From 7bd2cc8f2ede25bccf7043a24b300b0d2d16d0b1 Mon Sep 17 00:00:00 2001 From: Alex Maryewski <88265145+alexmaryewski@users.noreply.github.com> Date: Thu, 27 Jun 2024 14:56:47 +0200 Subject: [PATCH] Implement mGGA, SAP guess, orbital gradient --- .gitignore | 1 + AUTHORS.rst | 2 + sktools/src/sktools/calculators/sktwocnt.py | 4 +- sktools/src/sktools/calculators/slateratom.py | 66 +- sktools/src/sktools/xcfunctionals.py | 89 +- sktwocnt/lib/twocnt.f90 | 119 +- sktwocnt/lib/xcfunctionals.f90 | 38 + sktwocnt/prog/input.f90 | 25 +- sktwocnt/prog/main.f90 | 2 +- slateratom/lib/CMakeLists.txt | 1 + slateratom/lib/density.f90 | 138 +- slateratom/lib/dft.f90 | 70 +- slateratom/lib/globals.f90 | 17 +- slateratom/lib/hamiltonian.f90 | 41 +- slateratom/lib/output.f90 | 37 +- slateratom/lib/sap.f90 | 45265 ++++++++++++++++ slateratom/lib/utilities.f90 | 135 +- slateratom/lib/xcfunctionals.f90 | 817 +- slateratom/prog/main.f90 | 50 +- 19 files changed, 46787 insertions(+), 130 deletions(-) create mode 100644 slateratom/lib/sap.f90 diff --git a/.gitignore b/.gitignore index d1a19546..d42d53c7 100644 --- a/.gitignore +++ b/.gitignore @@ -11,3 +11,4 @@ __pycache__ _gitmsg.saved.txt *.egg-info dist +.vscode/ diff --git a/AUTHORS.rst b/AUTHORS.rst index 100af573..810a30eb 100644 --- a/AUTHORS.rst +++ b/AUTHORS.rst @@ -15,4 +15,6 @@ contributed to this package : * Christof Köhler (University of Bremen) +* Alexander Maryewski (Karlsruhe Institute of Technology, Germany) + * Thomas Niehaus (University of Lyon, France) diff --git a/sktools/src/sktools/calculators/sktwocnt.py b/sktools/src/sktools/calculators/sktwocnt.py index c58a56aa..d73f5668 100644 --- a/sktools/src/sktools/calculators/sktwocnt.py +++ b/sktools/src/sktools/calculators/sktwocnt.py @@ -11,7 +11,9 @@ SUPPORTED_FUNCTIONALS = {'lda' : 1, 'pbe' : 2, 'blyp' : 3, 'lcy-pbe' : 4, 'lcy-bnl' : 5, 'pbe0' : 6, 'b3lyp' : 7, - 'camy-b3lyp' : 8, 'camy-pbeh' : 9} + 'camy-b3lyp' : 8, 'camy-pbeh' : 9, 'tpss': 10, + 'scan': 11, 'r2scan': 12, 'r4scan': 13, 'task': 14, + 'task+cc': 15} INPUT_FILE = "sktwocnt.in" STDOUT_FILE = "output" diff --git a/sktools/src/sktools/calculators/slateratom.py b/sktools/src/sktools/calculators/slateratom.py index 5659ddb6..694489b4 100644 --- a/sktools/src/sktools/calculators/slateratom.py +++ b/sktools/src/sktools/calculators/slateratom.py @@ -16,9 +16,25 @@ LOGGER = logging.getLogger('slateratom') -SUPPORTED_FUNCTIONALS = {'lda' : 2, 'pbe' : 3, 'blyp' : 4, 'lcy-pbe' : 5, - 'lcy-bnl' : 6, 'pbe0' : 7, 'b3lyp' : 8, - 'camy-b3lyp' : 9, 'camy-pbeh' : 10} +SUPPORTED_FUNCTIONALS = { + "lda": 2, + "pbe": 3, + "blyp": 4, + "lcy-pbe": 5, + "lcy-bnl": 6, + "pbe0": 7, + "b3lyp": 8, + "camy-b3lyp": 9, + "camy-pbeh": 10, + "tpss": 11, + "scan": 12, + "r2scan": 13, + "r4scan": 14, + "task": 15, + "task+cc": 16 +} + +SUPPORTED_MIXERS = {1: 'simple', 2: "broyden"} INPUT_FILE = "slateratom.in" STDOUT_FILE = "output" @@ -63,12 +79,14 @@ class SlaterAtomSettings(sc.ClassDict): Maximal power for every angular momentum. """ - def __init__(self, exponents, maxpowers, scftol, maxscfiter): + def __init__(self, exponents, maxpowers, scftol, maxscfiter, mixer_id, mixing_parameter): super().__init__() self.exponents = exponents self.maxpowers = maxpowers self.scftol = scftol self.maxscfiter = maxscfiter + self.mixer = mixer_id + self.mixing_parameter = mixing_parameter @classmethod def fromhsd(cls, root, query): @@ -80,7 +98,11 @@ def fromhsd(cls, root, query): root, "scftolerance", converter=conv.float0, defvalue=1.0e-10) maxscfiter = query.getvalue( root, "maxscfiterations", converter=conv.int0, defvalue=120) - return cls(exponents, maxpowers, scftol, maxscfiter) + mixer_id = query.getvalue( + root, "mixer", converter=conv.int0, defvalue=2) + mixing_parameter = query.getvalue( + root, "mixingparameter", converter=conv.float0, defvalue=0.1) + return cls(exponents, maxpowers, scftol, maxscfiter, mixer_id, mixing_parameter) def __eq__(self, other): if not isinstance(other, SlaterAtomSettings): @@ -167,6 +189,14 @@ def __init__(self, settings, atomconfig, functional, compressions): msg = "Slateratom: Maximum number of SCF iterations must be >=1" raise sc.SkgenException(msg) + if self._settings.mixer not in SUPPORTED_MIXERS.keys(): + msg = f"Slateratom: mixer {self._settings.mixer} not found" + raise sc.SkgenException(msg) + + if not (0. <= self._settings.mixing_parameter <= 1.): + msg = "Slateratom: mixing parameter must lie within the [0, 1] interval" + raise sc.SkgenException(msg) + if self.isXCFunctionalSupported(functional): xcfkey = functional.type self._functional = SUPPORTED_FUNCTIONALS[xcfkey] @@ -326,8 +356,8 @@ def write(self, workdir): out.append("{:s} \t\t{:s} write eigenvectors".format( self._LOGICALSTRS[False], self._COMMENT)) - out.append("{} {:g} \t\t{:s} broyden mixer, mixing factor".format( - 2, 0.1, self._COMMENT)) + out.append("{} {:g} \t\t{:s} mixer, mixing factor".format( + self._settings.mixer, self._settings.mixing_parameter, self._COMMENT)) # Occupations for ll, occperl in enumerate(self._atomconfig.occupations): @@ -527,19 +557,15 @@ def get_density012(self): density : GridData Grid data with the density and its first and second derivatives. """ - fp = open(os.path.join(self._workdir, "dens.dat"), "r") - fp.readline() - fp.readline() - fp.readline() - fp.readline() - fp.readline() - ngrid = int(fp.readline()) - # noinspection PyNoneFunctionAssignment,PyTypeChecker - dens = np.fromfile(fp, dtype=float, count=ngrid * 7, sep=" ") - fp.close() - dens.shape = (ngrid, 7) - grid = oc.RadialGrid(dens[:,0], dens[:,1]) - density = dens[:,2:5] + + with open(os.path.join(self._workdir, "dens.dat"), 'r') as handle: + lines_ = [x.split() for x in handle.readlines()] + datarray = np.asarray(lines_[6:], dtype=float) + grid = oc.RadialGrid(datarray[:,0], datarray[:,1]) + density = datarray[:,2:5] + if datarray.shape[1] == 8: + density = np.column_stack([density, datarray[:, 7]]) + return oc.GridData(grid, density) def get_wavefunction012(self, ss, nn, ll): diff --git a/sktools/src/sktools/xcfunctionals.py b/sktools/src/sktools/xcfunctionals.py index 47e53ec5..e5cbc8cf 100644 --- a/sktools/src/sktools/xcfunctionals.py +++ b/sktools/src/sktools/xcfunctionals.py @@ -188,6 +188,69 @@ def fromhsd(cls, root, query): myself.beta = 1.0 return myself +class XCTPSS(sc.ClassDict): + """mGGA TPSS xc-functional.""" + + @classmethod + def fromhsd(cls, root, query): + """Creates instance from a HSD-node and with given query object.""" + myself = cls() + myself.type = "tpss" + return myself + + +class XCSCAN(sc.ClassDict): + """mGGA SCAN xc-functional.""" + + @classmethod + def fromhsd(cls, root, query): + """Creates instance from a HSD-node and with given query object.""" + myself = cls() + myself.type = "scan" + return myself + + +class XCR2SCAN(sc.ClassDict): + """mGGA r2SCAN xc-functional.""" + + @classmethod + def fromhsd(cls, root, query): + """Creates instance from a HSD-node and with given query object.""" + myself = cls() + myself.type = "r2scan" + return myself + + +class XCR4SCAN(sc.ClassDict): + """mGGA r4SCAN xc-functional.""" + + @classmethod + def fromhsd(cls, root, query): + """Creates instance from a HSD-node and with given query object.""" + myself = cls() + myself.type = "r4scan" + return myself + + +class XCTASK(sc.ClassDict): + """mGGA TASK xc-functional.""" + + @classmethod + def fromhsd(cls, root, query): + """Creates instance from a HSD-node and with given query object.""" + myself = cls() + myself.type = "task" + return myself + +class XCTASK_CC(sc.ClassDict): + """mGGA TASK+CC xc-functional.""" + + @classmethod + def fromhsd(cls, root, query): + """Creates instance from a HSD-node and with given query object.""" + myself = cls() + myself.type = "task+cc" + return myself class XCLocal(sc.ClassDict): '''Local xc-functional.''' @@ -235,14 +298,20 @@ def fromhsd(cls, root, query): # Registered xc-functionals with corresponding HSD name as key: XCFUNCTIONALS = { - 'lcy-bnl': XCLCYBNL, - 'lcy-pbe': XCLCYPBE, - 'local': XCLocal, - 'pbe': XCPBE, - 'lda': XCLDA, - 'blyp': XCBLYP, - 'pbe0': XCPBE0, - 'b3lyp': XCB3LYP, - 'camy-b3lyp': XCCAMYB3LYP, - 'camy-pbeh': XCCAMYPBEH + "lcy-bnl": XCLCYBNL, + "lcy-pbe": XCLCYPBE, + "local": XCLocal, + "pbe": XCPBE, + "lda": XCLDA, + "blyp": XCBLYP, + "pbe0": XCPBE0, + "b3lyp": XCB3LYP, + "camy-b3lyp": XCCAMYB3LYP, + "camy-pbeh": XCCAMYPBEH, + "tpss": XCTPSS, + "scan": XCSCAN, + "r2scan": XCR2SCAN, + "r4scan": XCR4SCAN, + "task": XCTASK, + "task+cc": XCTASK_CC } diff --git a/sktwocnt/lib/twocnt.f90 b/sktwocnt/lib/twocnt.f90 index 9c63bf24..a42de140 100644 --- a/sktwocnt/lib/twocnt.f90 +++ b/sktwocnt/lib/twocnt.f90 @@ -22,9 +22,11 @@ module twocnt use, intrinsic :: iso_c_binding, only : c_size_t use xc_f03_lib_m, only : xc_f03_func_t, xc_f03_func_init, xc_f03_func_end, xc_f03_lda_vxc,& - & xc_f03_gga_vxc, XC_LDA_X, XC_LDA_X_YUKAWA, XC_LDA_C_PW, XC_GGA_X_PBE, XC_GGA_C_PBE,& - & XC_GGA_X_B88, XC_GGA_C_LYP, XC_GGA_X_SFAT_PBE, XC_HYB_GGA_XC_B3LYP,& - & XC_HYB_GGA_XC_CAMY_B3LYP, XC_UNPOLARIZED, xc_f03_func_set_ext_params + & xc_f03_gga_vxc, xc_f03_mgga_vxc, XC_LDA_X, XC_LDA_X_YUKAWA, XC_LDA_C_PW, XC_GGA_X_PBE,& + & XC_GGA_C_PBE, XC_GGA_X_B88, XC_GGA_C_LYP, XC_GGA_X_SFAT_PBE, XC_MGGA_X_TPSS, XC_MGGA_C_TPSS,& + & XC_MGGA_X_SCAN, XC_MGGA_C_SCAN, XC_MGGA_X_R2SCAN, XC_MGGA_C_R2SCAN, XC_MGGA_X_R4SCAN,& + & XC_MGGA_X_TASK, XC_HYB_GGA_XC_B3LYP, XC_HYB_GGA_XC_CAMY_B3LYP, XC_MGGA_C_CC, & + & XC_UNPOLARIZED, xc_f03_func_set_ext_params implicit none private @@ -61,7 +63,7 @@ module twocnt type(TGridorb2) :: pot !> atomic density and 1st/2nd derivative on grid - type(TGridorb2) :: rho, drho, ddrho + type(TGridorb2) :: rho, drho, ddrho, tau end type TAtomdata @@ -122,6 +124,9 @@ module twocnt !! true, if a CAM functional is requested logical :: tCam + !! true, if a MGGA functional is requested + logical :: tMGGA + !> atomic properties of slateratom code, in the homonuclear case only atom1 is read type(TAtomdata) :: atom1, atom2 @@ -269,6 +274,24 @@ subroutine get_twocenter_integrals(inp, imap, skham, skover) call xc_f03_func_init(xcfunc_x, XC_GGA_X_PBE, XC_UNPOLARIZED) ! cpbe96 call xc_f03_func_init(xcfunc_c, XC_GGA_C_PBE, XC_UNPOLARIZED) + case(xcFunctional%MGGA_TPSS) + call xc_f03_func_init(xcfunc_x, XC_MGGA_X_TPSS, XC_UNPOLARIZED) + call xc_f03_func_init(xcfunc_c, XC_MGGA_C_TPSS, XC_UNPOLARIZED) + case(xcFunctional%MGGA_SCAN) + call xc_f03_func_init(xcfunc_x, XC_MGGA_X_SCAN, XC_UNPOLARIZED) + call xc_f03_func_init(xcfunc_c, XC_MGGA_C_SCAN, XC_UNPOLARIZED) + case(xcFunctional%MGGA_r2SCAN) + call xc_f03_func_init(xcfunc_x, XC_MGGA_X_R2SCAN, XC_UNPOLARIZED) + call xc_f03_func_init(xcfunc_c, XC_MGGA_C_R2SCAN, XC_UNPOLARIZED) + case(xcFunctional%MGGA_r4SCAN) + call xc_f03_func_init(xcfunc_x, XC_MGGA_X_R4SCAN, XC_UNPOLARIZED) + call xc_f03_func_init(xcfunc_c, XC_MGGA_C_R2SCAN, XC_UNPOLARIZED) + case(xcFunctional%MGGA_TASK) + call xc_f03_func_init(xcfunc_x, XC_MGGA_X_TASK, XC_UNPOLARIZED) + call xc_f03_func_init(xcfunc_c, XC_LDA_C_PW, XC_UNPOLARIZED) + case(xcFunctional%MGGA_TASK_CC) + call xc_f03_func_init(xcfunc_x, XC_MGGA_X_TASK, XC_UNPOLARIZED) + call xc_f03_func_init(xcfunc_c, XC_MGGA_C_CC, XC_UNPOLARIZED) end select if (inp%tLC .or. inp%tCam) then @@ -439,7 +462,8 @@ subroutine getskintegrals(beckeInt, radialHFQuadrature, nRad, nAng, atom1, atom2 !> xc-functional type !! (1: LDA-PW91, 2: GGA-PBE96, 3: GGA-BLYP, 4: LCY-PBE96, 5: LCY-BNL, 6: PBE0, 7: B3LYP, - !! 8: CAMY-B3LYP, 9: CAMY-PBEh) + !! 8: CAMY-B3LYP, 9: CAMY-PBEh, 10: TPSS, 11: SCAN, 12: r2SCAN, 13: r4SCAN, 14: TASK, + !! 15: TASK+CC) integer, intent(in) :: iXC !> CAM alpha parameter @@ -482,7 +506,7 @@ subroutine getskintegrals(beckeInt, radialHFQuadrature, nRad, nAng, atom1, atom2 real(dp), allocatable :: radval2(:,:), radval2p(:,:), radval2pp(:,:) !! total potential and electron density of two atoms - real(dp), allocatable :: potval(:), densval(:) + real(dp), allocatable :: potval(:), densval(:), tauval(:), taupotval(:) !! atomic 1st density derivatives of atom 1 real(dp), allocatable :: densval1p(:) @@ -511,9 +535,12 @@ subroutine getskintegrals(beckeInt, radialHFQuadrature, nRad, nAng, atom1, atom2 !! integral index integer :: ii + !! dummy laplacian + real(dp), allocatable :: lapl(:), vlapl(:) + !! libxc related objects real(dp), allocatable :: vxc(:), vx(:), vx_sr(:), vc(:) - real(dp), allocatable :: rhor(:), sigma(:), vxcsigma(:), vxsigma(:), vxsigma_sr(:), vcsigma(:) + real(dp), allocatable :: rhor(:), sigma(:), tau(:), vxcsigma(:), vxsigma(:), vxsigma_sr(:), vcsigma(:), vxtau(:), vctau(:) real(dp), allocatable :: divvxc(:), divvx(:), divvc(:) r1 => grid1(:, 1) @@ -564,6 +591,18 @@ subroutine getskintegrals(beckeInt, radialHFQuadrature, nRad, nAng, atom1, atom2 densval2p = atom2%drho%getValue(r2) ! care about correct 4pi normalization of density and compute sigma sigma = getLibxcSigma(densval1p, densval2p, dots) + if (xcFunctional%isMGGA(iXC)) then + allocate(tauval(nGrid)) + tauval(:) = atom1%tau%getValue(r1) + atom2%tau%getValue(r2) + tau = getLibxcTau(tauval) + + allocate(vxtau(nGrid)) + vxtau(:) = 0.0_dp + if (iXC /= xcFunctional%MGGA_TASK) then + allocate(vctau(nGrid)) + vctau(:) = 0.0_dp + end if + end if end if if (tGlobalHybrid .or. tCam) then allocate(vxc(nGrid)) @@ -593,6 +632,27 @@ subroutine getskintegrals(beckeInt, radialHFQuadrature, nRad, nAng, atom1, atom2 call getDivergence(nRad, nAng, densval1p, densval2p, r1, r2, theta1, theta2, vxsigma, divvx) call getDivergence(nRad, nAng, densval1p, densval2p, r1, r2, theta1, theta2, vcsigma, divvc) potval = vx + vc + divvx + divvc + ! 10: MGGA-TPSS, 11: MGGA-SCAN, 12: MGGA-r2SCAN, 13: MGGA-r4SCAN, + ! 14: MGGA-TASK, 15: MGGA-TASK+CC + case(10:15) + ! MGGA exchange + call xc_f03_mgga_vxc(xcfunc_x, nGridLibxc, rhor(1), sigma(1), lapl(1), tau(1),& + & vx(1), vxsigma(1), vlapl(1), vxtau(1)) + call getDivergence(nRad, nAng, densval1p, densval2p, r1, r2, theta1, theta2, vxsigma, divvx) + ! 11: MGGA-TPSS, 12: MGGA-SCAN, 13: MGGA-r2SCAN, 14: MGGA-TASK + if (iXC /= xcFunctional%MGGA_TASK) then + ! MGGA correlation + call xc_f03_mgga_vxc(xcfunc_c, nGridLibxc, rhor(1), sigma(1), lapl(1), tau(1),& + & vc(1), vcsigma(1), vlapl(1), vctau(1)) + call getDivergence(nRad, nAng, densval1p, densval2p, r1, r2, theta1, theta2, vcsigma, divvc) + potval = vx + vc + divvx + divvc + taupotval = vxtau + vctau + else + ! LDA correlation for TASK + call xc_f03_lda_vxc(xcfunc_c, nGridLibxc, rhor(1), vc(1)) + potval = vx + vc + divvx + taupotval = vxtau + end if ! 5: LCY-BNL case(xcFunctional%LCY_BNL) call xc_f03_lda_vxc(xcfunc_x, nGridLibxc, rhor(1), vx(1)) @@ -654,7 +714,7 @@ subroutine getskintegrals(beckeInt, radialHFQuadrature, nRad, nAng, atom1, atom2 ! calculate SK-quantities ! Hamiltonian integ1 = getHamiltonian(radval1(:, i1), radval2(:, i2), radval2p(:, i2), radval2pp(:, i2),& - & r2, l2, spherval1, spherval2, potval, weights) + & r2, l2, spherval1, spherval2, potval, taupotval, weights) ! overlap integral: \sum_{r,\Omega} R_1(r) Y_1(\Omega) R_2(r) Y_2(\Omega) weight integ2 = getOverlap(radval1(:, i1), radval2(:, i2), spherval1, spherval2, weights) ! total density: \int (|\phi_1|^2 + |\phi_2|^2) @@ -735,6 +795,20 @@ pure function getLibxcSigma(drho1, drho2, dots) result(sigma) end function getLibxcSigma + !> Calculates libXC renormalized density superposition of dimer. + pure function getLibxcTau(tau) result(tau_libxc) + + !> superposition of atomic densities of atom 1 and atom 2 + real(dp), intent(in) :: tau(:) + + !> renormalized density + real(dp), allocatable :: tau_libxc(:) + + ! renorm rho (incoming quantities are 4pi normed) + tau_libxc = tau * rec4pi + + end function getLibxcTau + !> Computes contribution div(v) to the xc-potential due to vsigma = deps/dsigma returned by libxc. !! div(v) = -2 div(vsigma grad(n)), evaluated in spherical coordinates r1, theta1 as: @@ -895,8 +969,8 @@ end function getdensity !> Calculates Hamiltonian for a fixed orbital and interaction configuration. - pure function getHamiltonian(rad1, rad2, rad2p, rad2pp, r2, l2, spher1, spher2, pot, weights)& - & result(res) + pure function getHamiltonian(rad1, rad2, rad2p, rad2pp, r2, l2, spher1,& + & spher2, pot, pot_tau, weights) result(res) !> radial grid-orbital portion of atom 1 and atom 2 real(dp), intent(in) :: rad1(:), rad2(:) @@ -916,18 +990,31 @@ pure function getHamiltonian(rad1, rad2, rad2p, rad2pp, r2, l2, spher1, spher2, !> effective potential on grid real(dp), intent(in) :: pot(:) + !> effective potential on grid + real(dp), intent(in), allocatable :: pot_tau(:) + !> integration weights real(dp), intent(in) :: weights(:) !! resulting Hamiltonian matrix element real(dp) :: res - res = sum((rad1 * spher1)& - & * (- 0.5_dp * rad2pp& - & - rad2p / r2& - & + 0.5_dp * l2 * (l2 + 1) * rad2 / r2**2& - & + pot * rad2)& - & * spher2 * weights) + if (allocated(pot_tau)) then + res = sum((rad1 * spher1)& + & * ((- 0.5_dp * rad2pp& + & - rad2p / r2& + & + 0.5_dp * l2 * (l2 + 1) * rad2 / r2**2)& + & * (1.0_dp + pot_tau)& + & + pot * rad2)& + & * spher2 * weights) + else + res = sum((rad1 * spher1)& + & * (- 0.5_dp * rad2pp& + & - rad2p / r2& + & + 0.5_dp * l2 * (l2 + 1) * rad2 / r2**2& + & + pot * rad2)& + & * spher2 * weights) + end if end function getHamiltonian diff --git a/sktwocnt/lib/xcfunctionals.f90 b/sktwocnt/lib/xcfunctionals.f90 index b12325d5..fe1b0800 100644 --- a/sktwocnt/lib/xcfunctionals.f90 +++ b/sktwocnt/lib/xcfunctionals.f90 @@ -37,10 +37,29 @@ module xcfunctionals !> CAMY-PBEh integer :: CAMY_PBEh = 9 + !> TPSS + integer :: MGGA_TPSS = 10 + + !> SCAN + integer :: MGGA_SCAN = 11 + + !> r2SCAN + integer :: MGGA_r2SCAN = 12 + + !> r4SCAN + integer :: MGGA_r4SCAN = 13 + + !> TASK + integer :: MGGA_TASK = 14 + + !> TASK+CC + integer :: MGGA_TASK_CC = 15 + contains procedure :: isLDA => TXcFunctionalsEnum_isLDA procedure :: isGGA => TXcFunctionalsEnum_isGGA + procedure :: isMGGA => TXcFunctionalsEnum_isMGGA procedure :: isGlobalHybrid => TXcFunctionalsEnum_isGlobalHybrid procedure :: isLongRangeCorrected => TXcFunctionalsEnum_isLongRangeCorrected procedure :: isCAMY => TXcFunctionalsEnum_isCAMY @@ -90,6 +109,25 @@ pure function TXcFunctionalsEnum_isGGA(this, xcnr) result(isGGA) end function TXcFunctionalsEnum_isGGA + pure function TXcFunctionalsEnum_isMGGA(this, xcnr) result(isMGGA) + + !> Class instance + class(TXcFunctionalsEnum), intent(in) :: this + + !> identifier of exchange-correlation type + integer, intent(in) :: xcnr + + !> True, if xc-functional index corresponds to a GGA functional + logical :: isMGGA + + isMGGA = .false. + + if (xcnr == this%MGGA_TPSS .or. xcnr == this%MGGA_SCAN& + & .or. xcnr == this%MGGA_r2SCAN .or. xcnr == this%MGGA_r4SCAN& + & .or. xcnr == this%MGGA_TASK .or. xcnr == this%MGGA_TASK_CC)& + & isMGGA = .true. + + end function TXcFunctionalsEnum_isMGGA pure function TXcFunctionalsEnum_isLongRangeCorrected(this, xcnr) result(isLongRangeCorrected) diff --git a/sktwocnt/prog/input.f90 b/sktwocnt/prog/input.f90 index 1c636b49..d626c32c 100644 --- a/sktwocnt/prog/input.f90 +++ b/sktwocnt/prog/input.f90 @@ -45,8 +45,8 @@ subroutine readInput(inp, fname) integer :: iErr !! xc-functional type - !! (1: LDA-PW91, 2: GGA-PBE96, 3: GGA-BLYP, 4: LCY-PBE96, 5: LCY-BNL, 6: PBE0, 7: B3LYP, - !! 8: CAMY-B3LYP, 9: CAMY-PBEh) + ! (1: LDA-PW91, 2: GGA-PBE96, 3: GGA-BLYP, 4: LCY-PBE96, 5: LCY-BNL, 6: PBE0, 7: B3LYP, + !! 8: CAMY-B3LYP, 9: CAMY-PBEh, 10: TPSS, 11: SCAN, 12: r2SCAN, 13: r4SCAN, 14: TASK) integer :: iXC !! potential data columns, summed up in order to receive the total atomic potential @@ -58,6 +58,7 @@ subroutine readInput(inp, fname) inp%tLC = .false. inp%tCam = .false. inp%tGlobalHybrid = .false. + inp%tMGGA = .false. fp = 14 open(fp, file=fname, form="formatted", action="read") @@ -107,6 +108,10 @@ subroutine readInput(inp, fname) case(xcFunctional%CAMY_PBEh) ! CAMY-PBEh (general CAM form) inp%tCam = .true. + case(xcFunctional%MGGA_TPSS, xcFunctional%MGGA_SCAN,& + & xcFunctional%MGGA_r2SCAN, xcFunctional%MGGA_r4SCAN,& + & xcFunctional%MGGA_TASK, xcFunctional%MGGA_TASK_CC) + inp%tMGGA = .true. case default call error_("Unknown exchange-correlation functional!", fname, line, iline) end select @@ -172,10 +177,10 @@ subroutine readInput(inp, fname) tReadRadDerivs = .not. inp%tHetero call readatom_(fname, fp, iLine, potcomps, inp%tDensitySuperpos, tReadRadDerivs,& - & (inp%tGlobalHybrid .or. inp%tLC .or. inp%tCam), inp%atom1) + & (inp%tGlobalHybrid .or. inp%tLC .or. inp%tCam), inp%tMGGA, inp%atom1) if (inp%tHetero) then call readatom_(fname, fp, iLine, potcomps, inp%tDensitySuperpos, .true., (inp%tGlobalHybrid& - & .or. inp%tLC .or. inp%tCam), inp%atom2) + & .or. inp%tLC .or. inp%tCam), inp%tMGGA, inp%atom2) end if close(fp) @@ -185,7 +190,7 @@ end subroutine readInput !