5453540467-2.46453794413.3924085381.25051518175.956.6070329854-2.31165618293.41243307611.18861994815.966.6578239797-2.15473039423.42894308981.12562945435.976.697378661-1.99486915823.44185244181.06188789325.986.7254662175-1.8332113093.45111132390.99774590065.996.7419759159-1.67091345253.45670665930.933556709466.7469183015-1.50913728893.45866209960.8696722926.016.7404250626-1.34903687953.45703761760.80643953086.026.7227475615-1.19174599733.45192870390.74419646056.036.6942540476-1.0383657023.44346517560.68326862236.046.6554255842-0.8899522753.43180961270.62396557056.056.6068507324-0.74750564763.41715544120.56657756826.066.5492190526-0.61195845083.39972468490.51137250856.076.4833134932-0.4841658063.37976541160.45859309446.086.4100017521-0.36489596943.3575489040.40845430626.096.3302267047-0.25482193433.33336658690.36114118416.16.2449960045-0.15451408163.30752674490.31680694896.116.1553709716-0.06443396183.28035106930.27557148016.126.06245488980.01507072473.25217107050.23752016636.135.96738084230.08376989323.22332439770.202703146.145.87129922020.14155354433.19415110650.17113490236.155.77536504090.18843291113.16498991440.14279434176.165.68072521570.22454027013.13617448680.11762514346.175.5885059080.25012742023.10802979410.0955365856.185.49980012010.26556284363.08086857840.07640470696.195.41565564650.27132758213.05498797020.06007384286.25.33706352530.26800987353.03066628960.04635849376.215.26494711570.25629860693.0081600680.03504552186.225.20015192150.23697566962.98770132180.02589663966.235.14343627290.21090726942.96949510670.01865116556.245.09546296920.1790343282.95371737830.01302901456.255.0567919740.14236205142.9405131820.00873389036.265.02787424470.10194879262.92999519030.00545664276.275.00904676220.05889432832.92224260230.00287875316.285.00052881760.01432767952.91730041550.00067590876.295.0024195954-0.030605392.9151790779-0.00147837416.35.0146970806-0.07475505922.9158545212-0.00390911636.315.0372183009-0.11698018112.9192685733-0.00693627476.325.069720903-0.15616091732.9253297458-0.01087120996.335.111826043-0.19121113842.9339143835-0.01601326276.345.1630425623-0.22109045332.9448681647-0.02264647736.355.2227723994-0.24481573432.9580079324-0.03103650556.365.2903171817-0.26147201132.9731238356-0.04142772576.375.3648859215-0.27022261592.9899817561-0.05404060766.385.4456037339-0.27031846183.0083259927-0.06906935036.395.531521478-0.26110636223.0278821725-0.08667981916.45.6216262185-0.24203628863.048360356-0.10700780256.415.7148523891-0.21266749543.0694583013-0.13015760616.425.8100935373-0.17267343933.0908648514-0.15620099996.435.9062145193-0.12184544123.1122634051-0.18517652666.446.0020640127-0.06009504963.1333354358-0.2170891796.456.09648720690.01254492013.1537640165-0.25191044716.466.18833853320.09592068233.1732373138-0.28957873446.476.27649429410.18975911093.1914520126-0.33000013596.486.3598650510.29367068273.2081166333-0.37304956896.496.43740763720.40715370383.2229547058-0.41857224236.56.50813665950.52959977133.2357077669-0.46638544656.516.57113536650.6603004113.2461381466-0.5162806446.526.62556575920.79845481643.2540315167-0.56802583546.536.67067783690.94317860653.2591991708-0.62136817436.546.70581787241.09351350263.2614800155-0.67603680136.556.73043562911.24843782043.2607422494-0.73174586526.566.7440904381.40687766043.2568847133-0.78819769626.576.74645606811.56771867343.2498378991-0.84508609836.586.73732433821.72981827173.2395646065-0.90209972076.596.71660742721.89201815183.2260602417-0.95892547426.66.68433886132.05315699043.2093527572-1.01525195226.616.64067316342.21208317323.189502234-1.07077282036