> Fills TAtomdata instance based on slateratom's output. subroutine readatom_(fname, fp, iLine, potcomps, tDensitySuperpos, tReadRadDerivs, tNonLocal,& - & atom) + & tMGGA, atom) !> filename character(len=*), intent(in) :: fname @@ -208,6 +213,9 @@ subroutine readatom_(fname, fp, iLine, potcomps, tDensitySuperpos, tReadRadDeriv !! true, there are non-local exchange contributions to calculate logical, intent(in) :: tNonLocal + !! true if tau needs to be read from density file + logical, intent(in) :: tMGGA + !> atomic properties instance type(TAtomdata), intent(out) :: atom @@ -302,7 +310,12 @@ subroutine readatom_(fname, fp, iLine, potcomps, tDensitySuperpos, tReadRadDeriv read(line, *, iostat=iErr) buffer call checkerror_(fname, line, iLine, iErr) if (tDensitySuperpos) then - call readdata_(buffer, [1, 3, 4, 5], data) + if (tMGGA) then + call readdata_(buffer, [1, 3, 4, 5, 6], data) + call TGridorb2_init(atom%tau, data(:, 1), data(:, 5)) + else + call readdata_(buffer, [1, 3, 4, 5], data) + end if call TGridorb2_init(atom%rho, data(:, 1), data(:, 2)) call TGridorb2_init(atom%drho, data(:, 1), data(:, 3)) call TGridorb2_init(atom%ddrho, data(:, 1), data(:, 4)) diff --git a/sktwocnt/prog/main.f90 b/sktwocnt/prog/main.f90 index 182c423d..f9d84ed0 100644 --- a/sktwocnt/prog/main.f90 +++ b/sktwocnt/prog/main.f90 @@ -22,7 +22,7 @@ program main call readInput(inp, "sktwocnt.in") write(*, "(A)") "Input done." - + call get_twocenter_integrals(inp, imap, skham, skover) write(*, "(A)") "Twocnt done." diff --git a/slateratom/lib/CMakeLists.txt b/slateratom/lib/CMakeLists.txt index 78399778..327e6057 100644 --- a/slateratom/lib/CMakeLists.txt +++ b/slateratom/lib/CMakeLists.txt @@ -24,6 +24,7 @@ set(sources-f90 mixer.f90 numerical_differentiation.f90 output.f90 + sap.f90 total_energy.f90 utilities.f90 xcfunctionals.f90 diff --git a/slateratom/lib/density.f90 b/slateratom/lib/density.f90 index 1af7c7f1..a46f5d36 100644 --- a/slateratom/lib/density.f90 +++ b/slateratom/lib/density.f90 @@ -13,8 +13,8 @@ module density public :: basis_times_basis, basis_times_basis_1st, basis_times_basis_2nd public :: basis_1st_times_basis_1st, basis_2nd_times_basis_2nd public :: basis_times_basis_times_r2, basis_times_basis_1st_times_r2,& - & basis_times_basis_2nd_times_r2, basis_times_basis_1st_times_r,& - & basis_1st_times_basis_1st_times_r2 + & basis_times_basis_2nd_times_r2, basis_times_basis_1st_times_r,& + & basis_1st_times_basis_1st_times_r2, tau_at_point contains @@ -221,6 +221,81 @@ pure function density_at_point_2nd(pp, max_l, num_alpha, poly_order, alpha, rr) end function density_at_point_2nd + !> Calculates kinetic energy density at a radial point in space analytically. + pure function tau_at_point(pp, max_l, num_alpha, poly_order, alpha, rr) + + !> density matrix supervector + real(dp), intent(in) :: pp(0:,:,:) + + !> maximum angular momentum + integer, intent(in) :: max_l + + !> number of exponents in each shell + integer, intent(in) :: num_alpha(0:) + + !> highest polynomial order + l in each shell + integer, intent(in) :: poly_order(0:) + + !> basis exponents + real(dp), intent(in) :: alpha(0:,:) + + !> radial point in space, i.e. abcissa + real(dp), intent(in) :: rr + + !> resulting analytical 2nd derivative at a radial point in space + real(dp) :: tau_at_point + + !> auxiliary variables + integer :: ii, jj, kk, ll, mm, nn, oo, start + + tau_at_point = 0.0_dp + + do ii = 0, max_l + ll = 0 + do jj = 1, num_alpha(ii) + do kk = 1, poly_order(ii) + ll = ll + 1 + + ! set global index correctly + oo = ll - 1 + do mm = jj, num_alpha(ii) + + ! catch start index for polynomials, different depending on alpha block + start = 1 + if (mm == jj) start = kk + + do nn = start, poly_order(ii) + oo = oo + 1 + + ! TODO: eq. 5, term T in 10.1103/RevModPhys.32.186 + ! TODO: fix H atom convergence; + ! second term seems unrelated, the problem must be in basis_1st_times_basis_1st + ! or in some normalization term + if (ll == oo) then + tau_at_point = tau_at_point + pp(ii, ll, oo) * (basis_1st_times_basis_1st(& + & alpha(ii, jj), kk, alpha(ii, mm), nn, ii, rr) + & + & basis_times_basis_times_rminus2(alpha(ii, jj), kk, alpha(ii, mm), nn, ii, rr) & + & * real(ii * (ii + 1), dp)) + + end if + + if (ll /= oo) then + tau_at_point = tau_at_point + 2.0_dp * pp(ii, ll, oo) * (basis_1st_times_basis_1st(& + & alpha(ii, jj), kk, alpha(ii, mm), nn, ii, rr) + & + & basis_times_basis_times_rminus2(alpha(ii, jj), kk, alpha(ii, mm), nn, ii, rr) & + & * real(ii * (ii + 1), dp)) + end if + + end do + end do + end do + end do + end do + + ! Normalize tau + tau_at_point = tau_at_point * 0.5_dp + + end function tau_at_point !> Calculates wavefunction at a radial point in space analytically. pure function wavefunction(cof, alpha, num_alpha, poly_order, ang, rr) @@ -786,6 +861,63 @@ pure function basis_times_basis_times_r2(alpha, poly1, beta, poly2, ll, rr) end function basis_times_basis_times_r2 + !> Evaluates product of two primitive Slater basis functions with r^(-2) at a radial point in space. + !> r^(-2)r^(m-1)*e^(-alpha*r)*r^(n-1)*exp(-beta*r)=r^(m+n-2)*exp(-(alpha+beta)*r) + pure function basis_times_basis_times_rminus2(alpha, poly1, beta, poly2, ll, rr) + + !> basis exponent of 1st basis + real(dp), intent(in) :: alpha + + !> highest polynomial order in 1st basis shell + integer, intent(in) :: poly1 + + !> basis exponent of 2nd basis + real(dp), intent(in) :: beta + + !> highest polynomial order in 2nd basis shell + integer, intent(in) :: poly2 + + !> angular momentum + integer, intent(in) :: ll + + !> radial point in space, i.e. abcissa + real(dp), intent(in) :: rr + + !> product of two primitive Slater basis functions at a radial point in space + real(dp) :: basis_times_basis_times_rminus2 + + !> normalization pre-factors + real(dp) :: normalization1, normalization2 + + ! auxiliary variables + integer :: mm, nn + real(dp) :: ab + + mm = poly1 + ll + nn = poly2 + ll + ab = - (alpha + beta) + + normalization1 = (2.0_dp * alpha)**(mm) * sqrt(2.0_dp * alpha) / sqrt(fak(2 * mm)) + normalization2 = (2.0_dp * beta)**(nn) * sqrt(2.0_dp * beta) / sqrt(fak(2 * nn)) + + ! catch 0^0 + if ((rr == 0.0_dp) .and. ((mm + nn - 4) == 0)) then + basis_times_basis_times_rminus2 = normalization1 * normalization2 * exp(ab * rr) + else + basis_times_basis_times_rminus2 = normalization1 * normalization2 * rr**(mm + nn - 4) * exp(ab * rr) + end if + + ! NOTE: there are cases where (mm + n - 4) < 0, resulting in singularity (for example, in calculation of + ! kinetic energy density of a product of 1s-orbitals). This, however, does not matter numerically, + ! because the product is later multiplied with \lambda (\lambda + 1), which is zero in such cases, + ! resulting in no numerical artifacts. The results of the calculations that rely on this function + ! were tested against NWChem 7.2.2. (binary distribution from conda-forge), and those usually + ! agree up to the 10^(-4) Hartree in total energies for very large basis sets. + + if (abs(basis_times_basis_times_rminus2) < 1.0d-20) basis_times_basis_times_rminus2 = 0.0_dp + + end function basis_times_basis_times_rminus2 + !> Evaluates product of a basis function with 1st derivative of another basis function and r^2. !! beta and poly2 are the arguments of the derivative. @@ -881,7 +1013,7 @@ pure function basis_times_basis_2nd_times_r2(alpha, poly1, beta, poly2, ll, rr) negative = real(2 * (nn - 1), dp) * beta * rr**(nn + mm - 1) basis_times_basis_2nd_times_r2 = normalization1 * normalization2& - & * (positive - negative) * exp(ab * rr) + & * (positive - negative) * exp(ab * rr) if (abs(basis_times_basis_2nd_times_r2) < 1.0d-20) basis_times_basis_2nd_times_r2 = 0.0_dp diff --git a/slateratom/lib/dft.f90 b/slateratom/lib/dft.f90 index cda52119..d5f6a3d0 100644 --- a/slateratom/lib/dft.f90 +++ b/slateratom/lib/dft.f90 @@ -5,15 +5,18 @@ module dft use common_accuracy, only : dp use common_constants, only : pi, rec4pi use xcfunctionals, only : xcFunctional, getExcVxc_LDA_PW91,& - & getExcVxc_GGA_PBE96, getExcVxc_GGA_BLYP, getExcVxc_LCY_PBE96, getExcVxc_LCY_BNL,& - & getExcVxc_HYB_B3LYP, getExcVxc_HYB_PBE0, getExcVxc_CAMY_B3LYP, getExcVxc_CAMY_PBEh + & getExcVxc_GGA_PBE96, getExcVxc_GGA_BLYP, getExcVxc_LCY_PBE96, getExcVxc_LCY_BNL,& + & getExcVxc_HYB_B3LYP, getExcVxc_HYB_PBE0, getExcVxc_CAMY_B3LYP, getExcVxc_CAMY_PBEh, & + & getExcVxc_MGGA_TPSS, getExcVxc_MGGA_SCAN, getExcVxc_MGGA_r2SCAN, getExcVxc_MGGA_r4SCAN,& + & getExcVxc_MGGA_TASK, getExcVxc_MGGA_TASK_CC use density, only : basis, basis_times_basis_times_r2, density_at_point, density_at_point_1st,& - & density_at_point_2nd + & density_at_point_2nd, tau_at_point, basis_1st_times_basis_1st_times_r2, basis_1st_times_basis_1st + use globals, only : xcnr implicit none private - public :: dft_start_pot, density_grid, dft_exc_energy, dft_vxc_energy + public :: thomas_fermi_start_pot, density_grid, dft_exc_energy, dft_vxc_energy public :: dft_exc_matrixelement, xalpha public :: check_accuracy @@ -25,7 +28,7 @@ module dft !! !! Generalized Thomas-Fermi atomic potential as published by R. Latter, !! Phys. Rev. 99, 510 (1955) eqn. 5/9 and implemented in Dirk Porezags scfatom. - pure subroutine dft_start_pot(abcissa, num_mesh_points, nuc, vxc) + pure subroutine thomas_fermi_start_pot(abcissa, num_mesh_points, nuc, vxc) !> numerical integration abcissas real(dp), intent(in) :: abcissa(:) @@ -59,13 +62,13 @@ pure subroutine dft_start_pot(abcissa, num_mesh_points, nuc, vxc) end do - end subroutine dft_start_pot + end subroutine thomas_fermi_start_pot !> Calculate and store density and density derivatives on radial grid. !! Further calculates and stores exchange-correlation potential and energy density on grid. subroutine density_grid(pp, max_l, num_alpha, poly_order, alpha, num_mesh_points, abcissa, dzdr,& - & dz, xcnr, omega, camAlpha, camBeta, rho, drho, ddrho, vxc, exc, xalpha_const) + & dz, xcnr, omega, camAlpha, camBeta, rho, drho, ddrho, tau, vxc, vtau, exc, xalpha_const) !> density matrix supervector real(dp), intent(in) :: pp(:, 0:,:,:) @@ -115,6 +118,12 @@ subroutine density_grid(pp, max_l, num_alpha, poly_order, alpha, num_mesh_points !> 2nd deriv. of density on grid real(dp), intent(out) :: ddrho(:,:) + !> kinetic energy density on grid + real(dp), intent(out) :: tau(:,:) + + !> orbital-dependent potential on grid + real(dp), intent(out) :: vtau(:,:) + !> xc potential on grid real(dp), intent(out) :: vxc(:,:) @@ -149,6 +158,8 @@ subroutine density_grid(pp, max_l, num_alpha, poly_order, alpha, num_mesh_points ddrho(:,:) = 0.0_dp exc(:) = 0.0_dp vxc(:,:) = 0.0_dp + vtau(:,:) = 0.0_dp + tau(:, :) = 0.0_dp ! get density on grid do ii = 1, num_mesh_points @@ -158,7 +169,7 @@ subroutine density_grid(pp, max_l, num_alpha, poly_order, alpha, num_mesh_points rho = max(rho, 0.0_dp) ! get density derivatives on grid - if (xcFunctional%isGGA(xcnr) .or. xcFunctional%isLongRangeCorrected(xcnr)& + if (xcFunctional%isGGA(xcnr) .or. xcFunctional%isMGGA(xcnr) .or. xcFunctional%isLongRangeCorrected(xcnr)& & .or. xcFunctional%isGlobalHybrid(xcnr) .or. xcFunctional%isCAMY(xcnr)) then do ii = 1, num_mesh_points @@ -178,7 +189,7 @@ subroutine density_grid(pp, max_l, num_alpha, poly_order, alpha, num_mesh_points rhor = transpose(rho) * rec4pi ! get contracted gradients of the density - if (xcFunctional%isGGA(xcnr) .or. xcFunctional%isLongRangeCorrected(xcnr)& + if (xcFunctional%isGGA(xcnr) .or. xcFunctional%isMGGA(xcnr) .or. xcFunctional%isLongRangeCorrected(xcnr)& & .or. xcFunctional%isGlobalHybrid(xcnr) .or. xcFunctional%isCAMY(xcnr)) then allocate(sigma(3, nn)) sigma(1, :) = drho(:, 1) * drho(:, 1) * rec4pi**2 @@ -186,6 +197,13 @@ subroutine density_grid(pp, max_l, num_alpha, poly_order, alpha, num_mesh_points sigma(3, :) = drho(:, 2) * drho(:, 2) * rec4pi**2 end if + if (xcFunctional%isMGGA(xcnr)) then + do ii = 1, num_mesh_points + tau(ii, 1) = tau_at_point(pp(1, :,:,:), max_l, num_alpha, poly_order, alpha, abcissa(ii)) + tau(ii, 2) = tau_at_point(pp(2, :,:,:), max_l, num_alpha, poly_order, alpha, abcissa(ii)) + end do + end if + select case (xcnr) case(xcFunctional%HF_Exchange) return @@ -217,6 +235,18 @@ subroutine density_grid(pp, max_l, num_alpha, poly_order, alpha, num_mesh_points case(xcFunctional%CAMY_PBEh) call getExcVxc_CAMY_PBEh(abcissa, dz, dzdr, rho, drho, sigma, omega, camAlpha, camBeta, exc,& & vxc) + case(xcFunctional%MGGA_TPSS) + call getExcVxc_MGGA_TPSS(abcissa, dz, dzdr, rho, drho, sigma, tau, exc, vxc, vtau) + case(xcFunctional%MGGA_SCAN) + call getExcVxc_MGGA_SCAN(abcissa, dz, dzdr, rho, drho, sigma, tau, exc, vxc, vtau) + case(xcFunctional%MGGA_r2SCAN) + call getExcVxc_MGGA_r2SCAN(abcissa, dz, dzdr, rho, drho, sigma, tau, exc, vxc, vtau) + case(xcFunctional%MGGA_r4SCAN) + call getExcVxc_MGGA_r4SCAN(abcissa, dz, dzdr, rho, drho, sigma, tau, exc, vxc, vtau) + case(xcFunctional%MGGA_TASK) + call getExcVxc_MGGA_TASK(abcissa, dz, dzdr, rho, drho, sigma, tau, exc, vxc, vtau) + case(xcFunctional%MGGA_TASK_CC) + call getExcVxc_MGGA_TASK_CC(abcissa, dz, dzdr, rho, drho, sigma, tau, exc, vxc, vtau) case default write(*, '(A,I2,A)') 'XCNR=', xcnr, ' not implemented!' stop @@ -299,8 +329,8 @@ end subroutine dft_vxc_energy !> Calculates a single matrix element of the exchange correlation potential. - pure subroutine dft_exc_matrixelement(num_mesh_points, weight, abcissa, vxc, alpha1, poly1,& - & alpha2, poly2, ll, exc_matrixelement) + pure subroutine dft_exc_matrixelement(num_mesh_points, weight, abcissa, vxc, vtau, alpha1, poly1,& + & alpha2, poly2, ll, exc_matrixelement) !> number of numerical integration points integer, intent(in) :: num_mesh_points @@ -314,6 +344,9 @@ pure subroutine dft_exc_matrixelement(num_mesh_points, weight, abcissa, vxc, alp !> xc potential on grid real(dp), intent(in) :: vxc(:,:) + !> orbital-dependent tau potential on grid + real(dp), intent(in) :: vtau(:,:) + !> basis exponent of 1st basis real(dp), intent(in) :: alpha1 @@ -332,10 +365,10 @@ pure subroutine dft_exc_matrixelement(num_mesh_points, weight, abcissa, vxc, alp !> single matrix element of the exchange correlation potential real(dp), intent(out) :: exc_matrixelement(2) - !> stores product of two basis functions and r^2 + ! stores product of two basis functions and r^2 real(dp) :: basis - !> auxiliary variable + ! auxiliary variable integer :: ii exc_matrixelement(:) = 0.0_dp @@ -345,11 +378,18 @@ pure subroutine dft_exc_matrixelement(num_mesh_points, weight, abcissa, vxc, alp exc_matrixelement(1) = exc_matrixelement(1) - weight(ii) * vxc(ii, 1) * basis exc_matrixelement(2) = exc_matrixelement(2) - weight(ii) * vxc(ii, 2) * basis - end do - end subroutine dft_exc_matrixelement + if (xcFunctional%isMGGA(xcnr)) then + ! «basis» for MGGA is a product of gradients + basis = basis_1st_times_basis_1st_times_r2(alpha1, poly1, alpha2, poly2, ll, abcissa(ii)) + exc_matrixelement(1) = exc_matrixelement(1) - weight(ii) * vtau(ii, 1) * basis * 0.5_dp + exc_matrixelement(2) = exc_matrixelement(2) - weight(ii) * vtau(ii, 2) * basis * 0.5_dp + end if + end do + end subroutine dft_exc_matrixelement + !> Calculates Xalpha potential and energy density. !! !! alpha=2/3 recovers the Gaspar/Kohn/Sham functional commonly used as exchange part in most diff --git a/slateratom/lib/globals.f90 b/slateratom/lib/globals.f90 index 6687874d..0b93e74c 100644 --- a/slateratom/lib/globals.f90 +++ b/slateratom/lib/globals.f90 @@ -81,7 +81,7 @@ module globals real(dp), allocatable :: cof(:,:,:,:) !> relative changes during scf - real(dp) :: change_max + real(dp) :: orb_grad_norm !> density matrix supervector real(dp), allocatable :: pp(:,:,:,:) @@ -99,7 +99,7 @@ module globals real(dp), allocatable :: eigval_scaled(:,:,:) !> total energy - real(dp) :: total_ene + real(dp) :: total_ene, total_ene_old, total_ene_diff !> kinetic energy real(dp) :: kinetic_energy @@ -149,6 +149,12 @@ module globals !> 2nd deriv. of density on grid real(dp), allocatable :: ddrho(:,:) + !> kinetic energy density on grid + real(dp), allocatable :: tau(:, :) + + !> orbital-dependent tau potential on grid + real(dp), allocatable :: vtau(:,:) + !> xc potential on grid real(dp), allocatable :: vxc(:,:) @@ -167,8 +173,8 @@ module globals !> true, if zero-order regular approximation for relativistic effects is desired logical :: tZora - !> true, if SCF cycle reached convergency - logical :: tConverged + !> true, if SCF cycle reached convergency on a quantity + logical :: tOrbGradConverged, tEnergyConverged !> identifier of mixer integer :: mixnr @@ -210,6 +216,8 @@ subroutine allocate_globals() allocate(rho(num_mesh_points, 2)) allocate(drho(num_mesh_points, 2)) allocate(ddrho(num_mesh_points, 2)) + allocate(tau(num_mesh_points, 2)) + allocate(vtau(num_mesh_points, 2)) allocate(exc(num_mesh_points)) allocate(vxc(num_mesh_points, 2)) @@ -245,6 +253,7 @@ subroutine allocate_globals() rho(:,:) = 0.0_dp drho(:,:) = 0.0_dp ddrho(:,:) = 0.0_dp + tau(:,:) = 0.0_dp eigval(:,:,:) = 0.0_dp eigval_scaled(:,:,:) = 0.0_dp diff --git a/slateratom/lib/hamiltonian.f90 b/slateratom/lib/hamiltonian.f90 index dab8d521..d1175c84 100644 --- a/slateratom/lib/hamiltonian.f90 +++ b/slateratom/lib/hamiltonian.f90 @@ -18,8 +18,8 @@ module hamiltonian !> Main driver routine for Fock matrix build-up. Also calls mixer with potential matrix. subroutine build_hamiltonian(pMixer, iScf, tt, uu, nuc, vconf, jj, kk, kk_lr, pp, max_l,& - & num_alpha, poly_order, problemsize, xcnr, num_mesh_points, weight, abcissa, vxc, alpha,& - & pot_old, pot_new, tZora, ff, camAlpha, camBeta) + & num_alpha, poly_order, problemsize, xcnr, num_mesh_points, weight, abcissa, vxc, vtau,& + & alpha, pot_old, pot_new, tZora, ff, camAlpha, camBeta) !> mixer instances type(TMixer), intent(inout) :: pMixer @@ -78,6 +78,9 @@ subroutine build_hamiltonian(pMixer, iScf, tt, uu, nuc, vconf, jj, kk, kk_lr, pp !> xc potential on grid real(dp), intent(in) :: vxc(:,:) + !> xc potential on grid + real(dp), intent(in) :: vtau(:,:) + !> basis exponents real(dp), intent(in) :: alpha(0:,:) @@ -138,34 +141,34 @@ subroutine build_hamiltonian(pMixer, iScf, tt, uu, nuc, vconf, jj, kk, kk_lr, pp end if ! pure DFT - if (xcFunctional%isLDA(xcnr) .or. xcFunctional%isGGA(xcnr)) then + if (xcFunctional%isLDA(xcnr) .or. xcFunctional%isGGA(xcnr) .or. xcFunctional%isMGGA(xcnr)) then call build_dft_exc_matrix(max_l, num_alpha, poly_order, alpha, num_mesh_points, abcissa,& - & weight, vxc, k_matrix) + & weight, vxc, vtau, k_matrix) end if ! HF - DFT hybrid if (xcFunctional%isLongRangeCorrected(xcnr)) then call build_hf_ex_matrix(kk_lr, pp, max_l, num_alpha, poly_order, k_matrix) call build_dft_exc_matrix(max_l, num_alpha, poly_order, alpha, num_mesh_points, abcissa,& - & weight, vxc, k_matrix2) + & weight, vxc, vtau, k_matrix2) k_matrix(:,:,:,:) = k_matrix + k_matrix2 elseif (xcnr == xcFunctional%HYB_B3LYP) then call build_hf_ex_matrix(kk, pp, max_l, num_alpha, poly_order, k_matrix) call build_dft_exc_matrix(max_l, num_alpha, poly_order, alpha, num_mesh_points, abcissa,& - & weight, vxc, k_matrix2) + & weight, vxc, vtau, k_matrix2) ! B3LYP parameters a=0.20, b=0.72, c=0.81 (libXC defaults) ! --> 0.20 * HF exchange + full libXC DFT exchange k_matrix(:,:,:,:) = 0.20_dp * k_matrix + k_matrix2 elseif (xcnr == xcFunctional%HYB_PBE0) then call build_hf_ex_matrix(kk, pp, max_l, num_alpha, poly_order, k_matrix) call build_dft_exc_matrix(max_l, num_alpha, poly_order, alpha, num_mesh_points, abcissa,& - & weight, vxc, k_matrix3) + & weight, vxc, vtau, k_matrix3) k_matrix(:,:,:,:) = camAlpha * k_matrix + k_matrix3 elseif (xcFunctional%isCAMY(xcnr)) then call build_hf_ex_matrix(kk, pp, max_l, num_alpha, poly_order, k_matrix) call build_hf_ex_matrix(kk_lr, pp, max_l, num_alpha, poly_order, k_matrix2) call build_dft_exc_matrix(max_l, num_alpha, poly_order, alpha, num_mesh_points, abcissa,& - & weight, vxc, k_matrix3) + & weight, vxc, vtau, k_matrix3) if (xcnr == xcFunctional%CAMY_B3LYP) then ! CAMY-B3LYP parameters (libXC defaults) k_matrix(:,:,:,:) = camAlpha * k_matrix + camBeta * k_matrix2 + k_matrix3 @@ -175,14 +178,23 @@ subroutine build_hamiltonian(pMixer, iScf, tt, uu, nuc, vconf, jj, kk, kk_lr, pp end if end if + ! build mixer input - pot_new(1, :,:,:) = - real(nuc, dp) * uu + j_matrix - k_matrix(1, :,:,:) - pot_new(2, :,:,:) = - real(nuc, dp) * uu + j_matrix - k_matrix(2, :,:,:) + if (iScf /= 0) then + pot_new(1, :,:,:) = - real(nuc, dp) * uu + j_matrix - k_matrix(1, :,:,:) + pot_new(2, :,:,:) = - real(nuc, dp) * uu + j_matrix - k_matrix(2, :,:,:) + else + pot_new(1, :,:,:) = -k_matrix(1, :,:,:) + pot_new(2, :,:,:) = -k_matrix(2, :,:,:) + end if ! mixer allocate(pot_diff, mold=pot_old) pot_diff(:,0:,:,:) = pot_old - pot_new - call TMixer_mix(pMixer, pot_new, pot_diff) + if (iScf /= 0) then + ! Do not call mixer on the 0th (guess) iteration + call TMixer_mix(pMixer, pot_new, pot_diff) + end if ! Not sure: before or after mixer (potential .ne. Matrix elements)? ! Should be irrelevant once self-consistency is reached. @@ -352,7 +364,7 @@ end subroutine build_hf_ex_matrix !> Builds DFT exchange matrix to be added to the Fock matrix by calculating the single matrix !! elements and putting them together. subroutine build_dft_exc_matrix(max_l, num_alpha, poly_order, alpha, num_mesh_points, abcissa,& - & weight, vxc, k_matrix) + & weight, vxc, vtau, k_matrix) !> maximum angular momentum integer, intent(in) :: max_l @@ -378,6 +390,9 @@ subroutine build_dft_exc_matrix(max_l, num_alpha, poly_order, alpha, num_mesh_po !> xc potential on grid real(dp), intent(in) :: vxc(:,:) + !> tau potential on grid + real(dp), intent(in) :: vtau(:,:) + !> DFT exchange matrix real(dp), intent(out) :: k_matrix(:,0:,:,:) @@ -405,7 +420,7 @@ subroutine build_dft_exc_matrix(max_l, num_alpha, poly_order, alpha, num_mesh_po do mm = start, poly_order(ii) tt = tt + 1 - call dft_exc_matrixelement(num_mesh_points, weight, abcissa, vxc, alpha(ii, jj), kk,& + call dft_exc_matrixelement(num_mesh_points, weight, abcissa, vxc, vtau, alpha(ii, jj), kk,& & alpha(ii, ll), mm, ii, exc_matrixelement) k_matrix(1, ii, ss, tt) = exc_matrixelement(1) diff --git a/slateratom/lib/output.f90 b/slateratom/lib/output.f90 index c24d7ae5..8997dfe4 100644 --- a/slateratom/lib/output.f90 +++ b/slateratom/lib/output.f90 @@ -8,7 +8,9 @@ module output & density_at_point_1st use coulomb_potential, only : cou_pot use common_taggedout, only : TTaggedwriter, TTaggedwriter_init, writetag + use globals, only : xcnr use utilities, only : fak + use xcfunctionals, only : xcFunctional implicit none private @@ -292,10 +294,10 @@ end subroutine write_potentials_file_standard !> Writes potentials and mesh info to file on standard (internal) integration mesh; !! in principle one could read in the points from another file to have other meshes! - subroutine write_densities_file_standard(num_mesh_points, abcissa, weight, rho, drho, ddrho) + subroutine write_densities_file_standard(num_mesh_points, abcissa, weight, rho, drho, ddrho, tau) real(dp), intent(in) :: abcissa(:), weight(:) - real(dp), intent(in) :: rho(:,:), drho(:,:), ddrho(:,:) + real(dp), intent(in) :: rho(:,:), drho(:,:), ddrho(:,:), tau(:,:) integer, intent(in) :: num_mesh_points real(dp) :: enumber, zeta, r_seitz integer :: ii @@ -313,22 +315,29 @@ subroutine write_densities_file_standard(num_mesh_points, abcissa, weight, rho, ! note division of total density by 4*pi in calculation of r_seitz ! commonly r_seitz=((4*pi*rho)/3)**(-1/3) but our rho is from the ! radial part only and the angular part must be taken into account - ! explicitely; during integration this happens implicitely, see enumber + ! explicitly; during integration this happens implicitely, see enumber do ii = 1, num_mesh_points - if ((rho(ii, 1) + rho(ii, 2)) > 1.0d-12) then - zeta = (rho(ii, 1) - rho(ii, 2)) / (rho(ii, 1) + rho(ii, 2)) - r_seitz = (4.0_dp * pi / 3.0_dp& - & * ((rho(ii, 1) + rho(ii, 2)) / 4.0_dp / pi))**(-1.0_dp / 3.0_dp) - else - zeta = 0.0_dp - r_seitz = 0.0_dp - end if - - write(95, '(7ES21.12E3)') abcissa(ii), weight(ii), rho(ii, 1) + rho(ii, 2),& + if ((rho(ii, 1) + rho(ii, 2)) > 1.0d-12) then + zeta = (rho(ii, 1) - rho(ii, 2)) / (rho(ii, 1) + rho(ii, 2)) + r_seitz = (4.0_dp * pi / 3.0_dp& + & * ((rho(ii, 1) + rho(ii, 2)) / 4.0_dp / pi))**(-1.0_dp / 3.0_dp) + else + zeta = 0.0_dp + r_seitz = 0.0_dp + end if + + if (xcFunctional%isMGGA(xcnr)) then + write(95, '(8ES21.12E3)') abcissa(ii), weight(ii), rho(ii, 1) + rho(ii, 2),& + & drho(ii, 1) + drho(ii, 2), ddrho(ii, 1) + ddrho(ii, 2), zeta, r_seitz,& + & tau(ii, 1) + tau(ii, 2) + else + write(95, '(7ES21.12E3)') abcissa(ii), weight(ii), rho(ii, 1) + rho(ii, 2),& & drho(ii, 1) + drho(ii, 2), ddrho(ii, 1) + ddrho(ii, 2), zeta, r_seitz - enumber = enumber + weight(ii) * (rho(ii, 1) + rho(ii, 2)) * abcissa(ii)**2 + end if + + enumber = enumber + weight(ii) * (rho(ii, 1) + rho(ii, 2)) * abcissa(ii)**2 end do close(95) diff --git a/slateratom/lib/sap.f90 b/slateratom/lib/sap.f90 new file mode 100644 index 00000000..151f6b91 --- /dev/null +++ b/slateratom/lib/sap.f90 @@ -0,0 +1,45265 @@ +!> Module for atomic guess through superposition of atomic potentials +!! (SAP) method +! +! References: +! S. Lehtola, "Assessment of Initial Guesses for Self-Consistent Field +! Calculations. Superposition of Atomic Potentials: Simple yet +! Efficient", J. Chem. Theory Comput. 15, 1593 (2019). +! DOI: 10.1021/acs.jctc.8b01089 +! +! S. Lehtola, L. Visscher, E. Engel, Efficient implementation of the +! superposition of atomic potentials initial guess for electronic +! structure calculations in Gaussian basis sets, J. Chem. Phys., in +! press (2020). +! +! S. Lehtola, "Fully numerical calculations on atoms with fractional +! occupations and range-separated exchange functionals", Phys. Rev. A +! 101, 012516 (2020). DOI: 10.1103/PhysRevA.101.012516 +! +! S. Lehtola, "Fully numerical Hartree-Fock and density functional +! calculations. I. Atoms", Int. J. Quantum Chem. e25945 (2019). +! DOI: 10.1002/qua.25945 + +module sap + + use common_accuracy, only: dp + use common_message, only: error + + implicit none + private + + public :: sap_start_pot + +contains + + !> Compute SAP potential for an atom on a grid. + subroutine sap_start_pot(abcissa, num_mesh_points, nuc, v) + + !> numerical integration abcissas + real(dp), intent(in) :: abcissa(:) + + !> number of numerical integration points + integer, intent(in) :: num_mesh_points + + !> nuclear charge, i.e. atomic number + integer, intent(in) :: nuc + + !> xc potential on grid for two spin channels v(:, 1) and v(:, 2) + real(dp), intent(out) :: v(:, :) + + ! auxiliary variables + integer :: ii, jj + + ! Storage variables for effective charge, vxc and abscissa + real(dp), dimension(1501) :: r_tab, v_tab + real(dp) :: Zeff + + ! Get tabulated references + call get_sap_data(r_tab, 0) + call get_sap_data(v_tab, nuc) + + jj = 1 + do ii = 1, num_mesh_points + ! Return 0.0 beyond range of tabulation + if (abcissa(ii) > r_tab(1501)) then + + v(ii, 1) = 0.0_dp + v(ii, 2) = 0.0_dp + + else + + ! Assumes that radial points are ordered + ! in ascending order in both arrays + do while (abcissa(ii) > r_tab(jj)) + jj = jj + 1 + end do + + ! Compute linear interpolation for v_tab + Zeff = (v_tab(jj - 1)*(r_tab(jj) - abcissa(ii)) + v_tab(jj)*(abcissa(ii) - r_tab(jj - 1)))& + & /(r_tab(jj) - r_tab(jj - 1)) + + ! Compute resulting potential + v(ii, 1) = -Zeff/abcissa(ii) + v(ii, 2) = v(ii, 1) + + end if + + end do + + end subroutine sap_start_pot + + !> Get tabulated SAP data array + subroutine get_sap_data(out, N) + + !> Output array (must be exactly 1501 elements long) + real(dp), intent(out) :: out(1501) + + !> Atomic number; if N == 0, returns radial mesh + ! for tabulation + integer, intent(in) :: N + + ! N == 0 corresponds to tabulated radial distance, + ! otherwise it's Z (atomic number) + ! + ! The array is adapted from PySCF implementation of SAP: + ! https://github.com/pyscf/pyscf/blob/master/pyscf/dft/sap_data.py + + ! Copyright (c) 2020, Susi Lehtola + ! All rights reserved. + ! Redistribution and use in source and binary forms, with or without + ! modification, are permitted provided that the following conditions are met: + ! * Redistributions of source code must retain the above copyright + ! notice, this list of conditions and the following disclaimer. + ! * Redistributions in binary form must reproduce the above copyright + ! notice, this list of conditions and the following disclaimer in the + ! documentation and/or other materials provided with the distribution. + ! * Neither the name of the nor the + ! names of its contributors may be used to endorse or promote products + ! derived from this software without specific prior written permission. + ! THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS + ! "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT + ! LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS + ! FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE + ! COPYRIGHT HOLDER BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, + ! SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT + ! LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF + ! USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND + ! ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, + ! OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT + ! OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + ! SUCH DAMAGE. + ! Routines for the implementation of the superposition of atomic + ! potentials guess for electronic structure calculations, see + ! S. Lehtola, "Assessment of Initial Guesses for Self-Consistent Field + ! Calculations. Superposition of Atomic Potentials: Simple yet + ! Efficient", J. Chem. Theory Comput. 15, 1593 (2019). + ! DOI: 10.1021/acs.jctc.8b01089 + ! This function evaluates the effective charge of a neutral atom, + ! given by exchange-only LDA on top of spherically symmetric + ! unrestricted Hartree-Fock calculations as described in + ! S. Lehtola, L. Visscher, E. Engel, Efficient implementation of the + ! superposition of atomic potentials initial guess for electronic + ! structure calculations in Gaussian basis sets, J. Chem. Phys., in + ! press (2020). + ! The potentials have been calculated for the ground-states of + ! spherically symmetric atoms at the non-relativistic level of theory + ! as described in + ! S. Lehtola, "Fully numerical calculations on atoms with fractional + ! occupations and range-separated exchange functionals", Phys. Rev. A + ! 101, 012516 (2020). DOI: 10.1103/PhysRevA.101.012516 + ! using accurate finite-element calculations as described in + ! S. Lehtola, "Fully numerical Hartree-Fock and density functional + ! calculations. I. Atoms", Int. J. Quantum Chem. e25945 (2019). + ! DOI: 10.1002/qua.25945 + + select case (N) + case (0) + out = [& + & 0.0000000000000000e+00_dp, 1.9095291060172699e-10_dp, 6.0955947806667901e-09_dp, 4.6100466017523503e-08_dp, & + & 1.9316341043525100e-07_dp, 5.8518541705930603e-07_dp, 1.4431474063426200e-06_dp, 3.0863676484665900e-06_dp, & + & 5.9443182316111196e-06_dp, 1.0564538040043300e-05_dp, 1.7616292318383701e-05_dp, 2.7889751976002900e-05_dp, & + & 4.2290595918512802e-05_dp, 6.1830073277808906e-05_dp, 8.7610695745079695e-05_dp, 1.2080785959011100e-04_dp, & + & 0.0001626478187771_dp, 0.0002143825414644_dp, 0.0002772620790033_dp, 0.0003525051566010_dp, & + & 0.0004412687558318_dp, 0.0005446174993975_dp, 0.0006634936667930_dp, 0.0007986886652215_dp, & + & 0.0009508167532628_dp, 0.0011202917660744_dp, 0.0013073075215358_dp, 0.0015118224985400_dp, & + & 0.0017335492739170_dp, 0.0019719490860152_dp, 0.0022262317639251_dp, 0.0024953611251482_dp, & + & 0.0027780658048384_dp, 0.0030728553403232_dp, 0.0033780411991833_dp, 0.0036917623113763_dp, & + & 0.0040120145491752_dp, 0.0043366834961819_dp, 0.0046635797611534_dp, 0.0049904760261249_dp, & + & 0.0053151449731316_dp, 0.0056353972109304_dp, 0.0059491183231235_dp, 0.0062543041819836_dp, & + & 0.0065490937174684_dp, 0.0068317983971586_dp, 0.0071009277583817_dp, 0.0073552104362916_dp, & + & 0.0075936102483897_dp, 0.0078153370237667_dp, 0.0080198520007710_dp, 0.0082068677562324_dp, & + & 0.0083763427690440_dp, 0.0085284708570853_dp, 0.0086636658555138_dp, 0.0087825420229093_dp, & + & 0.0088858907664750_dp, 0.0089746543657058_dp, 0.0090498974433035_dp, 0.0091127769808424_dp, & + & 0.0091645117035297_dp, 0.0092063516627167_dp, 0.0092395488265617_dp, 0.0092653294490290_dp, & + & 0.0092848689263883_dp, 0.0092992697703308_dp, 0.0093095432299884_dp, 0.0093165949842667_dp, & + & 0.0093212152040752_dp, 0.0093240731546583_dp, 0.0093257163749004_dp, 0.0093265743368897_dp, & + & 0.0093269663588963_dp, 0.0093271134218408_dp, 0.0093271534267120_dp, 0.0093271593313539_dp, & + & 0.0093271601059184_dp, 0.0093271781523447_dp, 0.0093273004197029_dp, 0.0093277498899082_dp, & + & 0.0093289480313741_dp, 0.0093315702306849_dp, 0.0093365924240223_dp, 0.0093453272119767_dp, & + & 0.0093594480440749_dp, 0.0093810004035493_dp, 0.0094123992990364_dp, 0.0094564127676191_dp, & + & 0.0095161315019038_dp, 0.0095949251213289_dp, 0.0096963860033275_dp, 0.0098242619623011_dp, & + & 0.0099823794032462_dp, 0.0101745588727976_dp, 0.0104045251751296_dp, 0.0106758144066244_dp, & + & 0.0109916803861568_dp, 0.0113550030136215_dp, 0.0117682010761543_dp, 0.0122331519394712_dp, & + & 0.0127511204128277_dp, 0.0133226988640867_dp, 0.0139477603918012_dp, 0.0146254265411583_dp, & + & 0.0153540506885909_dp, 0.0161312178254622_dp, 0.0169537610550243_dp, 0.0178177946899570_dp, & + & 0.0187187634116783_dp, 0.0196515065387106_dp, 0.0206103360608126_dp, 0.0215891267388584_dp, & + & 0.0225814162571620_dp, 0.0235805131535374_dp, 0.0245796100499127_dp, 0.0255718995682163_dp, & + & 0.0265506902462622_dp, 0.0275095197683641_dp, 0.0284422628953965_dp, 0.0293432316171178_dp, & + & 0.0302072652520504_dp, 0.0310298084816126_dp, 0.0318069756184839_dp, 0.0325355997659164_dp, & + & 0.0332132659152736_dp, 0.0338383274429880_dp, 0.0344099058942470_dp, 0.0349278743676035_dp, & + & 0.0353928252309205_dp, 0.0358060232934533_dp, 0.0361693459209180_dp, 0.0364852119004504_dp, & + & 0.0367565011319451_dp, 0.0369864674342771_dp, 0.0371786469038285_dp, 0.0373367643447736_dp, & + & 0.0374646403037473_dp, 0.0375661011857458_dp, 0.0376448948051710_dp, 0.0377046135394556_dp, & + & 0.0377486270080384_dp, 0.0377800259035255_dp, 0.0378015782629999_dp, 0.0378156990950980_dp, & + & 0.0378244338830524_dp, 0.0378294560763898_dp, 0.0378320782757006_dp, 0.0378332764171666_dp, & + & 0.0378337258873719_dp, 0.0378338481547300_dp, 0.0378338662011563_dp, 0.0378338677943125_dp, & + & 0.0378338990114269_dp, 0.0378341105122543_dp, 0.0378348880159300_dp, 0.0378369605879999_dp, & + & 0.0378414965273755_dp, 0.0378501840304259_dp, 0.0378652936631901_dp, 0.0378897201963173_dp, & + & 0.0379270019527330_dp, 0.0379813164687220_dp, 0.0380574519571201_dp, 0.0381607547675479_dp, & + & 0.0382970537435376_dp, 0.0384725630604126_dp, 0.0386937657718628_dp, 0.0389672808793569_dp, & + & 0.0392997172504388_dp, 0.0396975181351890_dp, 0.0401668003527027_dp, 0.0407131924320912_dp, & + & 0.0413416760889992_dp, 0.0420564353958445_dp, 0.0428607178620895_dp, 0.0437567113832465_dp, & + & 0.0447454406505750_dp, 0.0458266861470961_dp, 0.0469989283019068_dp, 0.0482593187485059_dp, & + & 0.0496036799506086_dp, 0.0510265337389549_dp, 0.0525211585641778_dp, 0.0540796745336850_dp, & + & 0.0556931545845249_dp, 0.0573517594685833_dp, 0.0590448936093834_dp, 0.0607613783478282_dp, & + & 0.0624896386420494_dp, 0.0642178989362706_dp, 0.0659343836747154_dp, 0.0676275178155154_dp, & + & 0.0692861226995739_dp, 0.0708996027504137_dp, 0.0724581187199210_dp, 0.0739527435451439_dp, & + & 0.0753755973334902_dp, 0.0767199585355928_dp, 0.0779803489821920_dp, 0.0791525911370027_dp, & + & 0.0802338366335238_dp, 0.0812225659008523_dp, 0.0821185594220093_dp, 0.0829228418882542_dp, & + & 0.0836376011950996_dp, 0.0842660848520075_dp, 0.0848124769313960_dp, 0.0852817591489097_dp, & + & 0.0856795600336600_dp, 0.0860119964047418_dp, 0.0862855115122360_dp, 0.0865067142236862_dp, & + & 0.0866822235405611_dp, 0.0868185225165509_dp, 0.0869218253269787_dp, 0.0869979608153767_dp, & + & 0.0870522753313658_dp, 0.0870895570877814_dp, 0.0871139836209086_dp, 0.0871290932536728_dp, & + & 0.0871377807567233_dp, 0.0871423166960989_dp, 0.0871443892681687_dp, 0.0871451667718444_dp, & + & 0.0871453782726719_dp, 0.0871454094897863_dp, 0.0871454119937853_dp, 0.0871454582052761_dp, & + & 0.0871457712953469_dp, 0.0871469222538740_dp, 0.0871499903351853_dp, 0.0871567050019657_dp, & + & 0.0871695653343703_dp, 0.0871919325092340_dp, 0.0872280917294016_dp, 0.0872832808645706_dp, & + & 0.0873636840282826_dp, 0.0874763893341569_dp, 0.0876293111199353_dp, 0.0878310779714063_dp, & + & 0.0880908888908394_dp, 0.0884183409080102_dp, 0.0888232322996593_dp, 0.0893153463410200_dp, & + & 0.0899042211395692_dp, 0.0905989115786682_dp, 0.0914077497135578_dp, 0.0923381101050022_dp, & + & 0.0933961865421474_dp, 0.0945867863961021_dp, 0.0959131484644118_dp, 0.0973767896236902_dp, & + & 0.0989773849173530_dp, 0.1007126848858250_dp, 0.1025784730195050_dp, 0.1045685652048520_dp, & + & 0.1066748519681490_dp, 0.1088873832283860_dp, 0.1111944941795240_dp, 0.1135829698625230_dp, & + & 0.1160382449873780_dp, 0.1185446346519120_dp, 0.1210855908018690_dp, 0.1236439786074650_dp, & + & 0.1262023664130600_dp, 0.1287433225630180_dp, 0.1312497122275520_dp, 0.1337049873524070_dp, & + & 0.1360934630354060_dp, 0.1384005739865440_dp, 0.1406131052467800_dp, 0.1427193920100780_dp, & + & 0.1447094841954250_dp, 0.1465752723291050_dp, 0.1483105722975770_dp, 0.1499111675912400_dp, & + & 0.1513748087505180_dp, 0.1527011708188280_dp, 0.1538917706727820_dp, 0.1549498471099280_dp, & + & 0.1558802075013720_dp, 0.1566890456362620_dp, 0.1573837360753610_dp, 0.1579726108739100_dp, & + & 0.1584647249152700_dp, 0.1588696163069200_dp, 0.1591970683240900_dp, 0.1594568792435230_dp, & + & 0.1596586460949940_dp, 0.1598115678807730_dp, 0.1599242731866470_dp, 0.1600046763503590_dp, & + & 0.1600598654855280_dp, 0.1600960247056960_dp, 0.1601183918805600_dp, 0.1601312522129640_dp, & + & 0.1601379668797450_dp, 0.1601410349610560_dp, 0.1601421859195830_dp, 0.1601424990096540_dp, & + & 0.1601425452211450_dp, 0.1601425487854200_dp, 0.1601426127883760_dp, 0.1601430464184020_dp, & + & 0.1601446404969840_dp, 0.1601488897923240_dp, 0.1601581896117760_dp, 0.1601760011835750_dp, & + & 0.1602069797406200_dp, 0.1602570602926570_dp, 0.1603334972938670_dp, 0.1604448557469950_dp, & + & 0.1606009526956980_dp, 0.1608127495047760_dp, 0.1610921967732050_dp, 0.1614520351272970_dp, & + & 0.1619055564618130_dp, 0.1624663313987360_dp, 0.1631479097829530_dp, 0.1639635019017860_dp, & + & 0.1649256487767310_dp, 0.1660458903116930_dp, 0.1673344402798800_dp, 0.1687998770847570_dp, & + & 0.1704488589395780_dp, 0.1722858715818200_dp, 0.1743130158869390_dp, 0.1765298417897780_dp, & + & 0.1789332337868260_dp, 0.1815173520085450_dp, 0.1842736314521880_dp, 0.1871908404894570_dp, & + & 0.1902551982493180_dp, 0.1934505489650500_dp, 0.1967585899066530_dp, 0.2001591481345350_dp, & + & 0.2036305000452550_dp, 0.2071497265689760_dp, 0.2106930959512340_dp, 0.2142364653334920_dp, & + & 0.2177556918572130_dp, 0.2212270437679330_dp, 0.2246276019958150_dp, 0.2279356429374170_dp, & + & 0.2311309936531500_dp, 0.2341953514130110_dp, 0.2371125604502800_dp, 0.2398688398939230_dp, & + & 0.2424529581156420_dp, 0.2448563501126900_dp, 0.2470731760155290_dp, 0.2491003203206480_dp, & + & 0.2509373329628900_dp, 0.2525863148177110_dp, 0.2540517516225880_dp, 0.2553403015907750_dp, & + & 0.2564605431257370_dp, 0.2574226900006820_dp, 0.2582382821195150_dp, 0.2589198605037320_dp, & + & 0.2594806354406550_dp, 0.2599341567751710_dp, 0.2602939951292630_dp, 0.2605734423976920_dp, & + & 0.2607852392067700_dp, 0.2609413361554730_dp, 0.2610526946086010_dp, 0.2611291316098110_dp, & + & 0.2611792121618480_dp, 0.2612101907188930_dp, 0.2612280022906920_dp, 0.2612373021101440_dp, & + & 0.2612415514054840_dp, 0.2612431454840660_dp, 0.2612435791140920_dp, 0.2612436431170480_dp, & + & 0.2612436479631590_dp, 0.2612437338115550_dp, 0.2612443154478470_dp, 0.2612464536161000_dp, & + & 0.2612521532776480_dp, 0.2612646273043010_dp, 0.2612885183080450_dp, 0.2613300704422820_dp, & + & 0.2613972444497030_dp, 0.2614997708691960_dp, 0.2616491381036360_dp, 0.2618585139424450_dp, & + & 0.2621426010750000_dp, 0.2625174290695010_dp, 0.2630000871730040_dp, 0.2636084040595340_dp, & + & 0.2643605822653020_dp, 0.2652747964577950_dp, 0.2663687658494160_dp, 0.2676593119534400_dp, & + & 0.2691619134648720_dp, 