.626.58588417152.36766741813.1666001123-1.12519013696.636.52036204312.51881515143.1407680807-1.17821756796.646.44460897882.6644785033.1121566373-1.22958346196.656.35923371282.80366778633.0809433409-1.27903375126.666.26494483042.93546233863.0473307701-1.32633464866.676.16254298593.05902060013.0115442177-1.37127511046.686.05291210753.17358932352.9738291432-1.41366903986.695.93700968523.27851180922.9344484144-1.45335720736.75.81585624943.37323507882.8936793693-1.49020886826.715.69052415533.45731590592.8518107303-1.52412306096.725.56212579743.53042563772.8091394059-1.55502957256.735.43180138333.59235375572.7659672154-1.58288956256.745.30070640173.64301013492.7225975729-1.60769583986.755.16999892353.68242597732.6793321674-1.62947279066.765.04082687343.71075340952.6364676748-1.64827595876.774.91431541593.72826374812.5942925391-1.6641912876.784.79155459053.73534445312.5530838569-1.6773340266.794.67358733633.73249480212.5131043988-1.68784732566.84.56139803443.72032033262.4745998018-1.69590052656.814.4559016973.69952611532.4377959595-1.70168716926.824.35793392033.67090893042.4028966425-1.70542274656.834.26824171393.63534843442.3700813693-1.70734222326.844.18747530473.59379741442.3395035549-1.70769735156.854.11618100973.54727123722.3112889519-1.70675381376.864.05479525173.49683660942.2855344042-1.70478822286.874.00363978773.44359977222.2623069222-1.70208501486.883.96291823.38869426132.241643091-1.69893326866.893.93271368973.33326836652.2235488149-1.6956234876.93.91298819673.27847242912.2079994013-1.69244437556.913.90358285663.22544611682.1949399806-1.68967965416.923.90421978723.17530581712.1842862561-1.68760493676.933.91450518833.12913228712.175925575-1.68648471246.943.93393371783.08795869612.1697183074-1.6865694626.953.9618940973.05275919322.1654995161-1.68809293936.963.99767588373.02443812472.1630808986-1.69126964856.974.04047733783.00382002182.1622529781-1.69629254316.984.08941429312.99164046662.1627875191-1.70333097166.994.14352993752.9885379392.1644401397-1.712528890874.20180539432.99504673412.1669530911-1.72400336627.014.26317098673.01159102622.1700581732-1.73784337427.024.32651806333.03848014752.1734797536-1.75410891857.034.39071125323.07590513152.1769378566-1.77283046847.044.45460101523.123936562.1801512872-1.7940087257.054.51703634453.18252373772.1828407575-1.81761471597.064.57687749563.25149520222.184731978-1.84359021557.074.63300858133.33056056582.1855586831-1.87184848677.084.68434991013.41931366712.1850655557-1.90227533267.094.7298699253.51723699772.1830110204-1.93473044657.14.76859661243.62370735752.1791698738-1.96904904447.114.79962825573.73800267262.1733357254-2.00504375947.124.82214341533.85930990462.1653232209-2.04250677877.134.83541002463.98673396122.1549700262-2.08121219577.144.8387935024.11930751122.1421385499-2.1209185537.154.83176378964.25600159632.1267173876-2.16137154637.164.81390124074.39573692162.1086224718-2.20230685867.174.78490129244.53739570132.0877979174-2.24345309467.184.74457787014.67983392892.0642165533-2.28453478047.194.69286548774.82189393652.0378801366-2.32527539687.24.62982001994.96241710542.0088192484-2.3654004137.214.55561813825.10025658741.9770928717-2.4046402857.224.47055541655.23428989711.9427876607-2.44273338967.234.37504312775.36343123661.9060169069-2.47942885777.244.2696037665.48664341611.8669192178-2.51448928067.254.15486534485.60294923971.8256569218-2.54769325557.264.03155453265.71144223181.7824142193-2.57883774727.273.90048870235.81129658351.7373951002-2.60774023717.283.76256698235.90177621251.6908210521-2.63424063947.293.61876040695.98224283441.6429285863