0.2708902703141100_dp, 0.2728558888786730_dp, 0.2750676999480260_dp, & + & 0.2775317203281000_dp, 0.2802507679635420_dp, 0.2832242391733010_dp, 0.2864479550726140_dp, & + & 0.2899140825321750_dp, 0.2936111331491080_dp, 0.2975240417244100_dp, 0.3016343237107780_dp, & + & 0.3059203090676560_dp, 0.3103574479913590_dp, 0.3149186821301210_dp, 0.3195748731969300_dp, & + & 0.3242952794027160_dp, 0.3290480688888880_dp, 0.3338008583750610_dp, 0.3385212645808470_dp, & + & 0.3431774556476560_dp, 0.3477386897864180_dp, 0.3521758287101210_dp, 0.3564618140669990_dp, & + & 0.3605720960533670_dp, 0.3644850046286690_dp, 0.3681820552456020_dp, 0.3716481827051630_dp, & + & 0.3748718986044760_dp, 0.3778453698142350_dp, 0.3805644174496770_dp, 0.3830284378297510_dp, & + & 0.3852402488991040_dp, 0.3872058674636670_dp, 0.3889342243129050_dp, 0.3904368258243370_dp, & + & 0.3917273719283610_dp, 0.3928213413199820_dp, 0.3937355555124750_dp, 0.3944877337182430_dp, & + & 0.3950960506047720_dp, 0.3955787087082760_dp, 0.3959535367027770_dp, 0.3962376238353320_dp, & + & 0.3964469996741410_dp, 0.3965963669085810_dp, 0.3966988933280740_dp, 0.3967660673354950_dp, & + & 0.3968076194697320_dp, 0.3968315104734760_dp, 0.3968439845001290_dp, 0.3968496841616760_dp, & + & 0.3968518223299300_dp, 0.3968524039662220_dp, 0.3968524898146180_dp, 0.3968524962592850_dp, & + & 0.3968526096927540_dp, 0.3968533782222300_dp, 0.3968562034333650_dp, 0.3968637345279080_dp, & + & 0.3968802167476470_dp, 0.3969117844831050_dp, 0.3969666882784980_dp, 0.3970554468471490_dp, & + & 0.3971909173749970_dp, 0.3973882797543010_dp, 0.3976649328895840_dp, 0.3980403037841530_dp, & + & 0.3985355726769750_dp, 0.3991733199851820_dp, 0.3999771031478480_dp, 0.4009709735968020_dp, & + & 0.4021789459402780_dp, 0.4036244329831810_dp, 0.4053296613798110_dp, 0.4073150834876500_dp, & + & 0.4095988013413870_dp, 0.4121960185835950_dp, 0.4151185356728200_dp, 0.4183743027538060_dp, & + & 0.4219670432419520_dp, 0.4258959594795300_dp, 0.4301555298095140_dp, 0.4347354041370970_dp, & + & 0.4396204025700210_dp, 0.4447906191126290_dp, 0.4502216297053210_dp, 0.4558848012226350_dp, & + & 0.4617476954415240_dp, 0.4677745595363770_dp, 0.4739268924150720_dp, 0.4801640742411510_dp, & + & 0.4864440448441040_dp, 0.4927240154470570_dp, 0.4989611972731360_dp, 0.5051135301518310_dp, & + & 0.5111403942466840_dp, 0.5170032884655730_dp, 0.5226664599828870_dp, 0.5280974705755790_dp, & + & 0.5332676871181870_dp, 0.5381526855511110_dp, 0.5427325598786940_dp, 0.5469921302086780_dp, & + & 0.5509210464462559_dp, 0.5545137869344010_dp, 0.5577695540153880_dp, 0.5606920711046121_dp, & + & 0.5632892883468210_dp, 0.5655730062005579_dp, 0.5675584283083970_dp, 0.5692636567050270_dp, & + & 0.5707091437479300_dp, 0.5719171160914061_dp, 0.5729109865403600_dp, 0.5737147697030260_dp, & + & 0.5743525170112320_dp, 0.5748477859040551_dp, 0.5752231567986240_dp, 0.5754998099339070_dp, & + & 0.5756971723132110_dp, 0.5758326428410590_dp, 0.5759214014097100_dp, 0.5759763052051030_dp, & + & 0.5760078729405610_dp, 0.5760243551603000_dp, 0.5760318862548430_dp, 0.5760347114659780_dp, & + & 0.5760354799954540_dp, 0.5760355934289230_dp, 0.5760356019185160_dp, 0.5760357510000570_dp, & + & 0.5760367610507910_dp, 0.5760404741244830_dp, 0.5760503719720020_dp, 0.5760720339624090_dp, & + & 0.5761135223052100_dp, 0.5761856803948340_dp, 0.5763023325990340_dp, 0.5764803766562761_dp, & + & 0.5767397629546570_dp, 0.5771033582505261_dp, 0.5775966947577450_dp, 0.5782476089049370_dp, & + & 0.5790857773246800_dp, 0.5801421607144650_dp, 0.5814483690087380_dp, 0.5830359637460220_dp, & + & 0.5849357155362990_dp, 0.5871768360743470_dp, 0.5897862051602490_dp, 0.5927876136491240_dp, & + & 0.5962010431432520_dp, 0.6000420025621770_dp, 0.6043209404960730_dp, 0.6090427504962860_dp, & + & 0.6142063842298700_dp, 0.6198045847809790_dp, 0.6258237493911309_dp, 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3.8118810540499502e-05_dp, 3.5332033991419800e-05_dp, 3.2959723084147199e-05_dp, 3.0945552842665001e-05_dp, & + & 2.9240717852929698e-05_dp, 2.7803059018505199e-05_dp, 2.6596184012128699e-05_dp, 2.5588621366035000e-05_dp, & + & 2.4753051057868601e-05_dp, 2.4065638618342399e-05_dp, 2.3505478784602300e-05_dp, 2.3054140302125600e-05_dp, & + & 2.2695298714348100e-05_dp, 2.2414445212448599e-05_dp, 2.2198662054218099e-05_dp, 2.2036455997298501e-05_dp, & + & 2.1917640434465599e-05_dp, 2.1833255475889300e-05_dp, 2.1775514101651801e-05_dp, 2.1737762243123599e-05_dp, & + & 2.1714441356901499e-05_dp, 2.1701043542932099e-05_dp, 2.1694051395515501e-05_dp, 2.1690857246014999e-05_dp, & + & 2.1689659110646401e-05_dp, 2.1689333198571200e-05_dp, 2.1689285094717001e-05_dp, 2.1689281240688800e-05_dp, & + & 2.1689210163877700e-05_dp, 2.1688728615409898e-05_dp, 2.1686958471822701e-05_dp, 2.1682240537002100e-05_dp, & + & 2.1671918586818599e-05_dp, 2.1652162825014399e-05_dp, 2.1617844923382802e-05_dp, 2.1562478672687599e-05_dp, & + & 2.1478241956973700e-05_dp, 2.1356096612024099e-05_dp, 2.1186021683328202e-05_dp, 2.0957371715035799e-05_dp, & + & 2.0659364181607702e-05_dp, 2.0281688824286301e-05_dp, 1.9815217067620202e-05_dp, 1.9252773256428501e-05_dp, & + & 1.8589912844424502e-05_dp, 1.7825637239066198e-05_dp, 1.6962961578048700e-05_dp, 1.6009242019832101e-05_dp, & + & 1.4976168663638500e-05_dp, 1.3879350760803700e-05_dp, 1.2737477090962701e-05_dp, 1.1571131121601600e-05_dp, & + & 1.0401453461428300e-05_dp, 9.2489109958515703e-06_dp, 8.1323785947606808e-06_dp, 7.0685441251328004e-06_dp, & + & 6.0714079386237100e-06_dp, 5.1515658641143602e-06_dp, 4.3152051101280603e-06_dp, 3.5632297943344301e-06_dp, & + & 2.8912710402506601e-06_dp, 2.2910376531459801e-06_dp, 1.7524267492685701e-06_dp, 1.2645414748657700e-06_dp, & + & 8.1233620086163004e-07_dp, 3.5502719542002099e-07_dp, 3.1726859117675598e-07_dp, 6.0945916535715096e-07_dp, & + & 7.9575747580218295e-07_dp, 9.3185830896125300e-07_dp, 1.0346604445432599e-06_dp, 1.1104850954346499e-06_dp, & + & 1.1635395514852899e-06_dp, 1.1991656110321701e-06_dp, 1.2238169148082200e-06_dp, 1.2433940642653200e-06_dp, & + & 1.2616724911485001e-06_dp, 1.2799010215003301e-06_dp, 1.2975678275184400e-06_dp, 1.3135927955376701e-06_dp, & + & 1.3272056619273400e-06_dp, 1.3382346976120700e-06_dp, 1.3469599542403900e-06_dp, 1.3538294820758500e-06_dp, & + & 1.3592507905890700e-06_dp, 1.3635173414794400e-06_dp, 1.3668281880763200e-06_dp, 1.3693352703958401e-06_dp, & + & 1.3711768898083699e-06_dp, 1.3724876785081700e-06_dp, 1.3733936058413200e-06_dp, 1.3740035934573001e-06_dp, & + & 1.3744046344355001e-06_dp, 1.3746618474641501e-06_dp, 1.3748218641307400e-06_dp, 1.3749173281008000e-06_dp, & + & 1.3749709660837401e-06_dp, 1.3749986029765199e-06_dp, 1.3750111460542101e-06_dp, 1.3750158377456900e-06_dp, & + & 1.3750171126147801e-06_dp, 1.3750173007975900e-06_dp, 1.3750173087911900e-06_dp, 1.3750173692983500e-06_dp, & + & 1.3750177804139301e-06_dp, 1.3750193054162801e-06_dp, 1.3750234761911201e-06_dp, 1.3750331375739201e-06_dp, & + & 1.3750536594914200e-06_dp, 1.3750955167868301e-06_dp, 1.3751790659544100e-06_dp, 1.3753419290107901e-06_dp, & + & 1.3756478601800701e-06_dp, 1.3761928487898700e-06_dp, 1.3770998650297600e-06_dp, 1.3784903847291500e-06_dp, & + & 1.3804236173031700e-06_dp, 1.3828097239487700e-06_dp, 1.3853341003233799e-06_dp, 1.3874664716029300e-06_dp, & + & 1.3886424304887500e-06_dp, 1.3886547507446799e-06_dp, 1.3881511126134799e-06_dp, 1.3889373889908200e-06_dp, & + & 1.3936633138644800e-06_dp, 1.4046316428872900e-06_dp, 1.4220520406782500e-06_dp, 1.4428053289883299e-06_dp, & + & 1.4609942829979499e-06_dp, 1.4706979721834701e-06_dp, 1.4697682306774600e-06_dp, 1.4622130836139399e-06_dp, & + & 1.4566465046383900e-06_dp, 1.4601737883257500e-06_dp, 1.4708064022261901e-06_dp, 1.4742197381734099e-06_dp, & + & 1.4483513511853700e-06_dp, 1.3734037291879301e-06_dp, 1.2414188403919700e-06_dp, 1.0607900639003599e-06_dp, & + & 8.5420701056992996e-07_dp, 6.5130410509261996e-07_dp, 4.7888602405787903e-07_dp, 3.5191752079111199e-07_dp, & + & 2.6859185398020500e-07_dp, -2.8865798640254102e-15_dp, -2.8865798640254102e-15_dp, -2.8865798640254102e-15_dp, & + & -2.8865798640254102e-15_dp, -2.8865798640254102e-15_dp, -2.8865798640254102e-15_dp, -2.8865798640254102e-15_dp, & + & -2.8865798640254102e-15_dp, -2.8865798640254102e-15_dp, -2.8865798640254102e-15_dp, -2.8865798640254102e-15_dp, & + & -2.8865798640254102e-15_dp, -2.8865798640254102e-15_dp, -2.8865798640254102e-15_dp, -2.8865798640254102e-15_dp, & + & -2.8865798640254102e-15_dp, -2.8865798640254102e-15_dp, -2.8865798640254102e-15_dp, -2.8865798640254102e-15_dp, & + & -2.8865798640254102e-15_dp, -2.8865798640254102e-15_dp, -2.8865798640254102e-15_dp, -2.8865798640254102e-15_dp, & + & -2.8865798640254102e-15_dp, -2.8865798640254102e-15_dp, -2.8865798640254102e-15_dp, -2.8865798640254102e-15_dp, & + & -2.8865798640254102e-15_dp, -2.8865798640254102e-15_dp, -2.8865798640254102e-15_dp, -2.8865798640254102e-15_dp, & + & -2.8865798640254102e-15_dp & + &] + case (2) + out = [& + & 2.0000000000000000_dp, 1.9999999996436999_dp, 1.9999999886262501_dp, 1.9999999139813101_dp, & + & 1.9999996395770401_dp, 1.9999989081040299_dp, 1.9999973072324699_dp, 1.9999942411389999_dp, & + & 1.9999889084477900_dp, 1.9999802874435300_dp, 1.9999671292019301_dp, 1.9999479590517599_dp, & + & 1.9999210865384700_dp, 1.9998846238098500_dp, 1.9998365120970001_dp, 1.9997745557254201_dp, & + & 1.9996964628686700_dp, 1.9995998920571201_dp, 1.9994825032813699_dp, 1.9993420123896599_dp, & + & 1.9991762473733601_dp, 1.9989832050673599_dp, 1.9987611067637501_dp, 1.9985084512478599_dp, & + & 1.9982240638149700_dp, 1.9979071399112700_dp, 1.9975572821628700_dp, 1.9971745297070600_dp, & + & 1.9967593789188001_dp, 1.9963127948270101_dp, 1.9958362127358700_dp, 1.9953315298014200_dp, & + & 1.9948010865575101_dp, 1.9942476386325101_dp, 1.9936743191436801_dp, 1.9930845924930800_dp, & 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1.9824287352437899_dp, 1.9824287009356800_dp, 1.9824284684928699_dp, 1.9824276140033401_dp, & + & 1.9824253362085400_dp, 1.9824203511101099_dp, 1.9824108032829200_dp, 1.9823941971298500_dp, & + & 1.9823673507224899_dp, 1.9823263742008399_dp, 1.9822666739744701_dp, 1.9821829832019700_dp, & + & 1.9820694182488501_dp, 1.9819195600613599_dp, 1.9817265586694000_dp, 1.9814832583665001_dp, & + & 1.9811823405289699_dp, 1.9808164805420601_dp, 1.9803785149111199_dp, 1.9798616143537699_dp, & + & 1.9792594584978700_dp, 1.9785664077464999_dp, 1.9777776679107100_dp, 1.9768894433467601_dp, & + & 1.9758990745588201_dp, 1.9748051565353200_dp, 1.9736076344688400_dp, 1.9723078739626700_dp, & + & 1.9709087033469199_dp, 1.9694144263093101_dp, 1.9678308036867200_dp, 1.9661650039563900_dp, & + & 1.9644255227016301_dp, 1.9626220720920300_dp, 1.9607654421967000_dp, 1.9588673367179601_dp, & + & 1.9569401864686400_dp, 1.9549969445908999_dp, 1.9530508681009600_dp, 1.9511152908157301_dp, & + & 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0.1614401314148460_dp, & + & 0.1577791099115900_dp, 0.1541752794757630_dp, 0.1506517699160180_dp, 0.1472296403674610_dp, & + & 0.1439276432193190_dp, 0.1407620639806460_dp, 0.1377466321555990_dp, 0.1348924960981300_dp, & + & 0.1322082534027310_dp, 0.1297000276486350_dp, 0.1273715821983280_dp, 0.1252244621734230_dp, & + & 0.1232581565828240_dp, 0.1214702737343670_dp, 0.1198567243903890_dp, 0.1184119085025180_dp, & + & 0.1171289026659300_dp, 0.1159996465720680_dp, 0.1150151276381100_dp, 0.1141655636041410_dp, & + & 0.1134405831941690_dp, 0.1128294049403380_dp, 0.1123210140006810_dp, 0.1119043363107480_dp, & + & 0.1115684087673410_dp, 0.1113025434293900_dp, 0.1110964830242070_dp, 0.1109405444528410_dp, & + & 0.1108257465739450_dp, 0.1107439183731680_dp, 0.1106877837347230_dp, 0.1106510194372320_dp, & + & 0.1106282836838040_dp, 0.1106152134064150_dp, 0.1106083896954980_dp, 0.1106052719202810_dp, & + & 0.1106041023407660_dp, 0.1106037841873100_dp, 0.1106037372285460_dp, 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0.0621707508768736_dp, & + & 0.0601675535325077_dp, 0.0582768897802257_dp, 0.0565035317589748_dp, 0.0548504450425424_dp, & + & 0.0533189420095210_dp, 0.0519088507368854_dp, 0.0506186900509871_dp, 0.0494458431574207_dp, & + & 0.0483867241835272_dp, 0.0474369338427243_dp, 0.0465914021439904_dp, 0.0458445175355600_dp, & + & 0.0451902430367781_dp, 0.0446222207523590_dp, 0.0441338666783428_dp, 0.0437184579157819_dp, & + & 0.0433692143371536_dp, 0.0430793764431670_dp, 0.0428422806541908_dp, 0.0426514326583165_dp, & + & 0.0425005787500652_dp, 0.0423837744048878_dp, 0.0422954487096900_dp, 0.0422304627673684_dp, & + & 0.0421841598628312_dp, 0.0421524050530566_dp, 0.0421316119396966_dp, 0.0421187546946866_dp, & + & 0.0421113639115509_dp, 0.0421075055050197_dp, 0.0421057426239120_dp, 0.0421050813155217_dp, & + & 0.0421049014244703_dp, 0.0421048748729591_dp, 0.0421048728011026_dp, 0.0421048352866746_dp, & + & 0.0421045811214027_dp, 0.0421036467903049_dp, 0.0421011562629099_dp, 0.0420957060901852_dp, & + & 0.0420852694516602_dp, 0.0420671234739469_dp, 0.0420378039434786_dp, 0.0419930912806654_dp, & + & 0.0419280312628354_dp, 0.0418369933943250_dp, 0.0417137689336640_dp, 0.0415517093216256_dp, & + & 0.0413439040610273_dp, 0.0410833949809515_dp, 0.0407634213407215_dp, 0.0403776875350381_dp, & + & 0.0399206424697969_dp, 0.0393877572707515_dp, 0.0387757861851190_dp, 0.0380829946587324_dp, & + & 0.0373093388883099_dp, 0.0364565828302457_dp, 0.0355283417201200_dp, 0.0345300454760498_dp, & + & 0.0334688206038010_dp, 0.0323532949224461_dp, 0.0311933350197107_dp, 0.0299997312373517_dp, & + & 0.0287838486508445_dp, 0.0275572645543471_dp, 0.0263314131964343_dp, 0.0251172569611660_dp, & + & 0.0239250000933362_dp, 0.0227638568393695_dp, 0.0216418810355155_dp, 0.0205658592676086_dp, & + & 0.0195412652435349_dp, 0.0185722693379917_dp, 0.0176617946183049_dp, 0.0168116091165489_dp, & + & 0.0160224436219396_dp, 0.0152941246748419_dp, 0.0146257135354784_dp, 0.0140156434386469_dp, & + & 0.0134618492000804_dp, 0.0129618850142847_dp, 0.0125130279301473_dp, 0.0121123659152778_dp, & + & 0.0117568705764999_dp, 0.0114434554821230_dp, 0.0111690216456628_dp, 0.0109304921086659_dp, & + & 0.0107248377366611_dp, 0.0105490963529853_dp, 0.0104003872140650_dp, 0.0102759226067892_dp, & + & 0.0101730180498523_dp, 0.0100891022292506_dp, 0.0100217274147871_dp, 0.0099685807109839_dp, & + & 0.0099274961141029_dp, 0.0098964670002735_dp, 0.0098736583800303_dp, 0.0098574180424320_dp, & + & 0.0098462855923192_dp, 0.0098389983658480_dp, 0.0098344932918248_dp, 0.0098319039400145_dp, & + & 0.0098305522443907_dp, 0.0098299346844515_dp, 0.0098297030230237_dp, 0.0098296400061244_dp, & + & 0.0098296307049832_dp, 0.0098296299730265_dp, 0.0098296166405767_dp, 0.0098295263116066_dp, & + & 0.0098291942578568_dp, 0.0098283091636535_dp, 0.0098263723554428_dp, 0.0098226638977534_dp, & + & 0.0098162172420029_dp, 0.0098058041293489_dp, 0.0097899314469876_dp, 0.0097668516752503_dp, & + & 0.0097345883856956_dp, 0.0096909778986358_dp, 0.0096337276294047_dp, 0.0095604908118956_dp, & + & 0.0094689561832189_dp, 0.0093569498868060_dp, 0.0092225453969341_dp, 0.0090641758320222_dp, & + & 0.0088807417969443_dp, 0.0086717070877258_dp, 0.0084371744076144_dp, 0.0081779338359072_dp, & + & 0.0078954782276748_dp, 0.0075919819551133_dp, 0.0072702422512023_dp, 0.0069335855874613_dp, & + & 0.0065857446321402_dp, 0.0062307139931104_dp, 0.0058725947977818_dp, 0.0055154389581187_dp, & + & 0.0051631036239863_dp, 0.0048191249204601_dp, 0.0044866178184666_dp, 0.0041682062294521_dp, & + & 0.0038659845158771_dp, 0.0035815089295452_dp, 0.0033158153212573_dp, 0.0030694579911401_dp, & + & 0.0028425638227443_dp, 0.0026348957984270_dp, 0.0024459204803220_dp, 0.0022748748812225_dp, & + & 0.0021208291767270_dp, 0.0019827427889325_dp, 0.0018595123973482_dp, 0.0017500113237077_dp, & + & 0.0016531204385215_dp, 0.0015677512270100_dp, 0.0014928619448096_dp, 0.0014274679299930_dp, & + & 0.0013706471655723_dp, 0.0013215421459485_dp, 0.0012793590175662_dp, 0.0012433648544725_dp, & + & 0.0012128838043921_dp, 0.0011872927108900_dp, 0.0011660166900862_dp, 0.0011485250220469_dp, & + & 0.0011343276085300_dp, 0.0011229721498678_dp, 0.0011140421029108_dp, 0.0011071553991409_dp, & + & 0.0011019638284484_dp, 0.0010981529323404_dp, 0.0010954422037672_dp, 0.0010935853622742_dp, & + & 0.0010923704649128_dp, 0.0010916196259618_dp, 0.0010911881504079_dp, 0.0010909629341480_dp, & + & 0.0010908600430488_dp, 0.0010908214469971_dp, 0.0010908109481189_dp, 0.0010908093985140_dp, & + & 0.0010908092754880_dp, 0.0010908070208719_dp, 0.0010907917456171_dp, 0.0010907355936682_dp, & + & 0.0010905859247412_dp, 0.0010902584365562_dp, 0.0010896314820226_dp, 0.0010885419051148_dp, & + & 0.0010867827434025_dp, 0.0010841031668996_dp, 0.0010802110295094_dp, 0.0010747783840355_dp, & + & 0.0010674502367900_dp, 0.0010578566770150_dp, 0.0010456282992051_dp, 0.0010304145433064_dp, & + & 0.0010119042234278_dp, 0.0009898471326268_dp, 0.0009640752494304_dp, 0.0009345217938685_dp, & + & 0.0009012362545668_dp, 0.0008643935925585_dp, 0.0008242961578411_dp, 0.0007813674291794_dp, & + & 0.0007361374575137_dp, 0.0006892207627462_dp, 0.0006412882731057_dp, 0.0005930355688939_dp, & + & 0.0005451500880254_dp, 0.0004982800144973_dp, 0.0004530073107585_dp, 0.0004098268261661_dp, & + & 0.0003691326911905_dp, 0.0003312123725845_dp, 0.0002962479193300_dp, 0.0002643232089268_dp, & + & 0.0002354355572614_dp, 0.0002095099690944_dp, 0.0001864145276294_dp, 0.0001659757670778_dp, & + & 0.0001479931481434_dp, 0.0001322519061224_dp, 0.0001185336748817_dp, 0.0001066245535597_dp, & + & 9.6320684514594705e-05_dp, 8.7431783436287005e-05_dp, 7.9783209330663905e-05_dp, 7.3217040115203206e-05_dp, & + & 6.7592378051095596e-05_dp, 6.2821406186408497e-05_dp, 5.8726348083126802e-05_dp, 5.5233566911283601e-05_dp, & + & 5.2248226981355097e-05_dp, 4.9782831250233501e-05_dp, 4.7703510589691702e-05_dp, 4.5958823141845100e-05_dp, & + & 4.4503133854512100e-05_dp, 4.3296521671010202e-05_dp, 4.2294222177829999e-05_dp, 4.1533627038958798e-05_dp, & + & 4.0923149230209801e-05_dp, 4.0443235566733897e-05_dp, 4.0073155730624401e-05_dp, 3.9794027355100097e-05_dp, & + & 3.9588958200553700e-05_dp, 3.9442953998047903e-05_dp, 3.9342856744895003e-05_dp, 3.9277320947661599e-05_dp, & + & 3.9236798755837299e-05_dp, 3.9213505235835603e-05_dp, 3.9201344629979901e-05_dp, 3.9195788500201398e-05_dp, & + & 3.9193704228779298e-05_dp, 3.9193137259196897e-05_dp, 3.9193053575914398e-05_dp, 3.9193046970531498e-05_dp, & + & 3.9192926448272699e-05_dp, 3.9192109878349902e-05_dp, 3.9189108050230500e-05_dp, 3.9181106047614398e-05_dp, & + & 3.9163592741253701e-05_dp, 3.9130048842928000e-05_dp, 3.9071706357418600e-05_dp, 3.8977395012018703e-05_dp, & + & 3.8833499773183198e-05_dp, 3.8624067554948697e-05_dp, 3.8331114466494398e-05_dp, 3.7935187646276300e-05_dp, & + & 3.7416222271602398e-05_dp, 3.6754701841168503e-05_dp, 3.5933062912718603e-05_dp, 3.4937088605246900e-05_dp, & + & 3.3755408068714098e-05_dp, 3.2434753610033299e-05_dp, 3.0947182324325702e-05_dp, 2.9286542550188699e-05_dp, & + & 2.7472599786193500e-05_dp, 2.5530806635032401e-05_dp, 2.3536460141748698e-05_dp, 2.1501481480612500e-05_dp, & + & 1.9442844830130899e-05_dp, 1.7399181317934199e-05_dp, 1.5455519068119399e-05_dp, 1.3602680652979899e-05_dp, & + & 1.1854494713858800e-05_dp, 1.0258360863879500e-05_dp, 8.8189439777508500e-06_dp, 7.5154224123963297e-06_dp, & + & 6.3630748448062499e-06_dp, 5.3837868696504600e-06_dp, 4.5291613792741697e-06_dp, 3.7841831677099002e-06_dp, & + & 3.1922260319561200e-06_dp, 2.6744132508582699e-06_dp, 2.2309076195270399e-06_dp, 1.8810089166265700e-06_dp, & + & 1.5789937846122400e-06_dp, 1.3487042620496900e-06_dp, 1.1722791031232300e-06_dp, 1.0140731694363600e-06_dp, & + & 8.6622585104834105e-07_dp, 7.7557970801223096e-07_dp, 6.8011544129831204e-07_dp, 5.8028099214624305e-07_dp, & + & 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0.1405197008083280_dp, & + & 0.1381099294269390_dp, 0.1354962072141340_dp, 0.1326915850492170_dp, 0.1297130902659300_dp, & + & 0.1265813181314710_dp, 0.1233198915482770_dp, 0.1199548162727840_dp, 0.1165137646537500_dp, & + & 0.1130253240681610_dp, 0.1095182466755310_dp, 0.1060207349046930_dp, 0.1025597925737450_dp, & + & 0.0991606652704711_dp, 0.0958463862645527_dp, 0.0926374365017306_dp, 0.0895515198214216_dp, & + & 0.0866034480081321_dp, 0.0838051250404437_dp, 0.0811656161668104_dp, 0.0786912852684782_dp, & + & 0.0763859832706277_dp, 0.0742512709258278_dp, 0.0722866608418471_dp, 0.0704898658538244_dp, & + & 0.0688570434507643_dp, 0.0673830286945432_dp, 0.0660615507001321_dp, 0.0648854301184247_dp, & + & 0.0638467570683794_dp, 0.0629370505406683_dp, 0.0621474014151158_dp, 0.0614686019033499_dp, & + & 0.0608912644733941_dp, 0.0604059331788420_dp, 0.0600031898599998_dp, 0.0596737569772934_dp, & + & 0.0594085979572387_dp, 0.0591990149635588_dp, 0.0590367430410197_dp, 0.0589140387046339_dp, & + & 0.0588237603443265_dp, 0.0587594373520517_dp, 0.0587153247018595_dp, 0.0586864398452445_dp, & + & 0.0586685792169188_dp, 0.0586583123450843_dp, 0.0586529524654562_dp, 0.0586505035727249_dp, & + & 0.0586495849215449_dp, 0.0586493350273827_dp, 0.0586492981435711_dp, 0.0586492952886122_dp, & + & 0.0586492438914625_dp, 0.0586488956688704_dp, 0.0586476155757936_dp, 0.0586442033944152_dp, & + & 0.0586367363085625_dp, 0.0586224374389026_dp, 0.0585975762567266_dp, 0.0585574065207979_dp, & + & 0.0584961470296914_dp, 0.0584070099596232_dp, 0.0582822807485677_dp, 0.0581134522679161_dp, & + & 0.0578914142853169_dp, 0.0576066969003541_dp, 0.0572497637297253_dp, 0.0568113472230820_dp, & + & 0.0562828148008805_dp, 0.0556565508237004_dp, 0.0549263361178518_dp, 0.0540877043363501_dp, & + & 0.0531382532656206_dp, 0.0520778896646270_dp, 0.0509089885724929_dp, 0.0496364522706934_dp, & + & 0.0482676600271787_dp, 0.0468123069323223_dp, 0.0452821379088597_dp, 0.0436905905603275_dp, & + & 0.0420523671133193_dp, 0.0403829605970802_dp, 0.0386981630749634_dp, 0.0370135839531045_dp, & + & 0.0353442042017935_dp, 0.0337039880813563_dp, 0.0321055682369291_dp, 0.0305600135166166_dp, & + & 0.0290766822990562_dp, 0.0276631581355069_dp, 0.0263252596113031_dp, 0.0250671128103690_dp, & + & 0.0238912727229224_dp, 0.0227988792926812_dp, 0.0217898343461620_dp, 0.0208629870922135_dp, & + & 0.0200163179085031_dp, 0.0192471124421019_dp, 0.0185521203923571_dp, 0.0179276955267049_dp, & + & 0.0173699153803462_dp, 0.0168746806437348_dp, 0.0164377954283825_dp, 0.0160550304366076_dp, & + & 0.0157221715800855_dp, 0.0154350568411914_dp, 0.0151896041976194_dp, 0.0149818332785863_dp, & + & 0.0148078831291105_dp, 0.0146640280609684_dp, 0.0145466930959621_dp, 0.0144524699884077_dp, & + & 0.0143781342791716_dp, 0.0143206633145621_dp, 0.0142772546914465_dp, 0.0142453441969259_dp, & + & 0.0142226220238868_dp, 0.0142070458845343_dp, 0.0141968496235769_dp, 0.0141905460508909_dp, & + & 0.0141869229568883_dp, 0.0141850316173180_dp, 0.0141841675039043_dp, 0.0141838433540702_dp, & + & 0.0141837551782960_dp, 0.0141837421637696_dp, 0.0141837411482264_dp, 0.0141837227601052_dp, & + & 0.0141835981783274_dp, 0.0141831402092087_dp, 0.0141819194829029_dp, 0.0141792482131571_dp, & + & 0.0141741334078986_dp, 0.0141652418345259_dp, 0.0141508790515239_dp, 0.0141289848025643_dp, & + & 0.0140971469730538_dp, 0.0140526360600592_dp, 0.0139924616268985_dp, 0.0139134514341865_dp, & + & 0.0138123528150338_dp, 0.0136859543906791_dp, 0.0135312244594310_dp, 0.0133454604596537_dp, & + & 0.0131264419986685_dp, 0.0128725783023338_dp, 0.0125830398524904_dp, 0.0122578637062603_dp, & + & 0.0118980227363252_dp, 0.0115054508851440_dp, 0.0110830194298313_dp, 0.0106344629808213_dp, & + & 0.0101642581079169_dp, 0.0096774616160360_dp, 0.0091795190613837_dp, 0.0086760566415922_dp, & + & 0.0081726707802261_dp, 0.0076747294220105_dp, 0.0071871973426365_dp, 0.0067144949374587_dp, & + & 0.0062603964082211_dp, 0.0058279694995971_dp, 0.0054195554077285_dp, 0.0050367845622166_dp, & + & 0.0046806219082551_dp, 0.0043514341771633_dp, 0.0040490713845252_dp, 0.0037729552829795_dp, & + & 0.0035221685078763_dp, 0.0032955394617851_dp, 0.0030917193865090_dp, 0.0029092494127383_dp, & + & 0.0027466165516241_dp, 0.0026022985391503_dp, 0.0024747981414475_dp, 0.0023626679884412_dp, & + & 0.0022645272589124_dp, 0.0021790716382348_dp, 0.0021050779565019_dp, 0.0020414048271746_dp, & + & 0.0019869904733607_dp, 0.0019408487708681_dp, 0.0019020643692453_dp, 0.0018697875844236_dp, & + & 0.0018432295953463_dp, 0.0018216583244222_dp, 0.0018043952379525_dp, 0.0017908131685740_dp, & + & 0.0017803351380117_dp, 0.0017724340482221_dp, 0.0017666330170165_dp, 0.0017625060645106_dp, & + & 0.0017596788148779_dp, 0.0017578288655660_dp, 0.0017566854954350_dp, 0.0017560284306875_dp, & + & 0.0017556854589458_dp, 0.0017555287695128_dp, 0.0017554699926734_dp, 0.0017554540042095_dp, & + & 0.0017554516443567_dp, 0.0017554514586457_dp, 0.0017554480759863_dp, 0.0017554251581089_dp, & + & 0.0017553409116484_dp, 0.0017551163574758_dp, 0.0017546250071323_dp, 0.0017536843226722_dp, & + & 0.0017520494349306_dp, 0.0017494096255497_dp, 0.0017453881045579_dp, 0.0017395456208273_dp, & + & 0.0017313884035293_dp, 0.0017203808256046_dp, 0.0017059629815392_dp, 0.0016875730683630_dp, & + & 0.0016646740497404_dp, 0.0016367835888627_dp, 0.0016035056995527_dp, 0.0015645620544653_dp, & + & 0.0015198204895857_dp, 0.0014693180475298_dp, 0.0014132759894210_dp, 0.0013521046260951_dp, & + & 0.0012863965752370_dp, 0.0012169080816822_dp, 0.0011445292254866_dp, 0.0010702450240920_dp, & + & 0.0009950904338947_dp, 0.0009201029147690_dp, 0.0008462764332542_dp, 0.0007745205148098_dp, & + & 0.0007056272623824_dp, 0.0006402482566834_dp, 0.0005788821069981_dp, 0.0005218723065532_dp, & + & 0.0004694141177097_dp, 0.0004215685732056_dp, 0.0003782813695548_dp, 0.0003394044231673_dp, & + & 0.0003047180911668_dp, 0.0002739524412103_dp, 0.0002468064062295_dp, 0.0002229641133233_dp, & + & 0.0002021080809129_dp, 0.0001839293001478_dp, 0.0001681344404236_dp, 0.0001544505494504_dp, & + & 0.0001426276762722_dp, 0.0001324398547737_dp, 0.0001236848640271_dp, 0.0001161831384593_dp, & + & 1.0977614086904500e-04_dp, 1.0432444216768001e-04_dp, 9.9705684638351499e-05_dp, 9.5812550396701099e-05_dp, & + & 9.2550817695880001e-05_dp, 8.9837562132544195e-05_dp, 8.7599541995331306e-05_dp, 8.5771792322830706e-05_dp, & + & 8.4296438519260205e-05_dp, 8.3121727891821706e-05_dp, 8.2201267263215500e-05_dp, 8.1493446801417195e-05_dp, & + & 8.0961024417902595e-05_dp, 8.0570840783167301e-05_dp, 8.0293631899763795e-05_dp, 8.0103904565476100e-05_dp, & + & 7.9979839959776200e-05_dp, 7.9903192645502900e-05_dp, 7.9859156313588601e-05_dp, 7.9836173577874106e-05_dp, & + & 7.9825674445643799e-05_dp, 7.9821736164831196e-05_dp, 7.9820664883101204e-05_dp, 7.9820506764249899e-05_dp, & + & 7.9820494212512499e-05_dp, 7.9820264140551003e-05_dp, 7.9818705385648099e-05_dp, 7.9812975464221795e-05_dp, & + & 7.9797703355311000e-05_dp, 7.9764289644401702e-05_dp, 7.9700332575427497e-05_dp, 7.9589217591546899e-05_dp, & + & 7.9409912901340403e-05_dp, 7.9137018284214405e-05_dp, 7.8741116761094104e-05_dp, 7.8189476093726298e-05_dp, & + & 7.7447136542119197e-05_dp, 7.6478400508506197e-05_dp, 7.5248706600916594e-05_dp, 7.3726826638420602e-05_dp, & + & 7.1887271312576204e-05_dp, 6.9712735816906997e-05_dp, 6.7196368712885105e-05_dp, 6.4343616584139300e-05_dp, & + & 6.1173393676838800e-05_dp, 5.7718357711067397e-05_dp, 5.4024145043740598e-05_dp, 5.0147527954180800e-05_dp, & + & 4.6153593725506398e-05_dp, 4.2112187941256700e-05_dp, 3.8093980776920903e-05_dp, 3.4166571612814798e-05_dp, & + & 3.0391021432762999e-05_dp, 2.6819102197705998e-05_dp, 2.3491417309173799e-05_dp, 2.0436431737991300e-05_dp, & + & 1.7670385082268998e-05_dp, 1.5198028878060700e-05_dp, 1.3014083876328200e-05_dp, 1.1105227333274600e-05_dp, & + & 9.4523303371118993e-06_dp, 8.0326449563017394e-06_dp, 6.8217254654001602e-06_dp, 5.7949935694523396e-06_dp, & + & 4.9289224097748300e-06_dp, 4.2017970756091901e-06_dp, 3.5939964906361899e-06_dp, 3.0878435204329001e-06_dp, & + & 2.6672754724899101e-06_dp, 2.3176876453589999e-06_dp, 2.0261344086946998e-06_dp, 1.7817619912818800e-06_dp, & + & 1.5761115719215000e-06_dp, 1.4029351689259801e-06_dp, 1.2575230989853000e-06_dp, 1.1359570297742001e-06_dp, & + & 1.0346595011867500e-06_dp, 9.5025094815071000e-07_dp, 8.7961009676007496e-07_dp, 8.2009608171063096e-07_dp, & + & 7.6978063745514202e-07_dp, 7.2745241652683003e-07_dp, 6.9235229283037803e-07_dp, 6.6384161456767298e-07_dp, & + & 6.4120795961741795e-07_dp, 6.2364434150197202e-07_dp, 6.1031642673015096e-07_dp, 6.0043279859201004e-07_dp, & + & 5.9328581514250800e-07_dp, 5.8826599413919201e-07_dp, 5.8486130960488904e-07_dp, 5.8264969382548802e-07_dp, & + & 5.8128950009006499e-07_dp, 5.8051021945004798e-07_dp, 5.8010416026377200e-07_dp, 5.7991881163843604e-07_dp, & + & 5.7984931167709398e-07_dp, 5.7983040768760898e-07_dp, 5.7982761880737101e-07_dp, 5.7982738610462505e-07_dp, & + & 5.7982293455438604e-07_dp, 5.7979278267339396e-07_dp, 5.7968195754654104e-07_dp, 5.7938670749990696e-07_dp, & + & 5.7874141212721497e-07_dp, 5.7750881765627995e-07_dp, 5.7537521591655097e-07_dp, 5.7195239122620499e-07_dp, & + & 5.6678783622032803e-07_dp, 5.5938294529767095e-07_dp, 5.4921616587932899e-07_dp, 5.3576546044098397e-07_dp, & + & 5.1852541460562005e-07_dp, 4.9702164695020201e-07_dp, 4.7083169008033099e-07_dp, 4.3960893592043201e-07_dp, & + & 4.0305973847409902e-07_dp, 3.6078136922412801e-07_dp, 3.1193492766590199e-07_dp, 2.5491524624499101e-07_dp, & + & 3.5527136788005001e-15_dp, 1.7763568394002501e-15_dp, 1.7763568394002501e-15_dp, 1.7763568394002501e-15_dp, & + & 2.0151311908023199e-07_dp, 2.4833635237087000e-07_dp, 2.9165804882325098e-07_dp, 3.3351508577084101e-07_dp, & + & 3.7239304440106501e-07_dp, 4.0453966398956698e-07_dp, 4.2577172543190003e-07_dp, 4.3430020291168598e-07_dp, & + & 4.3264735438697201e-07_dp, 4.2692113488840299e-07_dp, 4.2417301848729499e-07_dp, 4.2917375608908499e-07_dp, & + & 4.4185533276675002e-07_dp, 4.5809152204867598e-07_dp, 4.7317594820128798e-07_dp, 4.8393435569948895e-07_dp, & + & 4.8898350790693701e-07_dp, 4.8849602052314399e-07_dp, 4.8361430060595001e-07_dp, 4.7613965570292299e-07_dp, & + & 4.6880105308844101e-07_dp, 4.6456729663191302e-07_dp, 4.6488564819924202e-07_dp, 4.6918384732919099e-07_dp, & + & 4.7582467033180402e-07_dp, 4.8277650499528601e-07_dp, 4.8814106712313798e-07_dp, 4.9104722599224704e-07_dp, & + & 4.9204263241620104e-07_dp, 4.9243517707964202e-07_dp, 4.9328280127269895e-07_dp, 4.9491799281042901e-07_dp, & + & 4.9711895044879405e-07_dp, 4.9948439873048798e-07_dp, 5.0167764165109898e-07_dp, 5.0350393188125498e-07_dp, & + & 5.0489991032520699e-07_dp, 5.0589338407292004e-07_dp, 5.0655939709542995e-07_dp, 5.0698481679489802e-07_dp, & + & 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0.0259850755041420_dp, 0.0259431739137685_dp, 0.0259144496542980_dp, & + & 0.0258956462890563_dp, 0.0258840215021738_dp, 0.0258773399094814_dp, 0.0258738519526283_dp, & + & 0.0258722583760349_dp, 0.0258716605865708_dp, 0.0258714979748635_dp, 0.0258714739737727_dp, & + & 0.0258714720682729_dp, 0.0258714371475612_dp, 0.0258712005554553_dp, 0.0258703308307684_dp, & + & 0.0258680125633290_dp, 0.0258629395953900_dp, 0.0258532261846671_dp, 0.0258363405198594_dp, & + & 0.0258090650034468_dp, 0.0257674876971485_dp, 0.0257070291522226_dp, 0.0256225083812236_dp, & + & 0.0255082508202076_dp, 0.0253582396478453_dp, 0.0251663096836072_dp, 0.0249263802746640_dp, & + & 0.0246327202032539_dp, 0.0242802339351282_dp, 0.0238647548476631_dp, 0.0233833278949405_dp, & + & 0.0228344620161440_dp, 0.0222183319863074_dp, 0.0215369107474093_dp, 0.0207940167412541_dp, & + & 0.0199952663070864_dp, 0.0191479283973148_dp, 0.0182606869896027_dp, 0.0173433246951831_dp, & + & 0.0164063481616772_dp, 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8.6971427073478895e-05_dp, 8.6966561163137599e-05_dp, & + & 8.6965237557023997e-05_dp, 8.6965042196851500e-05_dp, 8.6965026403262895e-05_dp, 8.6964733357675100e-05_dp, & + & 8.6962747962715498e-05_dp, 8.6955449770442797e-05_dp, 8.6935998057313695e-05_dp, 8.6893441581636894e-05_dp, & + & 8.6811991113933104e-05_dp, 8.6670505336172696e-05_dp, 8.6442248720786097e-05_dp, 8.6094987873153200e-05_dp, & + & 8.5591497846593297e-05_dp, 8.4890548274430002e-05_dp, 8.3948426265578705e-05_dp, 8.2721024286413995e-05_dp, & + & 8.1166471666449497e-05_dp, 7.9248215572036402e-05_dp, 7.6938362818523802e-05_dp, 7.4220988857121001e-05_dp, & + & 7.1095029200662893e-05_dp, 6.7576328911300693e-05_dp, 6.3698478077966997e-05_dp, 5.9512224359181700e-05_dp, & + & 5.5083495691832200e-05_dp, 5.0490293116212101e-05_dp, 4.5818805208597302e-05_dp, 4.1158993964174301e-05_dp, & + & 3.6599705104833902e-05_dp, 3.2223312134149798e-05_dp, 2.8100237669193000e-05_dp, 2.4284330695678601e-05_dp, & + & 2.0810501574430900e-05_dp, 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0.2217601602066000_dp, 0.2204092597699660_dp, 0.2188267754227780_dp, 0.2169993107410860_dp, & + & 0.2149170320511300_dp, 0.2125741968023560_dp, 0.2099695584758850_dp, 0.2071066245050230_dp, & + & 0.2039937512798870_dp, 0.2006440696667550_dp, 0.1970752439711770_dp, 0.1933090769052690_dp, & + & 0.1893709810487840_dp, 0.1852893437428410_dp, 0.1810948165043560_dp, 0.1768195613057420_dp, & + & 0.1724384182010590_dp, 0.1681069582749150_dp, 0.1637921901728840_dp, 0.1595250140040250_dp, & + & 0.1553344708579920_dp, 0.1512472878935220_dp, 0.1472875239948180_dp, 0.1434763166769010_dp, & + & 0.1398317264356860_dp, 0.1363686710282280_dp, 0.1330989393583430_dp, 0.1300312727954620_dp, & + & 0.1271715008674370_dp, 0.1245227182722370_dp, 0.1220854909257460_dp, 0.1198580801371540_dp, & + & 0.1178366757902140_dp, 0.1160156314126400_dp, 0.1143876960528550_dp, 0.1129442397917960_dp, & + & 0.1116754713683610_dp, 0.1105706476964880_dp, 0.1096182759437010_dp, 0.1088063093048590_dp, & + & 0.1081223376535000_dp, 0.1075537739304800_dp, 0.1070880365031840_dp, 0.1067127268893110_dp, & + & 0.1064158012893600_dp, 0.1061857334237130_dp, 0.1060116653319540_dp, 0.1058835421636100_dp, & + & 0.1057922266502280_dp, 0.1057295889518010_dp, 0.1056885679370630_dp, 0.1056632006731240_dp, & + & 0.1056486179194560_dp, 0.1056410046701370_dp, 0.1056375261735420_dp, 0.1056362212790670_dp, & + & 0.1056358663170460_dp, 0.1056358139254280_dp, 0.1056358098372230_dp, 0.1056357358134950_dp, & + & 0.1056352342924140_dp, 0.1056333906565040_dp, 0.1056284762663450_dp, 0.1056177215800620_dp, & + & 0.1055971263582620_dp, 0.1055613151288740_dp, 0.1055034454943370_dp, 0.1054151761473590_dp, & + & 0.1052867005314600_dp, 0.1051068508251360_dp, 0.1048632752232720_dp, 0.1045426892344410_dp, & + & 0.1041311988496500_dp, 0.1036146899791110_dp, 0.1029792746023510_dp, 0.1022117798415230_dp, & + & 0.1013002619590450_dp, 0.1002345234957890_dp, 0.0990066088519619_dp, 0.0976112520149801_dp, & + & 0.0960462502393362_dp, 0.0943127395367505_dp, 0.0924153519124200_dp, 0.0903622402388056_dp, & + & 0.0881649641212601_dp, 0.0858382385104388_dp, 0.0833995554427460_dp, 0.0808686973672650_dp, & + & 0.0782671672998365_dp, 0.0756175659066098_dp, 0.0729429481301818_dp, 0.0702661919495515_dp, & + & 0.0676094093942172_dp, 0.0649934253475557_dp, 0.0624373435115775_dp, 0.0599582118286950_dp, & + & 0.0575707923727133_dp, 0.0552874338899230_dp, 0.0531180393330501_dp, 0.0510701162563301_dp, & + & 0.0491488950108181_dp, 0.0473574982945504_dp, 0.0456971456216895_dp, 0.0441673774213509_dp, & + & 0.0427662854491775_dp, 0.0414907386710031_dp, 0.0403365964635380_dp, 0.0392989036276479_dp, & + & 0.0383720641419369_dp, 0.0375499926767002_dp, 0.0368262445736303_dp, 0.0361941262519547_dp, & + & 0.0356467888352761_dp, 0.0351773082354416_dp, 0.0347787550224314_dp, 0.0344442572030914_dp, & + & 0.0341670585807350_dp, 0.0339405747303356_dp, 0.0337584478615582_dp, 0.0336146010183285_dp, & + & 0.0335032912452782_dp, 0.0334191606035876_dp, 0.0333572833025393_dp, 0.0333132067799671_dp, & + & 0.0332829843520699_dp, 0.0332631970785755_dp, 0.0332509627500048_dp, 0.0332439303739918_dp, & + & 0.0332402591729828_dp, 0.0332385818469607_dp, 0.0332379526363660_dp, 0.0332377814769913_dp, & + & 0.0332377562142661_dp, 0.0332377542262030_dp, 0.0332377180140710_dp, 0.0332374726722229_dp, & + & 0.0332365707794242_dp, 0.0332341667395859_dp, 0.0332289059389623_dp, 0.0332188323392533_dp, & + & 0.0332013188422167_dp, 0.0331730246632791_dp, 0.0331298838031007_dp, 0.0330671284213100_dp, & + & 0.0329793503882581_dp, 0.0328606034027388_dp, 0.0327045467147915_dp, 0.0325046296176925_dp, & + & 0.0322543134692914_dp, 0.0319473251499875_dp, 0.0315779327404915_dp, 0.0311412310831951_dp, & + & 0.0306334221344855_dp, 0.0300520730279530_dp, 0.0293963339495509_dp, 0.0286670986051085_dp, & + & 0.0278670924265736_dp, 0.0270008777100497_dp, 0.0260747703675897_dp, 0.0250966694410284_dp, & + & 0.0240758073200293_dp, 0.0230224349760366_dp, 0.0219474617233608_dp, 0.0208620724262421_dp, & + & 0.0197773462887980_dp, 0.0187039002866527_dp, 0.0176515771223986_dp, 0.0166291927784545_dp, & + & 0.0156443529482999_dp, 0.0147033415729645_dp, 0.0138110790740598_dp, 0.0129711432012680_dp, & + & 0.0121858420483623_dp, 0.0114563268695314_dp, 0.0107827317835465_dp, 0.0101643280747581_dp, & + & 0.0095996822853088_dp, 0.0090868093106504_dp, 0.0086233139492986_dp, 0.0082065165609446_dp, & + & 0.0078335604708961_dp, 0.0075015004129799_dp, 0.0072073725836894_dp, 0.0069482477929021_dp, & + & 0.0067212697784846_dp, 0.0065236810595621_dp, 0.0063528387951610_dp, 0.0062062230479754_dp, & + & 0.0060814396749471_dp, 0.0059762198140110_dp, 0.0058884176374416_dp, 0.0058160077157812_dp, & + & 0.0057570829956060_dp, 0.0057098540512257_dp, 0.0056726499339046_dp, 0.0056439206254115_dp, & + & 0.0056222408174058_dp, 0.0056063144996177_dp, 0.0055949796611792_dp, 0.0055872123026415_dp, & + & 0.0055821289282179_dp, 0.0055789867390157_dp, 0.0055771808723240_dp, 0.0055762382154150_dp, & + & 0.0055758075460961_dp, 0.0055756459933853_dp, 0.0055756020477151_dp, 0.0055755955614476_dp, & + & 0.0055755950464871_dp, 0.0055755856092112_dp, 0.0055755216705950_dp, 0.0055752866303305_dp, & + & 0.0055746601365687_dp, 0.0055732892595088_dp, 0.0055706645908806_dp, 0.0055661025380278_dp, & + & 0.0055587351339028_dp, 0.0055475087264902_dp, 0.0055311929013993_dp, 0.0055084008777868_dp, & + & 0.0054776223429176_dp, 0.0054372692043554_dp, 0.0053857340072820_dp, 0.0053214597866003_dp, & + & 0.0052430189413410_dp, 0.0051491974276701_dp, 0.0050390793131658_dp, 0.0049121257089215_dp, & + & 0.0047682415041628_dp, 0.0046078233618534_dp, 0.0044317832246499_dp, 0.0042415431624168_dp, & + & 0.0040389996715753_dp, 0.0038264582876746_dp, 0.0036065422591936_dp, 0.0033820816591899_dp, & + & 0.0031559912971506_dp, 0.0029311468400213_dp, 0.0027102685057265_dp, 0.0024958205800338_dp, & + & 0.0022899330193056_dp, 0.0020943488568346_dp, 0.0019103984092670_dp, 0.0017389987557408_dp, & + & 0.0015806749407012_dp, 0.0014355980231553_dp, 0.0013036345182193_dp, 0.0011844018817513_dp, & + & 0.0010773253131138_dp, 0.0009816920902992_dp, 0.0008967007115999_dp, 0.0008215031501120_dp, & + & 0.0007552394369750_dp, 0.0006970645273867_dp, 0.0006461679496166_dp, 0.0006017870921671_dp, & + & 0.0005632151651014_dp, 0.0005298049109417_dp, 0.0005009690806794_dp, 0.0004761785730150_dp, & + & 0.0004549589941973_dp, 0.0004368862544091_dp, 0.0004215816863677_dp, 0.0004087070580905_dp, & + & 0.0003979597556203_dp, 0.0003890683318346_dp, 0.0003817885521222_dp, 0.0003759000140260_dp, & + & 0.0003712033731098_dp, 0.0003675181687530_dp, 0.0003646812102573_dp, 0.0003625454548430_dp, & + & 0.0003609792849950_dp, 0.0003598660747954_dp, 0.0003591039240796_dp, 0.0003586054369418_dp, & + & 0.0003582974275247_dp, 0.0003581204513079_dp, 0.0003580280823670_dp, 0.0003579858847651_dp, & + & 0.0003579700560419_dp, 0.0003579657503447_dp, 0.0003579651148389_dp, 0.0003579650639214_dp, & + & 0.0003579641249996_dp, 0.0003579577637201_dp, 0.0003579343798279_dp, 0.0003578720533302_dp, & + & 0.0003577356857161_dp, 0.0003574746495101_dp, 0.0003570210934480_dp, 0.0003562890672235_dp, & + & 0.0003551746457120_dp, 0.0003535572402722_dp, 0.0003513022743213_dp, 0.0003482653624189_dp, & + & 0.0003442980564063_dp, 0.0003392551036985_dp, 0.0003330030019395_dp, 0.0003254294412898_dp, & + & 0.0003164530209023_dp, 0.0003060324416673_dp, 0.0002941742513141_dp, 0.0002809381901461_dp, & + & 0.0002664392886604_dp, 0.0002508461154047_dp, 0.0002343749525444_dp, 0.0002172801420404_dp, & + & 0.0001998413220416_dp, 0.0001823486700196_dp, 0.0001650875054011_dp, 0.0001483236406159_dp, & + & 1.3229072626863599e-04_dp, 1.1718058146570301e-04_dp, 1.0313720189536499e-04_dp, 9.0254807366463297e-05_dp, & + & 7.8579877408557804e-05_dp, 6.8116586806610298e-05_dp, 5.8834475586522203e-05_dp, 5.0676814888461797e-05_dp, & + & 