-2.65820296297.33.47010127566.05216295711.5939666067-2.67951670117.313.31767183736.11111372261.5441936551-2.69809793757.323.16259242546.15878752941.4938750598-2.71389015427.333.00600917276.19499538651.4432800219-2.72686473587.342.84908144386.21966896221.3926786706-2.73702116577.352.69296912086.23286130281.3423391201-2.74438691177.362.53881988486.23474621641.2925245598-2.74901700627.372.38775663096.22561632651.2434904114-2.75099332357.382.24086515756.2058798171.1954815821-2.75042356687.392.09918226426.1760559061.1487298445-2.74743997437.41.96368438956.13676909591.1034513714-2.74219776147.411.83527691426.08874226531.0598444523-2.73487331717.421.71478424716.03278867761.0180874154-2.72566217457.431.60294080335.96980299430.9783367776-2.71477677977.441.50038297445.9007513930.9407256417-2.70244408337.451.40764217755.82666089750.9053623572-2.68890298317.461.32513906255.74860803860.8723294593-2.67440164557.471.25317893795.66770697050.8416828956-2.65919473577.481.19194846875.58509717280.813451548-2.64354058867.491.14151368085.50193087470.7876370548-2.62769835057.51.10181929465.41936033890.7642139326-2.61192512317.511.07268939485.33852514590.7431299963-2.59647314287.521.05382942965.2605396190.7243070705-2.58158702417.531.04482951685.18648052730.7076419846-2.56750109877.541.04516901995.11737520390.6930078384-2.55443687877.551.05422234535.05419020850.6802555232-2.54260067027.561.07126589524.99782066050.6692154818-2.53218136567.571.09548614.94908035930.6596996858-2.5233484357.581.12598844284.90869280120.651503808-2.51625014057.591.16180737474.87728319160.6444095661-2.51101199077.61.20191701344.85537154020.6381872092-2.5077354527.611.24524250624.8433669160.632598122-2.50649692977.621.29067193274.84156292440.6273975146-2.50734702937.631.33706861594.85013445740.62233717-2.51031010437.641.38328370634.86913575120.6171682189-2.51538409577.651.42816894.89849977440.6116439094-2.52254066147.661.47058915114.93803895210.6055223433-2.53172559627.671.50943523814.98744721780.5985691469-2.54285953347.681.54363604595.04630337250.5905600501-2.55583892147.691.57217042895.11407571150.5812833417-2.57053726247.71.59407852245.19012786950.5705421793-2.58680659887.711.60847238055.27372581880.558156724-2.604479237.721.61454582125.36404594470.5439660812-2.62336963967.731.61158337145.4601841070.5278300246-2.64327661177.741.59896821225.56116559090.5096304858-2.66398551057.751.57618903815.6659558340.4892727945-2.68527070047.761.54284575445.77347181480.4666866566-2.70689807587.771.49865394895.88259397440.4418268594-2.72862767587.781.44344808985.99217854230.4146736988-2.75021635227.791.37718341466.10107012880.3852331244-2.77142046277.81.2999364886.20811444620.3535366006-2.79199855867.811.21190442426.31217101880.3196406891-2.81171403867.821.11340278126.41212574140.2836263561-2.83033773847.831.00486214976.50690314740.2455980134-2.84765042857.840.88682347656.59547825270.2056823067-2.86344519387.850.75993217096.67688784370.164026663-2.87752966717.860.62493106136.7502410860.1207976154-2.8897280967.870.48265227876.81472933580.0761789248-2.89988321697.880.33400815586.86963504760.0303695188-2.90785792057.890.17998124396.914339678-0.0164187273-2.91353668787.90.02161355536.9483305009-0.0639633435-2.91682678417.91-0.14000484876.9712062566-0.1120337258-2.91765919757.92-0.30374779936.9826815746-0.1603936756-2.91598931357.93-0.46846535956.9825901203-0.2088039917-2.91179731797.94-0.63299642516.9708864308-0.2570250844-2.90508832747.95-0.79618144856.9476464207-0.304819584-2.89589224387.96-0.95687514646.9130665512-0.3519549141-2.88426333777.97-1.11395904886