4.3568240766234098e-05_dp, 3.7420890944161997e-05_dp, 3.2152974434040998e-05_dp, 2.7642432133489999e-05_dp, & + & 2.3788439879268701e-05_dp, 2.0518666632440800e-05_dp, 1.7747795522993201e-05_dp, 1.5384145214625301e-05_dp, & + & 1.3371304209641701e-05_dp, 1.1693138800339399e-05_dp, 1.0271396245542500e-05_dp, 9.0716808838209300e-06_dp, & + & 8.0724511715146701e-06_dp, 7.2488395979064501e-06_dp, 6.5634389780910902e-06_dp, 5.9904239044783497e-06_dp, & + & 5.5453711134134698e-06_dp, 5.1884093270615503e-06_dp, 4.8961872547437199e-06_dp, 4.6566647995405202e-06_dp, & + & 4.4606823514925500e-06_dp, 4.3013162311922298e-06_dp, 4.1731504438757796e-06_dp, 4.0716672238261304e-06_dp, & + & 3.9928407495892796e-06_dp, 3.9329401175791603e-06_dp, 3.8885002098254501e-06_dp, 3.8563837119198803e-06_dp, & + & 3.8338502985624203e-06_dp, 3.8185838260318397e-06_dp, 3.8086757907507301e-06_dp, 3.8025858888346399e-06_dp, & + & 3.7990982395541601e-06_dp, 3.7972813267117502e-06_dp, 3.7964520771538399e-06_dp, 3.7961411418763200e-06_dp, & + & 3.7960565766326201e-06_dp, 3.7960440923967600e-06_dp, 3.7960430869787800e-06_dp, 3.7960244334556099e-06_dp, & + & 3.7958980421137801e-06_dp, 3.7954334235479299e-06_dp, 3.7941949226905102e-06_dp, 3.7914845698594499e-06_dp, & + & 3.7862942132704798e-06_dp, 3.7772693932680602e-06_dp, 3.7626876121521499e-06_dp, 3.7404556945119802e-06_dp, & + & 3.7081345887202099e-06_dp, 3.6630071420518098e-06_dp, 3.6022163314441998e-06_dp, 3.5230350743376002e-06_dp, & + & 3.4235444772434701e-06_dp, 3.3055027017781000e-06_dp, 3.1763145376118001e-06_dp, 3.0318413131169602e-06_dp, & + & 2.8677105046170898e-06_dp, 2.6844988507690502e-06_dp, 2.4846105670661700e-06_dp, 2.2714635576903700e-06_dp, & + & 2.0777744662581199e-06_dp, 1.8927983660432799e-06_dp, 1.7027358687471399e-06_dp, 1.5115762046491501e-06_dp, & + & 1.3285093238835099e-06_dp, 1.1554776140343401e-06_dp, 9.8499721268297001e-07_dp, 8.1885947444959605e-07_dp, & + & 6.7858044694446604e-07_dp, 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0.0301771013365464_dp, 0.0297234497314118_dp, 0.0293390991513789_dp, 0.0290170677059240_dp, & + & 0.0287505802711738_dp, 0.0285331051922171_dp, 0.0283583912938354_dp, 0.0282205059396485_dp, & + & 0.0281138739670581_dp, 0.0280333164945397_dp, 0.0279740879067063_dp, 0.0279319088227403_dp, & + & 0.0279029925834546_dp, 0.0278840627712498_dp, 0.0278723595044781_dp, 0.0278656326976616_dp, & + & 0.0278621211071144_dp, 0.0278605167257417_dp, 0.0278599148820007_dp, 0.0278597511673357_dp, & + & 0.0278597270034435_dp, 0.0278597251018553_dp, 0.0278596904648261_dp, 0.0278594557946246_dp, & + & 0.0278585931338959_dp, 0.0278562936873428_dp, 0.0278512618626170_dp, 0.0278416270704884_dp, & + & 0.0278248775747407_dp, 0.0277978206694236_dp, 0.0277565734031207_dp, 0.0276965878660036_dp, & + & 0.0276127145778702_dp, 0.0274993066275471_dp, 0.0273503657935112_dp, 0.0271597298445343_dp, & + & 0.0269212975720325_dp, 0.0266292849394993_dp, 0.0262785022631729_dp, 0.0258646388971862_dp, & + & 0.0253845389197842_dp, 0.0248364492915538_dp, 0.0242202213514524_dp, 0.0235374476993915_dp, & + & 0.0227915196629596_dp, 0.0219875955832780_dp, 0.0211324767135324_dp, 0.0202343949667618_dp, & + & 0.0193027242411414_dp, 0.0183476336764468_dp, 0.0173797061056291_dp, 0.0164095475277559_dp, & + & 0.0154474133402545_dp, 0.0145028744162214_dp, 0.0135845413452138_dp, 0.0126998589871743_dp, & + & 0.0118549767523479_dp, 0.0110546935267255_dp, 0.0103024705938886_dp, 0.0096005017462737_dp, & + & 0.0089498272843311_dp, 0.0083504777732788_dp, 0.0078016340333793_dp, 0.0073017914877234_dp, & + & 0.0068489192398307_dp, 0.0064406067200142_dp, 0.0060741931546939_dp, 0.0057468773042846_dp, & + & 0.0054558067684507_dp, 0.0051981475952356_dp, 0.0049711359227409_dp, 0.0047721139616037_dp, & + & 0.0045985528768551_dp, 0.0044480651509815_dp, 0.0043184088909243_dp, 0.0042074863354955_dp, & + & 0.0041133385584953_dp, 0.0040341380676150_dp, 0.0039681806886040_dp, 0.0039138778133943_dp, & + & 0.0038697497894731_dp, 0.0038344209407555_dp, 0.0038066164400821_dp, 0.0037851610040409_dp, & + & 0.0037689791581865_dp, 0.0037570966342866_dp, 0.0037486423208186_dp, 0.0037428501028724_dp, & + & 0.0037390599037153_dp, 0.0037367172786009_dp, 0.0037353710078900_dp, 0.0037346682800390_dp, & + & 0.0037343472313918_dp, 0.0037342268003791_dp, 0.0037341940407369_dp, 0.0037341892055007_dp, & + & 0.0037341888216265_dp, 0.0037341817865375_dp, 0.0037341341230572_dp, 0.0037339589112584_dp, & + & 0.0037334918931862_dp, 0.0037324699992123_dp, 0.0037305135769739_dp, 0.0037271133035688_dp, & + & 0.0037216228203647_dp, 0.0037132581810297_dp, 0.0037011052111833_dp, 0.0036841357965862_dp, & + & 0.0036612338965813_dp, 0.0036312316756604_dp, 0.0035929555300367_dp, 0.0035452809574714_dp, & + & 0.0034871942170991_dp, 0.0034178576383965_dp, 0.0033366743991916_dp, 0.0032433477713720_dp, & + & 0.0031379294141054_dp, 0.0030208514413648_dp, 0.0028929378092535_dp, 0.0027553920693464_dp, & + & 0.0026097606083812_dp, 0.0024578729094849_dp, 0.0023017627954278_dp, 0.0021435766779980_dp, & + & 0.0019854762052063_dp, 0.0018295431551749_dp, 0.0016776939306560_dp, 0.0015316096894491_dp, & + & 0.0013926862441380_dp, 0.0012620056562458_dp, 0.0011403292027623_dp, 0.0010281093701039_dp, & + & 0.0009255170024609_dp, 0.0008324789294250_dp, 0.0007487213980024_dp, 0.0006738152680121_dp, & + & 0.0006072198376650_dp, 0.0005483230073207_dp, 0.0004964761473953_dp, 0.0004510226295480_dp, & + & 0.0004113196590687_dp, 0.0003767537820085_dp, 0.0003467510190749_dp, 0.0003207827984344_dp, & + & 0.0002983687244438_dp, 0.0002790769331114_dp, 0.0002625225718109_dp, 0.0002483648797931_dp, & + & 0.0002363033638488_dp, 0.0002260735490349_dp, 0.0002174426928363_dp, 0.0002102057153408_dp, & + & 0.0002041814763185_dp, 0.0001992094550047_dp, 0.0001951468558055_dp, 0.0001918661505371_dp, & + & 0.0001892530574263_dp, 0.0001872049420442_dp, 0.0001856296079001_dp, 0.0001844444278554_dp, & + & 0.0001835757541855_dp, 0.0001829585362518_dp, 0.0001825360697421_dp, 0.0001822598012957_dp, & + & 0.0001820891168940_dp, 0.0001819910514200_dp, 0.0001819398701191_dp, 0.0001819164890051_dp, & + & 0.0001819077185985_dp, 0.0001819053328962_dp, 0.0001819049807725_dp, 0.0001819049525640_dp, & + & 0.0001819044323703_dp, 0.0001819009080233_dp, 0.0001818879526532_dp, 0.0001818534223261_dp, & + & 0.0001817778734488_dp, 0.0001816332645568_dp, 0.0001813820269412_dp, 0.0001809765997507_dp, & + & 0.0001803595357330_dp, 0.0001794642892801_dp, 0.0001782167931506_dp, 0.0001765379075458_dp, & + & 0.0001743467791684_dp, 0.0001715650740106_dp, 0.0001681219463219_dp, 0.0001639594826610_dp, & + & 0.0001590382293148_dp, 0.0001533422974767_dp, 0.0001468834743221_dp, 0.0001397037820325_dp, & + & 0.0001318760388749_dp, 0.0001235021780790_dp, 0.0001147093283294_dp, 0.0001056438891993_dp, & + & 9.6463996088758095e-05_dp, 8.7330868419499606e-05_dp, 7.8399647019722406e-05_dp, 6.9810541397430397e-05_dp, & + & 6.1681400662649794e-05_dp, 5.4102939373024101e-05_dp, 4.7137416707698803e-05_dp, 4.0820501430616198e-05_dp, & + & 3.5164875438198398e-05_dp, 3.0163638431446299e-05_dp, 2.5792312012384899e-05_dp, 2.2010170251718401e-05_dp, & + & 1.8763399138421699e-05_dp, 1.5991615310184701e-05_dp, 1.3635811816570299e-05_dp, 1.1644246015407601e-05_dp, & + & 9.9740105774515103e-06_dp, 8.5869939177030102e-06_dp, 7.4424540787987300e-06_dp, 6.4958071579468398e-06_dp, & + & 5.7060922706853001e-06_dp, 5.0411287144669401e-06_dp, 4.4773638592232601e-06_dp, 3.9989157194497702e-06_dp, & + & 3.5982572139658899e-06_dp, 3.2782285597221500e-06_dp, 3.0284706866723401e-06_dp, 2.8291013354220202e-06_dp, & + & 2.6689287135894801e-06_dp, 2.5389317830359902e-06_dp, 2.4327841163795900e-06_dp, 2.3458904578888000e-06_dp, & + & 2.2748186463417099e-06_dp, 2.2170015885336599e-06_dp, 2.1704432278113502e-06_dp, 2.1334699571440301e-06_dp, & + & 2.1045932481200701e-06_dp, 2.0824652651185699e-06_dp, 2.0658749502189300e-06_dp, 2.0537498688355501e-06_dp, & + & 2.0451534368248801e-06_dp, 2.0392786286294002e-06_dp, 2.0354408949430102e-06_dp, 2.0330714676219899e-06_dp, & + & 2.0317106770306698e-06_dp, 2.0310006245694000e-06_dp, 2.0306762902322400e-06_dp, 2.0305546364340898e-06_dp, & + & 2.0305215446825299e-06_dp, 2.0305166597012199e-06_dp, 2.0305162475864302e-06_dp, 2.0305084706961898e-06_dp, & + & 2.0304557626360499e-06_dp, 2.0302620384882201e-06_dp, 2.0297458718232498e-06_dp, 2.0286174269301699e-06_dp, & + & 2.0264608018294401e-06_dp, 2.0227242334414099e-06_dp, 2.0167212255728398e-06_dp, 2.0076455431450300e-06_dp, & + & 1.9946021474481802e-06_dp, 1.9766542695975899e-06_dp, 1.9528847374772302e-06_dp, 1.9224647740401199e-06_dp, & + & 1.8847052629666901e-06_dp, 1.8390300837722900e-06_dp, 1.7848080506865899e-06_dp, 1.7210883225260400e-06_dp, & + & 1.6464372603053301e-06_dp, 1.5592536026787200e-06_dp, 1.4639060346155500e-06_dp, 1.4084097337274700e-06_dp, & + & 1.3589881007192200e-06_dp, 1.2840823071513800e-06_dp, 1.1830265282952700e-06_dp, 1.1198497151809799e-06_dp, & + & 1.1249179259209501e-06_dp, 1.1215379593920701e-06_dp, 1.0915451209569899e-06_dp, 1.0284577491859201e-06_dp, & + & 9.8398588832537804e-07_dp, 9.8912616941504396e-07_dp, 9.9059616154306696e-07_dp, 1.0692544449852899e-06_dp, & + & 1.1210772576930601e-06_dp, 1.0961154526256699e-06_dp, 9.6813565875208994e-07_dp, 7.4091292212585803e-07_dp, & + & 6.6164570355908804e-07_dp, 6.2220082597264103e-07_dp, 5.5327843639929597e-07_dp, 4.4422867162552398e-07_dp, & + & 7.1054273576010003e-15_dp, 7.1054273576010003e-15_dp, 7.1054273576010003e-15_dp, 7.1054273576010003e-15_dp, & + & 7.1054273576010003e-15_dp, 7.1054273576010003e-15_dp, 7.1054273576010003e-15_dp, 7.1054273576010003e-15_dp, & + & 7.1054273576010003e-15_dp, 8.8817841970012507e-15_dp, 7.1054273576010003e-15_dp, 7.1054273576010003e-15_dp, & + & 7.1054273576010003e-15_dp, 7.1054273576010003e-15_dp, 7.1054273576010003e-15_dp, 7.1054273576010003e-15_dp, & + & 7.1054273576010003e-15_dp, 7.1054273576010003e-15_dp, 7.1054273576010003e-15_dp, 7.1054273576010003e-15_dp, & + & 8.8817841970012507e-15_dp, 7.1054273576010003e-15_dp, 8.8817841970012507e-15_dp, 7.1054273576010003e-15_dp, & + & 5.3290705182007498e-15_dp, 7.1054273576010003e-15_dp, 7.1054273576010003e-15_dp, 7.1054273576010003e-15_dp, & + & 8.8817841970012507e-15_dp, 5.3290705182007498e-15_dp, 7.1054273576010003e-15_dp, 5.3290705182007498e-15_dp, & + & 7.1054273576010003e-15_dp & + &] + case (16) + out = [& + & 16.0000000000000000_dp, 15.9999999913148994_dp, 15.9999997227538007_dp, 15.9999979032099997_dp, & + & 15.9999912143338001_dp, 15.9999733839333995_dp, 15.9999343609530005_dp, 15.9998596212025994_dp, & + & 15.9997296291377999_dp, 15.9995194763477997_dp, 15.9991987121359003_dp, 15.9987313758526000_dp, & + & 15.9980762346446994_dp, 15.9971872242202995_dp, 15.9960140843038001_dp, 15.9945031748484006_dp, & + & 15.9925984539733008_dp, 15.9902425941186994_dp, 15.9873782091900996_dp, 15.9839491625329995_dp, & + & 15.9799019234658992_dp, 15.9751869387906993_dp, 15.9697599851288992_dp, 15.9635834680534003_dp, & + & 15.9566276347292000_dp, 15.9488716680961993_dp, 15.9403046325024995_dp, 15.9309262431396004_dp, & + & 15.9207474346757003_dp, 15.9097907081856000_dp, 15.8980902398864998_dp, 15.8856917403340994_dp, & + & 15.8726520585999999_dp, 15.8590385324436003_dp, 15.8449280924667004_dp, 15.8304061354503993_dp, & + & 15.8155651892384999_dp, 15.8005033983087007_dp, 15.7853228652239999_dp, 15.7701278881595996_dp, & + & 15.7550231383831001_dp, 15.7401118237419997_dp, 15.7254938847736003_dp, 15.7112642690041007_dp, & + & 15.6975113264157997_dp, 15.6843153651145997_dp, 15.6717474011219000_dp, 15.6598681302131997_dp, & + & 15.6487271430862993_dp, 15.6383623981229007_dp, 15.6287999588536000_dp, 15.6200539961531994_dp, & + & 15.6121270483649006_dp, 15.6050105261241008_dp, 15.5986854427594004_dp, 15.5931233458756999_dp, & + & 15.5882874211804996_dp, 15.5841337358529994_dp, 15.5806125858573008_dp, 15.5776699096133004_dp, & + & 15.5752487294030999_dp, 15.5732905818410003_dp, 15.5717368996755994_dp, 15.5705303091078999_dp, & + & 15.5696158096668995_dp, 15.5689418074054000_dp, 15.5684609766849995_dp, 15.5681309309703000_dp, & + & 15.5679146887325004_dp, 15.5677809265897995_dp, 15.5677040180359008_dp, 15.5676638623433004_dp, & + & 15.5676455143057009_dp, 15.5676386312310999_dp, 15.5676367588592992_dp, 15.5676364825008005_dp, & + & 15.5676364462484003_dp, 15.5676356016107000_dp, 15.5676298790583001_dp, 15.5676088422326995_dp, & + & 15.5675527648766003_dp, 15.5674300363728992_dp, 15.5671949790501998_dp, 15.5667861574561996_dp, & + & 15.5661252455721009_dp, 15.5651165017962008_dp, 15.5636468839532007_dp, 15.5615868181560000_dp, & + & 15.5587916166437008_dp, 15.5551035213833000_dp, 15.5503543328161999_dp, 15.5443685671870000_dp, & + & 15.5369670717625006_dp, 15.5279710151271999_dp, 15.5172061596096000_dp, 15.5045073145294001_dp, & + & 15.4897228620370004_dp, 15.4727192415061001_dp, 15.4533852735428994_dp, 15.4316362008254000_dp, & + & 15.4074173206828000_dp, 15.3807070845573008_dp, 15.3515195435502996_dp, 15.3199060285871997_dp, & + & 15.2859559696066007_dp, 15.2497967813166007_dp, 15.2115927733776992_dp, 15.1715430792433992_dp, & + & 15.1298786382060992_dp, 15.0868583065022008_dp, 15.0427642122651992_dp, 14.9978965023375999_dp, & + & 14.9525676536631007_dp, 14.9070965363097994_dp, 14.8618024183945998_dp, 14.8169990957810995_dp, & + & 14.7729893129074004_dp, 14.7300596177240006_dp, 14.6884757660948999_dp, 14.6484787617397991_dp, & + & 14.6102815891704996_dp, 14.5740666708403008_dp, 14.5399840570366994_dp, 14.5081503383979005_dp, & + & 14.4786482563206995_dp, 14.4515269755190001_dp, 14.4268029749228006_dp, 14.4044615071963999_dp, & + & 14.3844585726406002_dp, 14.3667233494543005_dp, 14.3511610187825998_dp, 14.3376559193426996_dp, & + & 14.3260749626054000_dp, 14.3162712355760000_dp, 14.3080877144099006_dp, 14.3013610087726004_dp, & + & 14.2959250544409002_dp, 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5.4127619364407998e-07_dp, -1.0658141036401500e-14_dp, -1.0658141036401500e-14_dp, & + & -1.0658141036401500e-14_dp, -1.0658141036401500e-14_dp, -1.0658141036401500e-14_dp, -1.0658141036401500e-14_dp, & + & -1.0658141036401500e-14_dp, -1.0658141036401500e-14_dp, -1.0658141036401500e-14_dp, -1.0658141036401500e-14_dp, & + & -1.0658141036401500e-14_dp, -1.0658141036401500e-14_dp, -1.0658141036401500e-14_dp, -1.0658141036401500e-14_dp, & + & -1.0658141036401500e-14_dp, -1.0658141036401500e-14_dp, -1.0658141036401500e-14_dp, -1.0658141036401500e-14_dp, & + & -1.0658141036401500e-14_dp, -1.0658141036401500e-14_dp, -1.0658141036401500e-14_dp, -1.0658141036401500e-14_dp, & + & -1.0658141036401500e-14_dp & + &] + case (18) + out = [& + & 18.0000000000000000_dp, 17.9999999896303002_dp, 17.9999996689778001_dp, 17.9999974965069995_dp, & + & 17.9999895102256993_dp, 17.9999682213566992_dp, 17.9999216292830013_dp, 17.9998323925895996_dp, & + & 17.9996771863897003_dp, 17.9994262705697992_dp, 17.9990432872857014_dp, 17.9984852991916995_dp, & + & 17.9977030727275000_dp, 17.9966416035510015_dp, 17.9952408741463010_dp, 17.9934368269762999_dp, & + & 17.9911625305033986_dp, 17.9883495101236015_dp, 17.9849292116788000_dp, 17.9808345617813998_dp, & + & 17.9760015867177998_dp, 17.9703710501594003_dp, 17.9638900692172001_dp, 17.9565136684665987_dp, & + & 17.9482062323341012_dp, 17.9389428176578001_dp, 17.9287102902667002_dp, 17.9175082521263001_dp, & + & 17.9053497290250014_dp, 17.8922615930409989_dp, 17.8782846992075015_dp, 17.8634737219497985_dp, & + & 17.8478966839951987_dp, 17.8316341784317984_dp, 17.8147782932350012_dp, 17.7974312565495012_dp, & + & 17.7797038299448005_dp, 17.7617134852877996_dp, 17.7435824083581011_dp, 17.7254353784504985_dp, & + & 17.7073975776268000_dp, 17.6895923857603989_dp, 17.6721392179705994_dp, 17.6551514594694012_dp, & + & 17.6387345494040986_dp, 17.6229842601904991_dp, 17.6079852123989014_dp, 17.5938096578096008_dp, & + & 17.5805165551358016_dp, 17.5681509544333991_dp, 17.5567436976734008_dp, 17.5463114345775004_dp, & + & 17.5368569448183997_dp, 17.5283697502091016_dp, 17.5208269936895995_dp, 17.5141945558528995_dp, & + & 17.5084283745243994_dp, 17.5034759285947992_dp, 17.4992778439730010_dp, 17.4957695772284012_dp, & + & 17.4928831312945015_dp, 17.4905487575334995_dp, 17.4886965995404999_dp, 17.4872582362906002_dp, & + & 17.4861680855546986_dp, 17.4853646328790013_dp, 17.4847914567091998_dp, 17.4843980263326984_dp, & + & 17.4841402560296011_dp, 17.4839808059824016_dp, 17.4838891278987987_dp, 17.4838412607352005_dp, & + & 17.4838193891609990_dp, 17.4838111842698005_dp, 17.4838089523301008_dp, 17.4838086229001988_dp, & + & 17.4838085796858991_dp, 17.4838075728452012_dp, 17.4838007513419988_dp, 17.4837756746388990_dp, & + & 17.4837088283100996_dp, 17.4835625314516996_dp, 17.4832823351462991_dp, 17.4827950078347989_dp, & + & 17.4820071866286995_dp, 17.4808047545101992_dp, 17.4790529825780006_dp, 17.4765974546468001_dp, & + & 17.4732657692894016_dp, 17.4688699925429987_dp, 17.4632098136617984_dp, 17.4560763370926999_dp, & + & 17.4472564266893002_dp, 17.4365375032825014_dp, 17.4237126840389998_dp, 17.4085861412860012_dp, & + & 17.3909785492772997_dp, 17.3707324793319984_dp, 17.3477175967645998_dp, 17.3218355073164005_dp, & + & 17.2930240972439009_dp, 17.2612612112171995_dp, 17.2265675175707997_dp, 17.1890084231302005_dp, & + & 17.1486949214105984_dp, 17.1057832891830017_dp, 17.0604735868091986_dp, 17.0130069655035001_dp, & + & 16.9636618366279990_dp, 16.9127490101313001_dp, 16.8606059567556983_dp, 16.8075903874136010_dp, & + & 16.7540733698330015_dp, 16.7004322152787985_dp, 16.6470433665555007_dp, 16.5942755038709997_dp, & + & 16.5424830599829988_dp, 16.4920003036738017_dp, 16.4431361145216002_dp, 16.3961695354799986_dp, & + & 16.3513461556123012_dp, 16.3088753453528987_dp, 16.2689283418838997_dp, 16.2316371628505998_dp, & + & 16.1970943123097015_dp, 16.1653532326788003_dp, 16.1364294495263003_dp, 16.1103023512383992_dp, & + & 16.0869175419542998_dp, 16.0661897029064988_dp, 16.0480058938809016_dp, 16.0322292226389003_dp, & + & 16.0187028057479992_dp, 16.0072539395232987_dp, 15.9976983950120992_dp, 15.9898447466283997_dp, & + & 15.9834986407221997_dp, 15.9784669086213000_dp, 15.9745614290798006_dp, 15.9716026480676998_dp, & + & 15.9694226698038992_dp, 15.9678678420221996_dp, 15.9668007706574002_dp, 15.9661017141940995_dp, & + & 15.9656693254054005_dp, 15.9654207274897999_dp, 15.9652909319555008_dp, 15.9652316261579994_dp, & + & 15.9652093783205000_dp, 15.9652033263517001_dp, 15.9652024330932001_dp, 15.9652023542354993_dp, & + & 15.9652008090570003_dp, 15.9651903402389994_dp, 15.9651518556604994_dp, 15.9650492691649006_dp, & + & 15.9648247573781994_dp, 15.9643947760781995_dp, 15.9636469900243991_dp, 15.9624382482429006_dp, & + & 15.9605937116067000_dp, 15.9579072112396005_dp, 15.9541428847985998_dp, 15.9490381030589994_dp, & + & 15.9423076615930999_dp, 15.9336491720456994_dp, 15.9227495452699994_dp, 15.9092924154569992_dp, & + & 15.8929663118411000_dp, 15.8734733444560003_dp, 15.8505381349439993_dp, 15.8239166950507997_dp, & + & 15.7934049367519993_dp, 15.7588464915424993_dp, 15.7201395245733000_dp, 15.6772422538084992_dp, & + & 15.6301769259821999_dp, 15.5790320593384006_dp, 15.5239628356912007_dp, 15.4651896072163009_dp, & + & 15.4029945708195992_dp, 15.3377167480438992_dp, 15.2697454840372000_dp, 15.1995127386473996_dp, & + & 15.1274844815117007_dp, 15.0541515189073998_dp, 14.9800200738190998_dp, 14.9056024154410007_dp, & + & 14.8314077953868999_dp, 14.7579339012684994_dp, 14.6856589898915004_dp, 14.6150348168593993_dp, & + & 14.5464804400146992_dp, 14.4803769423001008_dp, 14.4170630952256005_dp, 14.3568319660989996_dp, & + & 14.2999284589736995_dp, 14.2465477692992994_dp, 14.1968347242440007_dp, 14.1508839736907994_dp, & + & 14.1087409904721994_dp, 14.0704038322485001_dp, 14.0358256114230002_dp, 14.0049176135155005_dp, & + & 13.9775529983675995_dp, 13.9535710122527004_dp, 13.9327816322954998_dp, 13.9149705575136000_dp, & + & 13.8999044533731997_dp, 13.8873363492850999_dp, 13.8770110814296004_dp, 13.8686706673229008_dp, & + & 13.8620594943817999_dp, 13.8569292031868994_dp, 13.8530431479344998_dp, 13.8501803222905995_dp, & + & 13.8481386488991003_dp, 13.8467375452508001_dp, 13.8458196972625007_dp, 13.8452519942271994_dp, & + & 13.8449256039396005_dp, 13.8447551937425004_dp, 13.8446773307622006_dp, 13.8446481214835000_dp, & + & 13.8446401758339004_dp, 13.8446390030720003_dp, 13.8446389090020006_dp, 13.8446371729330000_dp, & + & 13.8446254108045999_dp, 13.8445821718930002_dp, 13.8444669121880999_dp, 13.8442146658868008_dp, & + & 13.8437315715653995_dp, 13.8428914274368999_dp, 13.8415334263104004_dp, 13.8394611934741008_dp, & + & 13.8364432196120006_dp, 13.8322147457743991_dp, 13.8264811180952005_dp, 13.8189225863015999_dp, & + & 13.8092004723611996_dp, 13.7969645846691993_dp, 13.7818617005007997_dp, 13.7635448872746000_dp, & + & 13.7416833844701998_dp, 13.7159727263135007_dp, 13.6861447543391002_dp, 13.6519771521991995_dp, & + & 13.6133021354646999_dp, 13.5700139483147009_dp, 13.5220748569918996_dp, 13.4695193850572004_dp, & + & 13.4124566044831006_dp, 13.3510703749656994_dp, 13.2856175064463002_dp, 13.2164239018279996_dp, & + & 13.1438788141811003_dp, 13.0684274223883996_dp, 12.9905619892066007_dp, 12.9108119146138005_dp, & + & 12.8297330334708999_dp, 12.7478965277779004_dp, 12.6658778276049997_dp, 12.5842458588778996_dp, & + & 12.5035529598735007_dp, 12.4243257333935002_dp, 12.3470570330252993_dp, 12.2721992070948005_dp, & + & 12.2001586513446991_dp, 12.1312916587085002_dp, 12.0659015070575997_dp, 12.0042366954704995_dp, & + & 11.9464902252887004_dp, 11.8927998206316001_dp, 11.8432489897579991_dp, 11.7978688394070996_dp, & + & 11.7566405655230994_dp, 11.7194985532124996_dp, 11.6863340250598000_dp, 11.6569991795693007_dp, & + & 11.6313117605595995_dp, 11.6090599942205994_dp, 11.5900078238367996_dp, 11.5739003635749000_dp, & + & 11.5604694830427999_dp, 11.5494394244109007_dp, 11.5405323447306998_dp, 11.5334736686841008_dp, & + & 11.5279971323653996_dp, 11.5238493977618006_dp, 11.5207941211175005_dp, 11.5186153668612992_dp, & + & 11.5171202724283006_dp, 11.5161408879513001_dp, 11.5155351378638002_dp, 11.5151868780480999_dp, & + & 11.5150050510737003_dp, 11.5149219719220000_dp, 11.5148908059174993_dp, 11.5148823279946999_dp, & + & 11.5148810766705996_dp, 11.5148809801564003_dp, 11.5148792470718000_dp, 11.5148675051646006_dp, & + & 11.5148243406134991_dp, 11.5147092793212007_dp, 11.5144574682288994_dp, 11.5139752111698996_dp, & + & 11.5131365348921992_dp, 11.5117809380018006_dp, 11.5097124491526994_dp, 11.5067000905506003_dp, & + & 11.5024798082434003_dp, 11.4967578912646005_dp, 11.4892158571409997_dp, 11.4795167316861999_dp, & + & 11.4673125971133008_dp, 11.4522532258761007_dp, 11.4339955607703008_dp, 11.4122137480958994_dp, & + & 11.3866093842298994_dp, 11.3569216013389997_dp, 11.3229365996675995_dp, 11.2844962356594003_dp, & + & 11.2415052995799005_dp, 11.1939371637978002_dp, 11.1418375515559003_dp, 11.0853262615015993_dp, & + & 11.0245967788572994_dp, 10.9599138018758993_dp, 10.8916088039465997_dp, 10.8200738302902000_dp, & + & 10.7457537888064998_dp, 10.6691375353764002_dp, 10.5907480756554992_dp, 10.5111322109518994_dp, & + & 10.4308499487937993_dp, 10.3504639825226992_dp, 10.2705295209026009_dp, 10.1915847193518996_dp, & + & 10.1141419293414998_dp, 10.0386799420813997_dp, 9.9656373577881308_dp, 9.8954071644231298_dp, & + & 9.8283325624500097_dp, 9.7647040278922805_dp, 9.7047575676370492_dp, 9.6486740906894397_dp, & + & 9.5965797981068608_dp, 9.5485474826773000_dp, 9.5045986260854605_dp, 9.4647061846093692_dp, & + & 9.4287979621435003_dp, 9.3967604792800206_dp, 9.3684432571918599_dp, 9.3436634434236403_dp, & + & 9.3222107121848197_dp, 9.3038523736920808_dp, 9.2883386254230000_dp, 9.2754078732284295_dp, & + & 9.2647920429500505_dp, 9.2562217946678196_dp, 9.2494315433336993_dp, 9.2441641827703496_dp, & + & 9.2401754062002208_dp, 9.2372375167862195_dp, 9.2351426269592203_dp, 9.2337051560171499_dp, & + & 9.2327635515845401_dp, 9.2321811815318604_dp, 9.2318463679593403_dp, 9.2316715625998391_dp, & + & 9.2315916920162806_dp, 9.2315617297105703_dp, 9.2315535792282208_dp, 9.2315523762337808_dp, & + & 9.2315522851466696_dp, 9.2315506715475504_dp, 9.2315397391741598_dp, 9.2314995505839601_dp, & + & 9.2313924223336894_dp, 9.2311579736413698_dp, 9.2307089719926498_dp, 9.2299281407334597_dp, & + & 9.2286660732724108_dp, 9.2267403748904293_dp, 9.2239361259055208_dp, 9.2200077284600699_dp, & + & 9.2146821628671507_dp, 9.2076636378471495_dp, 9.1986395721087195_dp, 9.1872877932118797_dp, & + & 9.1732847849180494_dp, 9.1563147585704900_dp, 9.1360792705745002_dp, 9.1123070605493908_dp, & + & 9.0847637473754705_dp, 9.0532609973287901_dp, 9.0176647734866098_dp, 8.9779022913620992_dp, & + & 8.9339673436862608_dp, 8.8859237171068006_dp, 8.8339065031641102_dp, 8.7781212012228806_dp, & + & 8.7188406164024705_dp, 8.6563996639824605_dp, 8.5911882955199204_dp, 8.5236428531759998_dp, & + & 8.4542362303748106_dp, 8.3834672632598597_dp, 8.3118497950358599_dp, 8.2399018434721700_dp, & + & 8.1681352627932409_dp, 8.0970462297709993_dp, 8.0271068070068008_dp, 7.9587577522102997_dp, & + & 7.8924026588506999_dp, 7.8284034379818896_dp, 7.7670770886501099_dp, 7.7086936581832299_dp, & + & 7.6534752646700399_dp, 7.6015960409285102_dp, 7.5531828596470101_dp, 7.5083167097426600_dp, & + & 7.4670346106594403_dp, 7.4293319709011199_dp, 7.3951653166901599_dp, 7.3644553340970900_dp, & + & 7.3370901818573504_dp, 7.3129290416028203_dp, 7.2918058771443297_dp, 7.2735333749281201_dp, & + & 7.2579070343394703_dp, 7.2447093698499998_dp, 7.2337141779744298_dp, 7.2246908116107003_dp, & + & 7.2174083936642797_dp, 7.2116398920244196_dp, 7.2071659700839197_dp, 7.2037785221132999_dp, & + & 7.2012838018025800_dp, 7.1995050558185598_dp, 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0.1212179787988500_dp, 0.1170591113175380_dp, & + & 0.1128954991254430_dp, 0.1087613013344470_dp, 0.1046887142445530_dp, 0.1007073099087030_dp, & + & 0.0968435264103853_dp, 0.0931203166792933_dp, 0.0895569524675039_dp, 0.0861689714967291_dp, & + & 0.0829682492721453_dp, 0.0799631728643106_dp, 0.0771588920487289_dp, 0.0745576233152114_dp, & + & 0.0721589840270980_dp, 0.0699603369632307_dp, 0.0679571291464462_dp, 0.0661432128253310_dp, & + & 0.0645111403816081_dp, 0.0630524285195264_dp, 0.0617577901831190_dp, 0.0606173351427799_dp, & + & 0.0596207420589216_dp, 0.0587574060759550_dp, 0.0580165666639800_dp, 0.0573874205681300_dp, & + & 0.0568592244176216_dp, 0.0564213908682127_dp, 0.0560635811897683_dp, 0.0557757960568246_dp, & + & 0.0555484650535654_dp, 0.0553725341663025_dp, 0.0552395494076379_dp, 0.0551417337911637_dp, & + & 0.0550720542327632_dp, 0.0550242746514940_dp, 0.0549929916074561_dp, 0.0549736492396242_dp, & + & 0.0549625310144783_dp, 0.0549567267966573_dp, 0.0549540749152371_dp, 0.0549530801213507_dp, & + & 0.0549528095150258_dp, 0.0549527695741645_dp, 0.0549527664575145_dp, 0.0549527100253790_dp, & + & 0.0549523276903194_dp, 0.0549509222004012_dp, 0.0549471757893549_dp, 0.0549389774137623_dp, & + & 0.0549232786640310_dp, 0.0548959850412558_dp, 0.0548518891023377_dp, 0.0547846517055532_dp, & + & 0.0546868371122322_dp, 0.0545500068594755_dp, 0.0543648759447137_dp, 0.0541215328061142_dp, & + & 0.0538097217500564_dp, 0.0534191828644346_dp, 0.0529400401848434_dp, 0.0523632242135754_dp, & + & 0.0516809102350884_dp, 0.0508869497561619_dp, 0.0499772694205554_dp, 0.0489502104956188_dp, & + & 0.0478067829848321_dp, 0.0465508118649645_dp, 0.0451889588706393_dp, 0.0437306113078222_dp, & + & 0.0421876388958786_dp, 0.0405740296720261_dp, 0.0389054254511798_dp, 0.0371985851364975_dp, & + & 0.0354708094140896_dp, 0.0337393624521134_dp, 0.0320209249845753_dp, 0.0303311088516800_dp, & + & 0.0286840563322741_dp, 0.0270921393457364_dp, 0.0255657648405538_dp, 0.0241132843988865_dp, & + & 0.0227409990656149_dp, 0.0214532451858211_dp, 0.0202525438384598_dp, 0.0191397952424168_dp, & + & 0.0181145000212268_dp, 0.0171749910432837_dp, 0.0163186622471372_dp, 0.0155421839755689_dp, & + & 0.0148416975029200_dp, 0.0142129843696459_dp, 0.0136516086568719_dp, 0.0131530323532800_dp, & + & 0.0127127054705518_dp, 0.0123261335853009_dp, 0.0119889260906483_dp, 0.0116968287064623_dp, & + & 0.0114457438020388_dp, 0.0112317418958590_dp, 0.0110510673700084_dp, 0.0109001410136642_dp, & + & 0.0107755615223191_dp, 0.0106741075528944_dp, 0.0105927413895053_dp, 0.0105286147332997_dp, & + & 0.0104790766135139_dp, 0.0104416829514840_dp, 0.0104142069194992_dp, 0.0103946489468001_dp, & + & 0.0103812450547380_dp, 0.0103724721637768_dp, 0.0103670491070460_dp, 0.0103639322975582_dp, & + & 0.0103623053059572_dp, 0.0103615619802966_dp, 0.0103612831429238_dp, 0.0103612072933146_dp, & + & 0.0103611960981098_dp, 0.0103611952170937_dp, 0.0103611791696494_dp, 0.0103610704463293_dp, & + & 0.0103606707753059_dp, 0.0103596054559425_dp, 0.0103572743190519_dp, 0.0103528110182793_dp, & + & 0.0103450527585771_dp, 0.0103325226282607_dp, 0.0103134267428615_dp, 0.0102856683696366_dp, & + & 0.0102468809999152_dp, 0.0101944818878756_dp, 0.0101257468002167_dp, 0.0100379055720410_dp, & + & 0.0099282565371510_dp, 0.0097942960591624_dp, 0.0096338573745918_dp, 0.0094452509909395_dp, & + & 0.0092273972448638_dp, 0.0089799406305389_dp, 0.0087033354477768_dp, 0.0083988934012140_dp, & + & 0.0080687860738635_dp, 0.0077159985827251_dp, 0.0073442348889365_dp, 0.0069577796995119_dp, & + & 0.0065613260828847_dp, 0.0061597812436887_dp, 0.0057580648877860_dp, 0.0053609149754088_dp, & + & 0.0049727143824079_dp, 0.0045973492955724_dp, 0.0042381064957979_dp, 0.0038976125867904_dp, & + & 0.0035778142718357_dp, 0.0032799954400069_dp, 0.0030048244117538_dp, 0.0027524233453100_dp, & + & 0.0025224514839977_dp, 0.0023141944674201_dp, 0.0021266530928941_dp, 0.0019586264277542_dp, & + & 0.0018087857830231_dp, 0.0016757375623016_dp, 0.0015580742662031_dp, 0.0014544139045185_dp, & + & 0.0013634287436162_dp, 0.0012838647283111_dp, 0.0012145531124190_dp, 0.0011544158608849_dp, & + & 0.0011024662981889_dp, 0.0010578063182045_dp, 0.0010196212778162_dp, 0.0009871734993538_dp, & + & 0.0009597951220996_dp, 0.0009368808789070_dp, 0.0009178812310786_dp, 0.0009022961713150_dp, & + & 0.0008896698973757_dp, 0.0008795864645315_dp, 0.0008716664412063_dp, 0.0008655645176212_dp, & + & 0.0008609679524341_dp, 0.0008575956883732_dp, 0.0008551979274394_dp, 0.0008535559315455_dp, & + & 0.0008524818080389_dp, 0.0008518180519808_dp, 0.0008514366472738_dp, 0.0008512375744942_dp, & + & 0.0008511466290138_dp, 0.0008511125142476_dp, 0.0008511032343961_dp, 0.0008511018647148_dp, & + & 0.0008511017559769_dp, 0.0008510997631461_dp, 0.0008510862615196_dp, 0.0008510366296690_dp, & + & 0.0008509043412772_dp, 0.0008506148917355_dp, 0.0008500607924766_dp, 0.0008490979324911_dp, & + & 0.0008475436350395_dp, 0.0008451767642654_dp, 0.0008417402475729_dp, 0.0008369463578575_dp, & + & 0.0008304850263947_dp, 0.0008220353153057_dp, 0.0008112799571975_dp, 0.0007979225693688_dp, & + & 0.0007817067888034_dp, 0.0007624361866156_dp, 0.0007399934640411_dp, 0.0007143571740045_dp, & + & 0.0006856141251461_dp, 0.0006539657674409_dp, 0.0006197272585879_dp, 0.0005833185524793_dp, & + & 0.0005452476695886_dp, 0.0005060871964666_dp, 0.0004664458815711_dp, 0.0004269378130459_dp, & + & 0.0003881519656055_dp, 0.0003506248232412_dp, 0.0003148183226074_dp, 0.0002811046006101_dp, & + & 0.0002497581254914_dp, 0.0002209549343455_dp, 0.0001947780470850_dp, 0.0001712277273036_dp, & + & 0.0001502350615219_dp, 0.0001316772519644_dp, 0.0001153930556086_dp, 0.0001011970130946_dp, & + & 8.8891547694203195e-05_dp, 7.8276604938309902e-05_dp, 6.9157010724296697e-05_dp, 6.1347929555921596e-05_dp, & + & 5.4678712711364603e-05_dp, 4.8995234617876797e-05_dp, 4.4160740340970499e-05_dp, 4.0055382633852298e-05_dp, & + & 3.6574893872654002e-05_dp, 3.3628951502606703e-05_dp, 3.1139644843136700e-05_dp, 2.9040155649084899e-05_dp, & + & 2.7273531131299899e-05_dp, 2.5791414454800999e-05_dp, 2.4552753007611700e-05_dp, 2.3522600745451400e-05_dp, & + & 2.2671078795610800e-05_dp, 2.1972486987209499e-05_dp, 2.1404557166704301e-05_dp, 2.0947854842745501e-05_dp, & + & 2.0585320548605099e-05_dp, 2.0301920219623101e-05_dp, 2.0084373659301501e-05_dp, 1.9920944478002401e-05_dp, & + & 1.9801284242504400e-05_dp, 1.9716323674146000e-05_dp, 1.9658199274630299e-05_dp, 1.9620201516801200e-05_dp, & + & 1.9596730439275200e-05_dp, 1.9583246917420601e-05_dp, 1.9576210210203699e-05_dp, 1.9572995739736099e-05_dp, & + & 1.9571789987793399e-05_dp, 1.9571462004819299e-05_dp, 1.9571413595542701e-05_dp, 1.9571409719532102e-05_dp, & + & 1.9571338192747600e-05_dp, 1.9570853638128900e-05_dp, 1.9569072449598900e-05_dp, 1.9564325146603799e-05_dp, & + & 1.9553939349492600e-05_dp, 1.9534062882797801e-05_dp, 1.9499539956058199e-05_dp, 1.9443855190814899e-05_dp, & + & 1.9359162223509002e-05_dp, 1.9236414246393000e-05_dp, 1.9065612065105601e-05_dp, 1.8836181336467900e-05_dp, & + & 1.8537483441605201e-05_dp, 1.8159454455712899e-05_dp, 1.7693351292535901e-05_dp, 1.7132560820698500e-05_dp, & + & 1.6473399728766901e-05_dp, 1.5715817777817199e-05_dp, 1.4863932229047800e-05_dp, 1.3926336976055600e-05_dp, & + & 1.2916073931279501e-05_dp, 1.1850049499884099e-05_dp, 1.0747775128550100e-05_dp, 9.6297251701571406e-06_dp, & + & 8.5157918832123903e-06_dp, 7.4238575820118100e-06_dp, 6.3686553026798299e-06_dp, 5.3623845595041101e-06_dp, & + & 4.4168092969698600e-06_dp, 3.5413987369281598e-06_dp, 2.7369918171871198e-06_dp, 1.9978139746967801e-06_dp, & + & 1.3157318079493101e-06_dp, 6.5191391485086601e-07_dp, 6.5815489236342696e-07_dp, 1.1720697337125300e-06_dp, & + & 1.4974247974919300e-06_dp, 1.6718524911141201e-06_dp, 1.7925426796239199e-06_dp, 1.9178400343378101e-06_dp, & + & 2.0191002754188499e-06_dp, 2.0883905058610699e-06_dp, 2.1589456977722000e-06_dp, 2.2273125921401498e-06_dp, & + & 2.2652010329693401e-06_dp, 2.2805718806751000e-06_dp, 2.3011024339325601e-06_dp, 2.3294870210577301e-06_dp, & + & 2.3525195018692098e-06_dp, 2.3676147407059000e-06_dp, 2.3800045205746301e-06_dp, 2.3922296250589200e-06_dp, & + & 2.4053037250837402e-06_dp, 2.4213423550634199e-06_dp, 2.4409520555934701e-06_dp, 2.4614963649582899e-06_dp, & + & 2.4793070423356801e-06_dp, 2.4923146213495801e-06_dp, 2.5005195638527800e-06_dp, 2.5050403742454802e-06_dp, & + & 2.5071609428550801e-06_dp, 2.5078934342559499e-06_dp, 2.5079136385386400e-06_dp, 2.5076313754368601e-06_dp, & + & 2.5072742815268599e-06_dp, 2.5069532405552802e-06_dp, 2.5067090412278499e-06_dp, 2.5065444617666799e-06_dp, & + & 2.5064451349976501e-06_dp, 2.5063919046886002e-06_dp, 2.5063672666192398e-06_dp, 2.5063579762729702e-06_dp, & + & 2.5063554431881100e-06_dp, 2.5063550701531801e-06_dp, 2.5063550346260399e-06_dp, 2.5063543453995900e-06_dp, & + & 2.5063496842392401e-06_dp, 2.5063325672647398e-06_dp, 2.5062870818715102e-06_dp, 2.5061882773513802e-06_dp, & + & 2.5060016426437002e-06_dp, 2.5056841259640801e-06_dp, 2.5051855487845400e-06_dp, 2.5044470497448401e-06_dp, & + & 2.5033941071228600e-06_dp, 2.5019406528770101e-06_dp, 2.5000709449329899e-06_dp, 2.4981092785481000e-06_dp, & + & 2.4971591479072698e-06_dp, 2.4992039762139501e-06_dp, 2.5058712509462600e-06_dp, 2.5158216878651299e-06_dp, & + & 2.5238333911659100e-06_dp, 2.5257244651300000e-06_dp, 2.5261147733601800e-06_dp, 2.5358802524522200e-06_dp, & + & 2.5553845155457098e-06_dp, 2.5719493379483500e-06_dp, 2.5893286483835701e-06_dp, 2.6347275472460301e-06_dp, & + & 2.6998912936448998e-06_dp, 2.7249921288330400e-06_dp, 2.6953864669110300e-06_dp, 2.6833684465543700e-06_dp, & + & 2.7135928526433902e-06_dp, 2.7172971037714399e-06_dp, 2.7098384016710501e-06_dp, 2.7412527394687901e-06_dp, & + & 2.6958284031763898e-06_dp, 2.6457651038924702e-06_dp, 3.1839216276807700e-06_dp, 4.1482572328277498e-06_dp, & + & 4.8991753516247602e-06_dp, 5.1589811924657203e-06_dp, 4.9124961201130199e-06_dp, 4.2989490012246304e-06_dp, & + & 3.5254673242946002e-06_dp, 2.7759627521106701e-06_dp, 2.1334538722328502e-06_dp, 1.6111667058282800e-06_dp, & + & 1.3582545186352501e-06_dp, 1.4757981467994301e-06_dp, 1.6207636868159600e-06_dp, 1.5956679249029500e-06_dp, & + & 1.3924717627844500e-06_dp, 1.0700961290410800e-06_dp, 7.0927196205161604e-07_dp, 4.2304430536432799e-07_dp, & + & 3.5527136788005001e-15_dp, 4.2208207062799401e-07_dp, 4.0810549251091299e-07_dp, 3.5527136788005001e-15_dp, & + & 3.5527136788005001e-15_dp, 3.5527136788005001e-15_dp, 3.5527136788005001e-15_dp, 3.5527136788005001e-15_dp, & + & 3.5527136788005001e-15_dp, 3.5527136788005001e-15_dp, 3.5527136788005001e-15_dp, 3.5527136788005001e-15_dp, & + & 3.5527136788005001e-15_dp, 3.5527136788005001e-15_dp, 3.5527136788005001e-15_dp, 3.5527136788005001e-15_dp, & + & 3.5527136788005001e-15_dp, 3.5527136788005001e-15_dp, 3.5527136788005001e-15_dp, 3.5527136788005001e-15_dp, & + & 3.5527136788005001e-15_dp & + &] + case (19) + out = [& + & 19.0000000000000000_dp, 18.9999999888122986_dp, 18.9999996428677989_dp, 18.9999972990388990_dp, & + & 18.9999886828232007_dp, 18.9999657147492016_dp, 18.9999154476189993_dp, 18.9998191721488006_dp, & + & 18.9996517235668989_dp, 18.9993810157276997_dp, 18.9989678224950005_dp, 18.9983658187539994_dp, & + & 18.9975218856836001_dp, 18.9963766771198017_dp, 18.9948654362349991_dp, 18.9929190445910017_dp, & + & 18.9904652791314987_dp, 18.9874302470208001_dp, 18.9837399635507005_dp, 18.9793220346771996_dp, & + & 18.9741074031216002_dp, 18.9680321153220994_dp, 18.9610390657796017_dp, 18.9530796753880004_dp, & + & 18.9441154611107017_dp, 18.9341194557847992_dp, 18.9230774389140990_dp, 18.9109889420907997_dp, & + & 18.8978679962633009_dp, 18.8837435925693988_dp, 18.8686598339890992_dp, 18.8526757617280012_dp, & + & 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0.1191641142970990_dp, & + & 0.1188720857603690_dp, 0.1186457579176580_dp, 0.1184744878622970_dp, 0.1183484067400010_dp, & + & 0.1182585375789350_dp, 0.1181968876438050_dp, 0.1181565115849710_dp, 0.1181315423973930_dp, & + & 0.1181171882201220_dp, 0.1181096942276380_dp, 0.1181062702020630_dp, 0.1181049857385690_dp, & + & 0.1181046363339890_dp, 0.1181045847626230_dp, 0.1181045807384290_dp, 0.1181045078736280_dp, & + & 0.1181040142043270_dp, 0.1181021994303000_dp, 0.1180973619592360_dp, 0.1180867755268980_dp, & + & 0.1180665022188270_dp, 0.1180312498215630_dp, 0.1179742807810980_dp, 0.1178873792691630_dp, & + & 0.1177608818805710_dp, 0.1175837762116320_dp, 0.1173438699016920_dp, 0.1170280305721820_dp, & + & 0.1166224944254530_dp, 0.1161132380839400_dp, 0.1154864046519890_dp, 0.1147287711516500_dp, & + & 0.1138282406898550_dp, 0.1127743393026040_dp, 0.1115586947784200_dp, 0.1101754732772910_dp, & + & 0.1086217495663600_dp, 0.1068977884188240_dp, 0.1050072182409420_dp, 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0.0432185455094327_dp, & + & 0.0431846549264208_dp, 0.0431624639216359_dp, 0.0431487425468404_dp, 0.0431408551170058_dp, & + & 0.0431367374573703_dp, 0.0431348561307843_dp, 0.0431341503909337_dp, 0.0431339584135912_dp, & + & 0.0431339300781772_dp, 0.0431339278483023_dp, 0.0431338872317042_dp, 0.0431336120488517_dp, & + & 0.0431326004563637_dp, 0.0431299039895912_dp, 0.0431240031799973_dp, 0.0431127037342058_dp, & + & 0.0430930580039899_dp, 0.0430613162908493_dp, 0.0430129122821583_dp, 0.0429424865300057_dp, & + & 0.0428439512587673_dp, 0.0427105988157521_dp, 0.0425352546694846_dp, 0.0423104739526146_dp, & + & 0.0420287781418018_dp, 0.0416829256423483_dp, 0.0412662069664940_dp, 0.0407727521198602_dp, & + & 0.0401978350710159_dp, 0.0395381581531602_dp, 0.0387920983075816_dp, 0.0379598975388546_dp, & + & 0.0370437820033978_dp, 0.0360479978135047_dp, 0.0349787567211237_dp, 0.0338440909538704_dp, & + & 0.0326536230410177_dp, 0.0314182628117372_dp, 0.0301498491788053_dp, 0.0288607582317475_dp, & + & 0.0275635011304125_dp, 0.0262703351353153_dp, 0.0249929089290752_dp, 0.0237419595112556_dp, & + & 0.0225270729031664_dp, 0.0213565152863389_dp, 0.0202371356285482_dp, 0.0191743358634433_dp, & + & 0.0181721006988589_dp, 0.0172330763885320_dp, 0.0163586863860594_dp, 0.0155492716132457_dp, & + & 0.0148042438888645_dp, 0.0141222425765335_dp, 0.0135012864163855_dp, 0.0129389145416638_dp, & + & 0.0124323126538570_dp, 0.0119784221094150_dp, 0.0115740311805084_dp, 0.0112158489559491_dp, & + & 0.0109005632390868_dp, 0.0106248843965524_dp, 0.0103855774505774_dp, 0.0101794848319017_dp, & + & 0.0100035421662774_dp, 0.0098547892942591_dp, 0.0097303784556964_dp, 0.0096275812328912_dp, & + & 0.0095437954636068_dp, 0.0094765529256904_dp, 0.0094235281804274_dp, 0.0093825485625132_dp, & + & 0.0093516049422142_dp, 0.0093288625827874_dp, 0.0093126711931184_dp, 0.0093015731470132_dp, & + & 0.0092943088164859_dp, 0.0092898180457226_dp, 0.0092872369663297_dp, 0.0092858896039871_dp, & + & 0.0092852740272420_dp, 