.8674616717-0.3982058025-2.87027956627.98-1.26635375456.8112615587-0.4433567021-2.85404163217.99-1.4130307556.745006189-0.4872040944-2.83567179838-1.55302369846.6693397998-0.5295586527-2.81531246928.01-1.68543896926.5850038013-0.5702472404-2.79312455688.02-1.80946546566.492828619-0.6091147229-2.76928564988.03-1.924383476.3937245567-0.6460255755-2.74398800778.04-2.02957251126.2886717802-0.6808652683-2.71743640078.05-2.12451813456.178709532-0.7135414156-2.68984582168.06-2.20881750416.0649246957-0.7439846774-2.66143909488.07-2.28218377585.9484398371-0.7721494033-2.63244440828.08-2.34444919235.8304008517-0.7980140141-2.60309279718.09-2.39556686745.7119643571-0.8215811172-2.57361560658.1-2.43561123815.5942849669-0.842877356-2.54424196058.11-2.46477718125.4785025881-0.8619529949-2.51519626678.12-2.48337780285.3657298807-0.8788812476-2.48669578228.13-2.49184092685.257040018-0.8937573548-2.45894826888.14-2.49070431845.1534548828-0.906697424-2.43214976158.15-2.48060969785.0559338292-0.9178370449-2.40648247598.16-2.46229560934.965363133-0.9273296958-2.38211287538.17-2.43658922294.882546249-0.9353449599-2.35918991998.18-2.40439716094.8081949799-0.9420665723-2.33784351468.19-2.36669544934.7429216562-0.9476903186-2.31818317398.2-2.32451870494.6872324121-0.9524218104-2.30029691578.21-2.27894867694.6415216318-0.9564741607-2.28425039668.22-2.23110226994.606067627-0.9600655878-2.27008629688.23-2.18211918024.5810295944-0.9634169712-2.25782395998.24-2.13314928064.5664458848-0.9667493897-2.24745929168.25-2.08533989364.5622336047-0.9702816659-2.2389649168.26-2.03982309324.5681895537-0.9742279469-2.23229058848.27-1.99770317484.5839924874-0.9787953452-2.22736385758.28-1.96004443084.6092066819-0.984181667-2.22409096948.29-1.9278593684.6432867589-0.9905732524-2.22235800278.3-1.90209749494.6855837203-0.99814295-2.22203222128.31-1.88363480354.7353521236-1.0070482486-2.22296362768.32-1.87326406134.7917583212-1.0174295851-2.22498670198.33-1.87168601994.8538896715-1.0294088472-2.22792230318.34-1.87950163794.9207646203-1.0430880862-2.23157971328.35-1.89720540294.9913435426-1.0585484532-2.23575880178.36-1.92517982685.0645402242-1.0758493696-2.24025228328.37-1.96369117455.1392338566-1.0950279404-2.24484804698.38-2.01288647425.2142814148-1.1160986148-2.24933152868.39-2.07279183995.288530279-1.1390530986-2.25348810088.4-2.14331212775.3608309634-1.1638605161-2.25710545468.41-2.22423192695.4300498108-1.1904678207-2.25997594618.42-2.31521787685.4950815133-1.2188004477-2.26189888268.43-2.41582228285.5548613216-1.248763201-2.26268272358.44-2.52548799225.6083768078-1.2802413644-2.26214717168.45-2.6435544765.6546790527-1.3131020218-2.26012513328.46-2.76926504995.6928931335-1.3471955739-2.25646452458.47-2.90177515485.7222277983-1.382357432-2.25102990648.48-3.04016160535.7419842178-1.41840987-2.24370393028.49-3.18343270495.7515637211-1.4551640139-2.23438857768.5-3.33053911625.7504744274-1.4924219458-2.22300618498.51-3.48038536635.7383367033-1.5299789004-2.20950023818.52-3.63184186095.7148873833-1.5676255265-2.19383593288.53-3.78375727435.6799827079-1.6051501915-2.17600049398.54-3.93497117985.6335999479-1.6423413017-2.15600325088.55-4.08432677995.5758376951-1.6789896128-2.13387547038.56-4.23068359795.5069148176-1.7148905061-2.10966994838.57-4.37292998915.4271680908-1.7498462043-2.08346036758.58-4.5099953365.33704853-1.7836679047-2.05534042688.59-4.64086179085.2371164655-1.816177804-2.02542275558.6-4.7645754385.1280354135-1.847210995-1.99383762288.61-4.88025675295.0105648116-1.8766172148-1.96073145918.62-4.98711024124.8855516978-1.9042624237-1.92626520528.63-5.08443315294.7539214249-1.9300302012-1.89061250958.64-1.9538229421-1.85395779158.65-1.975562841-1.81649419578.66-1.9951926564-1.77842145778.67-2.0126762443-1.73994370548.68-2.0279988599-1.70126722288.69-2.041167221-1.66259819698.7-2.0522093369-1.62414047628.71-2.0611741035-1.58609336368.72-2.0681306704-1.5486494688.73-2.0731675886-1.51199263858.74-2.0763917482-1.47629600288.75-2.0779271186-1.44172013178.76-2.0779133071-1.40841134948.77-2.0765039506-1.37650020678.78-2.0738649603-1.34610013418.79-2.0701726383-1.31730628888.8-2.0656116881-1.29019460718.81-2.0603731407-1.26482107188.82-2.0546522196-1.24122120268.83-2.0486461689-1.21940977318.84-2.0425520672-1.19938075768.85-2.0365646537-1.18110750638.86-2.0308741876-1.1645431478.87-2.0256643665-1.1496212088.88-2.0211103251-1.13625645328.89-2.0173767364-1.12434592128.9-2.0146160362-1.11377015458.91-2.0129667886-1.10439460558.92-2.0125522121-1.09607120338.93-2.0134788791-1.0886400628.94-2.0158356055-1.08193131318.95-2.0196925393-1.07576703998.96-2.0251004584-1.06996329298.97-2.0320902848-1.06433216338.98-2.0406728193-1.05868389218.99-2.050838699-1.05282899079-2.0625585762-1.04658035069.01-2.0757835178-1.03975531829.02-2.0904456175-1.03217771239.03-2.1064588157-1.02367976269.04-2.1237199149-1.01410394789.05-2.1421097806-1.00330471359.06-2.1614947126-0.99115005229.07-2.1817279714-0.97752292749.08-2.2026514418-0.96232252789.09-2.2240974157-0.94546533789.1-2.2458904734-0.92688601349.11-2.2678494422-0.90653805549.12-2.2897894111-0.88439427199.13-2.3115237788-0.86044702729.14-2.3328663117-0.83470827389.15-2.3536331911-0.80720937039.16-2.3736450247-0.77800068499.17-2.3927288027-0.74715099259.18-2.4107197755-0.71474667179.19-2.4274632336-0.68089071059.2-2.4428161699-0.64570153479.21-2.4566488079-0.60931166989.22-2.4688459771-0.57186625429.23-2.479308324-0.53352141859.24-2.4879533435-0.49444255179.25-2.4947162218-0.45480247119.26-2.4995504814-0.41477951889.27-2.5024284223-0.37455560459.28-2.5033413549-0.33431421659.29-2.5022996233-0.29423842439.3-2.49933242-0.25450889239.31-2.494487393-0.21530192919.32-2.4878300537-0.17678759159.33-2.4794429887-0.13912786569.34-2.4694248895-0.10247494249.35-2.4578894071-0.066969619.36-2.4449638489-0.03273977559.37-2.43078772920.00010086429.38-2.41551119260.03145399099.39-2.39929332660.06123765949.4-2.38230038250.08938710869.41-2.3647039260.11585537939.42-2.34667893560.14061373529.43-2.32840187230.16365188089.44-2.31004874030.18497797659.45-2.29179316130.20461845049.46-2.27380448240.22261761019.47-2.25624593930.23903705989.48-2.23927289360.25395492929.49-2.22303116460.26746492419.5-2.20765547270.27967520999.51-2.19326801120.29070713979.52-2.17997716180.30069384429.53-2.16787636780.30977869599.54-2.15704317530.31811366849.55-2.14753845450.32585760729.56-2.13940580660.3331744329.57-2.13267116410.34023129059.58-2.12734258660.34719668419.59-2.12341025440.35423858689.6-2.12084665910.36152257699.61-2.1196069880.36921000319.62-2.11962969730.37745620429.63-2.12083726770.38640880289.64-2.12313713250.39620608969.65-2.12642276780.40697551849.66-2.1305749320.41883232549.67-2.13546304040.43187828879.68-2.14094665940.44620064119.69-2.1468771030.46187114729.7-2.15309911440.47894535469.71-2.15945261240.49746202649.72-2.16577448490.51744276079.73-2.1719004090.53889180069.74-2.17766667590.56179603629.75-2.18291200370.58612519699.76-2.18747931540.61183223279.77-2.19121746420.63885387799.78-2.19398288620.66711139189.79-2.19564116470.69651146579.8-2.19606848610.72694728789.81-2.1951529750.7582997529.82-2.19279589220.7904387979.83-2.18891268360.82322486119.84-2.18343386930.85651043579.85-2.17630576360.89014170029.86-2.16749101860.923960229.87-2.15696898580.95780468849.88-2.1447358930.99151269359.89-2.13080483561.02492249089.9-2.11520558151.05787476049.91-2.09798419471.09021433249.92-2.07920248071.1217918589.93-2.05893726111.1524654129.94-2.03727948691.18210200629.95-2.0143331991.21057899899.96-1.99021435011.23778538579.97-1.96504949971.26362295699.98-1.93897439831.28800730989.99-1.91213247581.310868705510-1.88467325251.33215276110.01-1.85675068871.351820970510.02-1.82852149251.369851048910.03-1.80014340481.386237097310.04-1.77177347891.400989586910.05-1.74356637581.414135163410.06-1.71567269181.425716274510.07-1.68823733791.43579062510.08-1.6613979891.444430467710.09-1.63528361761.451721735410.1-1.61001313071.457763028110.11-1.58569412181.462664463810.12-1.56242175261.466546408110.13-1.5402777771.469538096210.14-1.51932971511.47177616310.15-1.49963018791.473403098210.16-1.48121641891.47456564310.17-1.46410990621.47541314710.18-1.44831626991.476095902910.19-1.43382527431.47676347810.2-1.42061102451.477563060610.21-1.40863233441.478637838610.22-1.39783326231.4801254310.23-1.38814380521.482156380310.24-1.37948074691.48485274410.25-1.37174864611.488326765510.26-1.36484095731.492679673610.27-1.35864126711.498000601710.28-1.3530246361.504365645810.29-1.3478590281.511837069610.3-1.34300681211.52046266610.31-1.33832632041.530275279210.32-1.33367344371.541292494110.33-1.32890324791.55351649510.34-1.32387159331.566934094410.35-1.31843673811.581516930410.36-1.31246091021.597221831210.37-1.30581182791.613991341110.38-1.29836415571.631754400810.39-1.29000087631.650427176310.4-1.28061456711.669914023810.41-1.27010856531.690108581910.42-1.25839801051.710894976810.43-1.24541075311.732149128110.44-1.23108811981.753740139410.45-1.2153855271.775531758610.46-1.19827293791.797383892110.47-1.17973515731.819154154410.48-1.1597719621.840699437710.49-1.13839806611.861877483710.5-1.11564292231.882548438510.51-1.09155036231.902576377110.52-1.06617807951.921830777410.53-1.03959696261.940187929610.54-1.01189028571.957532265410.55-0.98315276641.973757592310.56-0.9534895011.988768220410.57-0.92301479032.002479969510.58-0.89185086882.014821045110.59-0.86012655182.025732776210.6-0.82797581512.035170204710.61-0.79553632452.04310252310.62-0.76294792962.049513353810.63-0.73035114012.054400870610.64-0.69788560142.057777757810.65-0.66568858452.059671011610.66-0.63389350922.06012158510.67-0.60262851532.059183880210.68-0.5720150972.056925095910.69-0.54216681652.053424436610.7-0.51318810932.048772193210.71-0.48517319552.043068705410.72-0.45820510662.036423218610.73-0.43235484042.028952646810.74-0.40768065052.020780257110.75-0.38422747982.012034289110.76-0.36202654142.002846526110.77-0.34109505351.993350832810.78-0.32143612781.98368167610.79-0.30303881491.973972645410.8-0.28587830271.964354989610.81-0.26991626741.954956184310.82-0.25510137141.94589854810.83-0.24136990181.937297919210.84-0.22864654311.929262412210.85-0.2168452741.921891260810.86-0.20587037831.915273766610.87-0.19561755821.909488359210.88-0.18597513791.904601781310.89-0.17682534311.900668404910.9-0.16804564231.897729686610.91-0.15951013551.895813767910.92-0.15109097361.894935223110.93-0.14265979461.895094957810.94-0.13408915831.896280258310.95-0.12525396591.

Coulomb Crystals and Ground State Cooling of Single Ca + Ions in a Penning T rap

Documents

micromotionbig trap

trap centreto

penning trap axialmod

trap centremagnetron

ttypical trap frequencies

ion traps

single ion

nm diode laser