0.0092850431103031_dp, 0.0092849802959805_dp, 0.0092849710247442_dp, & + & 0.0092849702886788_dp, 0.0092849567993696_dp, 0.0092848654076896_dp, 0.0092845294478821_dp, & + & 0.0092836339459481_dp, 0.0092816743828621_dp, 0.0092779224319557_dp, 0.0092714004072469_dp, & + & 0.0092608661921823_dp, 0.0092448104340193_dp, 0.0092214677407689_dp, 0.0091888434433649_dp, & + & 0.0091447571205023_dp, 0.0090869034672814_dp, 0.0090129301842303_dp, 0.0089205313676430_dp, & + & 0.0088075534423524_dp, 0.0086721091012159_dp, 0.0085126931658195_dp, 0.0083282929744364_dp, & + & 0.0081184850730196_dp, 0.0078835098557200_dp, 0.0076243165386920_dp, 0.0073425725160376_dp, & + & 0.0070406336665840_dp, 0.0067214753389706_dp, 0.0063885871972680_dp, 0.0060458384469335_dp, & + & 0.0056973227540524_dp, 0.0053471940496763_dp, 0.0049995051082910_dp, 0.0046580601793487_dp, & + & 0.0043262910814299_dp, 0.0040071632966061_dp, 0.0037031151961600_dp, 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27.9539717057474988_dp, & + & 27.9539278530927007_dp, 27.9539114022451010_dp, 27.9539069271964991_dp, 27.9539062666880014_dp, & + & 27.9539061800432016_dp, 27.9539041613235000_dp, 27.9538904841850986_dp, 27.9538402053539983_dp, & + & 27.9537061787309007_dp, 27.9534128560202006_dp, 27.9528510745114005_dp, 27.9518740271667987_dp, & + & 27.9502945781765000_dp, 27.9478840507620987_dp, 27.9443725741046016_dp, 27.9394510337880995_dp, & + & 27.9327746261533001_dp, 27.9239679725617016_dp, 27.9126317059311013_dp, 27.8983503999942002_dp, & + & 27.8807016722991996_dp, 27.8592662553117982_dp, 27.8336387959903000_dp, 27.8034391124555995_dp, & + & 27.7683236064626016_dp, 27.7279965023966994_dp, 27.6822205586545991_dp, 27.6308268781864008_dp, & + & 27.5737234360109014_dp, 27.5109019481573007_dp, 27.4424427345227997_dp, 27.3685172821125988_dp, & + & 27.2893882968760018_dp, 27.2054071396336994_dp, 27.1170086676434003_dp, 27.0247036372963017_dp, & + & 26.9290689518781008_dp, 26.8307361475416997_dp, 26.7303785891194998_dp, 26.6286978878748002_dp, & + & 26.5264100539518992_dp, 26.4242318607590008_dp, 26.3228678348623006_dp, 26.2229982037967986_dp, & + & 26.1252680466544014_dp, 26.0302778082056996_dp, 25.9385752638393008_dp, 25.8506489638606993_dp, & + & 25.7669231427313008_dp, 25.6877540503788993_dp, 25.6134276459794989_dp, 25.5441585861820997_dp, & + & 25.4800904362767007_dp, 25.4212970314640003_dp, 25.3677849140745018_dp, 25.3194967699632016_dp, & + & 25.2763157826524001_dp, 25.2380708168992989_dp, 25.2045423343590009_dp, 25.1754689332630015_dp, & + & 25.1505543920910988_dp, 25.1294750847631008_dp, 25.1118876227186014_dp, 25.0974365683033014_dp, & + & 25.0857620551143015_dp, 25.0765071453961994_dp, 25.0693247531802008_dp, 25.0638839654838002_dp, & + & 25.0598756031712000_dp, 25.0570168783672003_dp, 25.0550550266226004_dp, 25.0537698189426017_dp, & + & 25.0529748905357010_dp, 25.0525178585610000_dp, 25.0522792388263014_dp, 25.0521702097049008_dp, & + & 25.0521293088271015_dp, 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18.6190085977418995_dp, 18.4894034620763001_dp, & + & 18.3647241862957991_dp, 18.2455839619433995_dp, 18.1325040130615989_dp, 18.0259102372613000_dp, & + & 17.9261317806610982_dp, 17.8334013861624996_dp, 17.7478573371775994_dp, 17.6695468158063989_dp, & + & 17.5984305016355016_dp, 17.5343882504529986_dp, 17.4772257071513017_dp, 17.4266817205182996_dp, & + & 17.3824364370418998_dp, 17.3441199548358007_dp, 17.3113214168589984_dp, 17.2835984151496014_dp, & + & 17.2604865659112008_dp, 17.2415091006476011_dp, 17.2261863031405014_dp, 17.2140446081678995_dp, & + & 17.2046251676916988_dp, 17.1974916858981999_dp, 17.1922373276795994_dp, 17.1884905171022986_dp, & + & 17.1859194636727999_dp, 17.1842352846094997_dp, 17.1831936299313988_dp, 17.1825947623839994_dp, & + & 17.1822820938840017_dp, 17.1821392317692982_dp, 17.1820856390484984_dp, 17.1820710605092017_dp, & + & 17.1820689087466008_dp, 17.1820687427820005_dp, 17.1820657625897013_dp, 17.1820455713436004_dp, & + & 17.1819713461154997_dp, 17.1817734883573010_dp, 17.1813404786939010_dp, 17.1805112026612008_dp, & + & 17.1790690511210009_dp, 17.1767380607311004_dp, 17.1731813155121991_dp, 17.1680017795413988_dp, & + & 17.1607456721117018_dp, 17.1509084292731018_dp, 17.1379432188136995_dp, 17.1212718894994005_dp, & + & 17.1002981409477997_dp, 17.0744226005000996_dp, 17.0430593920817017_dp, 17.0056536850790998_dp, & + & 16.9616996257358004_dp, 16.9107579872720990_dp, 16.8524728356529003_dp, 16.7865865026073990_dp, & + & 16.7129521912696006_dp, 16.6315436151364011_dp, 16.5424611870313001_dp, 16.4459344267418999_dp, & + & 16.3423204354768998_dp, 16.2320984803134998_dp, 16.1158609278698002_dp, 15.9943009477404008_dp, & + & 15.8681975574730991_dp, 15.7383986891384993_dp, 15.6058030142182993_dp, 15.4713412657036002_dp, & + & 15.3359577472946995_dp, 15.2005926286710000_dp, 15.0661655064754001_dp, 14.9335605785755998_dp, & + & 14.8036136494280992_dp, 14.6771010693425996_dp, 14.5547306181802991_dp, 14.4371342778033007_dp, & + & 14.3248627964086008_dp, 14.2183819275984007_dp, 14.1180702219600001_dp, 14.0242182531557003_dp, & + & 13.9370291690485004_dp, 13.8566204675723004_dp, 13.7830269047198009_dp, 13.7162044471455005_dp, & + & 13.6560351841921008_dp, 13.6023331137132004_dp, 13.5548507130044005_dp, 13.5132862005426997_dp, & + & 13.4772913860726007_dp, 13.4464799959744994_dp, 13.4204363480672004_dp, 13.3987242356412004_dp, & + & 13.3808958655374006_dp, 13.3665006807938003_dp, 13.3550938863356006_dp, 13.3462444880955999_dp, & + & 13.3395426534600006_dp, 13.3346062054627996_dp, 13.3310860757061995_dp, 13.3286705620260992_dp, & + & 13.3270882662696000_dp, 13.3261096243517994_dp, 13.3255469835604003_dp, 13.3252532288873002_dp, & + & 13.3251190087009999_dp, 13.3250686578730999_dp, 13.3250549612080000_dp, 13.3250529396082005_dp, & + & 13.3250527865387998_dp, 13.3250500749288001_dp, 13.3250317033672001_dp, 13.3249641674848007_dp, & + & 13.3247841410163996_dp, 13.3243901544389995_dp, 13.3236356113038994_dp, 13.3223234178244994_dp, & + & 13.3202024659212999_dp, 13.3169661690593006_dp, 13.3122532032690000_dp, 13.3056505518866004_dp, & + & 13.2966988908613004_dp, 13.2849002814109998_dp, 13.2697280584487007_dp, 13.2506387177653995_dp, & + & 13.2270855149868005_dp, 13.1985333989320992_dp, 13.1644748167665000_dp, 13.1244458549863001_dp, & + & 13.0780421260816002_dp, 13.0249337825976994_dp, 12.9648790438193000_dp, 12.8977356585512997_dp, & + & 12.8234698003819005_dp, 12.7421619956921006_dp, 12.6540098124695994_dp, 12.5593271801733000_dp, & + & 12.4585403568895998_dp, 12.3521806998701997_dp, 12.2408745213505004_dp, 12.1253304183585993_dp, & + & 12.0063245508828995_dp, 11.8846844069115996_dp, 11.7612716353433999_dp, 11.6369645473017993_dp, & + & 11.5126408800265008_dp, 11.3891613816734996_dp, 11.2673547079025997_dp, 11.1480040238994000_dp, & + & 11.0318355858210992_dp, 10.9195094460944997_dp, 10.8116123027885997_dp, 10.7086524087221999_dp, & + & 10.6110563809364002_dp, 10.5191677091284994_dp, 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0.0145065800080033_dp, 0.0142768708567935_dp, 0.0140066006570407_dp, 0.0136941037741103_dp, & + & 0.0133387270050740_dp, 0.0129409560457496_dp, 0.0125024904901672_dp, 0.0120262570956449_dp, & + & 0.0115163554538960_dp, 0.0109779357451387_dp, 0.0104170143162605_dp, 0.0098402386592333_dp, & + & 0.0092546181890611_dp, 0.0086672403544803_dp, 0.0080849926221127_dp, 0.0075143096363206_dp, & + & 0.0069609615984021_dp, 0.0064298951480843_dp, 0.0059251324772980_dp, 0.0054497288277098_dp, & + & 0.0050057836099775_dp, 0.0045944966450691_dp, 0.0042162587365411_dp, 0.0038707649583643_dp, & + & 0.0035571394987493_dp, 0.0032740623086518_dp, 0.0030198897860032_dp, 0.0027927639262764_dp, & + & 0.0025907065019517_dp, 0.0024116967046126_dp, 0.0022537321863254_dp, 0.0021148745340547_dp, & + & 0.0019932809176240_dp, 0.0018872240200345_dp, 0.0017951024617417_dp, 0.0017154438474201_dp, & + & 0.0016469023667334_dp, 0.0015882526274886_dp, 0.0015383811286256_dp, 0.0014962765186119_dp, & + & 0.0014610195426457_dp, 0.0014317733668179_dp, 0.0014077747777925_dp, 0.0013883265905612_dp, & + & 0.0013727914498354_dp, 0.0013605870797591_dp, 0.0013511829198620_dp, 0.0013440979831962_dp, & + & 0.0013388996875108_dp, 0.0013352033464073_dp, 0.0013326719684201_dp, 0.0013310160010072_dp, & + & 0.0013299926746520_dp, 0.0013294046485903_dp, 0.0013290977286324_dp, 0.0013289575132411_dp, & + & 0.0013289049166580_dp, 0.0013288906094040_dp, 0.0013288884976888_dp, 0.0013288883285014_dp, & + & 0.0013288852085900_dp, 0.0013288640708922_dp, 0.0013287863689051_dp, 0.0013285792624842_dp, & + & 0.0013281261092999_dp, 0.0013272586273949_dp, 0.0013257511971645_dp, 0.0013233178153485_dp, & + & 0.0013196122554291_dp, 0.0013142320057291_dp, 0.0013067265230759_dp, 0.0012966102254453_dp, & + & 0.0012833804264609_dp, 0.0012665400698317_dp, 0.0012456246552404_dp, 0.0012202321837549_dp, & + & 0.0011900543470631_dp, 0.0011549066260308_dp, 0.0011147545562906_dp, 0.0010697332741003_dp, & + & 0.0010201576675222_dp, 0.0009665210750036_dp, 0.0009094814766293_dp, 0.0008498354126232_dp, & + & 0.0007884812634309_dp, 0.0007263748115847_dp, 0.0006644809514924_dp, 0.0006037258482898_dp, & + & 0.0005449537045337_dp, 0.0004888916247197_dp, 0.0004361250161082_dp, 0.0003870847073841_dp, & + & 0.0003420456645138_dp, 0.0003011359705631_dp, 0.0002643537517990_dp, 0.0002315891371971_dp, & + & 0.0002026482775079_dp, 0.0001772769431128_dp, 0.0001551820703405_dp, 0.0001360504826948_dp, & + & 1.1956457039730100e-04_dp, 1.0541488622450900e-04_dp, 9.3309577216871303e-05_dp, 8.2980601092685902e-05_dp, & + & 7.4186916013019299e-05_dp, 6.6715160890851193e-05_dp, 6.0378555051698902e-05_dp, 5.5014765937500001e-05_dp, & + & 5.0483363228437397e-05_dp, 4.6663266456192800e-05_dp, 4.3450382392507001e-05_dp, 4.0755479844278900e-05_dp, & + & 3.8502273813634199e-05_dp, 3.6625674084689301e-05_dp, 3.5070172476281400e-05_dp, 3.3788371560206101e-05_dp, & + & 3.2739673585524502e-05_dp, 3.1889146303143400e-05_dp, 3.1206569737207701e-05_dp, 3.0665654460193503e-05_dp, & + & 3.0243414666841800e-05_dp, 2.9919677515977101e-05_dp, 2.9676710958881399e-05_dp, 2.9498951786166599e-05_dp, & + & 2.9372813905581599e-05_dp, 2.9286555317753499e-05_dp, 2.9230181812778299e-05_dp, 2.9195366732182000e-05_dp, & + & 2.9175368684519801e-05_dp, 2.9164932882963499e-05_dp, 2.9160165809116700e-05_dp, 2.9158377699900501e-05_dp, & + & 2.9157891308528901e-05_dp, 2.9157819518843600e-05_dp, 2.9157813713709398e-05_dp, 2.9157705931481801e-05_dp, & + & 2.9156975713817701e-05_dp, 2.9154291507182998e-05_dp, 2.9147137567520100e-05_dp, 2.9131487277567200e-05_dp, & + & 2.9101537847964199e-05_dp, 2.9049526606428300e-05_dp, 2.8965653068979701e-05_dp, 2.8838134259245900e-05_dp, & + & 2.8653422873503600e-05_dp, 2.8396615753933899e-05_dp, 2.8052072885031999e-05_dp, 2.7604251808810401e-05_dp, & + & 2.7038739361273700e-05_dp, 2.6343432825370900e-05_dp, 2.5509791299782602e-05_dp, 2.4534053231661801e-05_dp, & + & 2.3418308199296699e-05_dp, 2.2171322601849400e-05_dp, 2.0809042023728400e-05_dp, 1.9354707109897601e-05_dp, & + & 1.7838511762846599e-05_dp, 1.6296676641047701e-05_dp, 1.4769623362553799e-05_dp, 1.3298643949610800e-05_dp, & + & 1.1920819545707700e-05_dp, 1.0664340759802801e-05_dp, 9.5496992713606199e-06_dp, 8.5998852235036304e-06_dp, & + & 7.8503648168748407e-06_dp, 7.3374352282939998e-06_dp, 7.0538374892237201e-06_dp, 6.9060141640875398e-06_dp, & + & 6.7321125705177599e-06_dp, 6.3749697432058400e-06_dp, 5.7491935159248399e-06_dp, 4.8688835789789698e-06_dp, & + & 3.8367034669306602e-06_dp, 2.8056396317310798e-06_dp, 1.9277567204767399e-06_dp, 1.3033282293406501e-06_dp, & + & 9.3955604896223100e-07_dp, 7.4059156318639897e-07_dp, 5.8924893053813300e-07_dp, 5.0293000697365599e-07_dp, & + & 5.7456191981941597e-07_dp, 6.5794706571864502e-07_dp, 6.5332386611771696e-07_dp, 5.5963593226238096e-07_dp, & + & 4.1059185207359400e-07_dp, 7.1054273576010003e-15_dp, 7.1054273576010003e-15_dp, 7.1054273576010003e-15_dp, & + & 3.5527136788005001e-15_dp, 7.1054273576010003e-15_dp, 3.5527136788005001e-15_dp, 7.1054273576010003e-15_dp, & + & 3.5527136788005001e-15_dp, 7.1054273576010003e-15_dp, 7.1054273576010003e-15_dp, 7.1054273576010003e-15_dp, & + & 7.1054273576010003e-15_dp, 7.1054273576010003e-15_dp, 7.1054273576010003e-15_dp, 3.5527136788005001e-15_dp, & + & 3.5527136788005001e-15_dp, 7.1054273576010003e-15_dp, 3.5527136788005001e-15_dp, 3.5527136788005001e-15_dp, & + & 7.1054273576010003e-15_dp, 3.5527136788005001e-15_dp, 7.1054273576010003e-15_dp, 3.5527136788005001e-15_dp, & + & 3.5527136788005001e-15_dp & + &] + case (31) + out = [& + & 31.0000000000000000_dp, 30.9999999767594012_dp, 30.9999992581150003_dp, 30.9999943891853000_dp, & + & 30.9999764903717008_dp, 30.9999287778349988_dp, 30.9998243556955018_dp, 30.9996243578688997_dp, & + & 30.9992765069636000_dp, 30.9987141450857990_dp, 30.9978557771353991_dp, 30.9966051517330996_dp, & + & 30.9948518888399995_dp, 30.9924726470229999_dp, 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0.0001330494270491_dp, 0.0001133493196939_dp, & + & 9.5478811680038702e-05_dp, 7.9414098681951400e-05_dp, 6.5123450703197196e-05_dp, 5.2575114906972003e-05_dp, & + & 4.1697763503378797e-05_dp, 3.2386415082186197e-05_dp, 2.4547321700651998e-05_dp, 1.8076453503823600e-05_dp, & + & 1.2857651462638799e-05_dp, 8.7644246704598993e-06_dp, 5.6622860959976202e-06_dp, 3.4113202254104601e-06_dp, & + & 1.8689135536931200e-06_dp, 8.9265175517994098e-07_dp, 3.4345590904649699e-07_dp, -1.7763568394002501e-14_dp, & + & -1.7763568394002501e-14_dp & + &] + case (32) + out = [& + & 32.0000000000000000_dp, 31.9999999756516011_dp, 31.9999992227504002_dp, 31.9999941217261998_dp, & + & 31.9999753697024012_dp, 31.9999253827772989_dp, 31.9998159829725992_dp, 31.9996064514715997_dp, & + & 31.9992420187673012_dp, 31.9986528491534017_dp, 31.9977535620426998_dp, 31.9964433164064985_dp, & + & 31.9946064677852995_dp, 31.9921137904565001_dp, 31.9888242410736012_dp, 31.9845872250098999_dp, & + & 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14.3359852607094993_dp, & + & 14.3342146721810995_dp, 14.3331195770661992_dp, 14.3324899867134992_dp, 14.3321612781807008_dp, & + & 14.3320110872517006_dp, 14.3319547452411999_dp, 14.3319394188284992_dp, 14.3319371566814002_dp, & + & 14.3319369853984995_dp, 14.3319339511379003_dp, 14.3319133935706997_dp, 14.3318378217029991_dp, & + & 14.3316363742641997_dp, 14.3311955085001994_dp, 14.3303511864347008_dp, 14.3288828676499005_dp, & + & 14.3265095784832006_dp, 14.3228882822744996_dp, 14.3176147232552999_dp, 14.3102268568457003_dp, & + & 14.3002109104770998_dp, 14.2870100409102996_dp, 14.2700354664735993_dp, 14.2486798569717994_dp, & + & 14.2223326629715991_dp, 14.1903969641385004_dp, 14.1523073192155007_dp, 14.1075480152394004_dp, & + & 14.0556710484056993_dp, 13.9963131310899005_dp, 13.9292110151612007_dp, 13.8542144550392994_dp, & + & 13.7712962063028996_dp, 13.6805585653824000_dp, 13.5822360983147004_dp, 13.4766943746191004_dp, & + & 13.3644247070896007_dp, 13.2460350892781999_dp, 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0.3552312292923360_dp, 0.3552001545130070_dp, 0.3551839309110140_dp, 0.3551765182665390_dp, & + & 0.3551737375363050_dp, 0.3551729811110680_dp, 0.3551728694643190_dp, 0.3551728608224030_dp, & + & 0.3551727052439380_dp, 0.3551716511775850_dp, 0.3551677763276540_dp, 0.3551574474732890_dp, & + & 0.3551348433979520_dp, 0.3550915553066180_dp, 0.3550162813868170_dp, 0.3548946306246920_dp, & + & 0.3547090491566220_dp, 0.3544388801907240_dp, 0.3540605656990220_dp, 0.3535479944793920_dp, & + & 0.3528729966651770_dp, 0.3520059792439770_dp, 0.3509166906801510_dp, 0.3495750955206770_dp, & + & 0.3479523322861160_dp, 0.3460217205702140_dp, 0.3437597768016970_dp, 0.3411471933446820_dp, & + & 0.3381697332932030_dp, 0.3348189940710820_dp, 0.3310929971433510_dp, 0.3269965687843990_dp, & + & 0.3225414875311120_dp, 0.3177463868857230_dp, 0.3126364159215990_dp, 0.3072426744166950_dp, & + & 0.3016014517273860_dp, 0.2957533087295230_dp, 0.2897420490168660_dp, 0.2836136287783720_dp, & + & 0.2774150544015370_dp, 0.2711933132573920_dp, 0.2649943769705700_dp, 0.2588623085724780_dp, & + & 0.2528384961178500_dp, 0.2469610263934210_dp, 0.2412642039088980_dp, 0.2357782129256910_dp, & + & 0.2305289141714050_dp, 0.2255377632804180_dp, 0.2208218349274350_dp, 0.2163939350039530_dp, & + & 0.2122627828651250_dp, 0.2084332464302180_dp, 0.2049066145111060_dp, 0.2016808929182300_dp, & + & 0.1987511134082780_dp, 0.1961096471628810_dp, 0.1937465170210300_dp, 0.1916497049629700_dp, & + & 0.1898054532327930_dp, 0.1881985589040520_dp, 0.1868126625922320_dp, 0.1856305323884260_dp, & + & 0.1846343439573170_dp, 0.1838059571678340_dp, 0.1831271886967410_dp, 0.1825800788778090_dp, & + & 0.1821471497969110_dp, 0.1818116503962240_dp, 0.1815577832915660_dp, 0.1813709072516260_dp, & + & 0.1812377089395620_dp, 0.1811463376427010_dp, 0.1810864973400330_dp, 0.1810494915574560_dp, & + & 0.1810282179729010_dp, 0.1810171115537460_dp, 0.1810120370097080_dp, 0.1810101333844610_dp, & + & 0.1810096155533180_dp, 0.1810095391225670_dp, 0.1810095331585520_dp, 0.1810094251700920_dp, & + & 0.1810086935331730_dp, 0.1810060039691730_dp, 0.1809988346612670_dp, 0.1809831452236670_dp, & + & 0.1809530996731540_dp, 0.1809008552140450_dp, 0.1808164277182700_dp, 0.1806876436659620_dp, & + & 0.1805001868902210_dp, 0.1802377465903110_dp, 0.1798822705799810_dp, 0.1794143244855380_dp, & + & 0.1788135535259700_dp, 0.1780592386184770_dp, 0.1771309330051520_dp, 0.1760091596892650_dp, & + & 0.1746761441410810_dp, 0.1731165515450390_dp, 0.1713181939393030_dp, 0.1692726705624030_dp, & + & 0.1669759050904960_dp, 0.1644285465460800_dp, 0.1616362065426810_dp, 0.1586095139392220_dp, & + & 0.1553639783390500_dp, 0.1519196653414670_dp, 0.1483006980254870_dp, 0.1445346097587860_dp, & + & 0.1406515821080420_dp, 0.1366836076264160_dp, 0.1326636201554270_dp, 0.1286246348962830_dp, & + & 0.1245989371086050_dp, 0.1206173523904150_dp, 0.1167086237933080_dp, 0.1128989123457200_dp, & + & 0.1092114287200270_dp, 0.1056661955297040_dp, 0.1022799326668600_dp, 0.0990660525745817_dp, & + & 0.0960347485711175_dp, 0.0931931573005187_dp, 0.0905455759318201_dp, 0.0880937156161750_dp, & + & 0.0858369746250602_dp, 0.0837727171901044_dp, 0.0818965470168713_dp, 0.0802025674685503_dp, & + & 0.0786836232900328_dp, 0.0773315213120078_dp, 0.0761372297327654_dp, 0.0750910572607992_dp, & + & 0.0741828145855479_dp, 0.0734019613328769_dp, 0.0727377418849926_dp, 0.0721793132544377_dp, & + & 0.0717158676628777_dp, 0.0713367516649761_dp, 0.0710315826617176_dp, 0.0707903625599400_dp, & + & 0.0706035872535793_dp, 0.0704623496272703_dp, 0.0703584330032641_dp, 0.0702843914463855_dp, & + & 0.0702336131596972_dp, 0.0702003633714554_dp, 0.0701798036217767_dp, 0.0701679851672345_dp, & + & 0.0701618152633756_dp, 0.0701589962734275_dp, 0.0701579387875491_dp, 0.0701576511271256_dp, & + & 0.0701576086691027_dp, 0.0701576053278430_dp, 0.0701575444675946_dp, 0.0701571321312571_dp, & + & 0.0701556163513821_dp, 0.0701515759317779_dp, 0.0701427340443210_dp, 0.0701258025808436_dp, & + & 0.0700963642838062_dp, 0.0700487993650931_dp, 0.0699762629146825_dp, 0.0698707187888061_dp, & + & 0.0697230347102824_dp, 0.0695231418607491_dp, 0.0692602601657342_dp, 0.0689231876873180_dp, & + & 0.0685006490479623_dp, 0.0679816937260860_dp, 0.0673561306303512_dp, 0.0666149809454240_dp, & + & 0.0657509273250199_dp, 0.0647587346272580_dp, 0.0636356160739631_dp, 0.0623815194095130_dp, & + & 0.0609993105972784_dp, 0.0594948378330677_dp, 0.0578768658924780_dp, 0.0561568794919296_dp, & + & 0.0543487636207125_dp, 0.0524683777463899_dp, 0.0505330484501734_dp, 0.0485610105817074_dp, & + & 0.0465708298601086_dp, 0.0445808397509317_dp, 0.0426086225497500_dp, 0.0406705593662586_dp, & + & 0.0387814668400779_dp, 0.0369543307653828_dp, 0.0352001391902910_dp, 0.0335278107139416_dp, & + & 0.0319442081726393_dp, 0.0304542240043730_dp, 0.0290609213969049_dp, 0.0277657147391466_dp, & + & 0.0265685736406738_dp, 0.0254682365100685_dp, 0.0244624220280087_dp, 0.0235480294890316_dp, & + & 0.0227213216466247_dp, 0.0219780861760377_dp, 0.0213137740262574_dp, 0.0207236146907022_dp, & + & 0.0202027097629269_dp, 0.0197461070807243_dp, 0.0193488583450971_dp, 0.0190060633842357_dp, & + & 0.0187129042676624_dp, 0.0184646723075836_dp, 0.0182567906539752_dp, 0.0180848347330915_dp, & + & 0.0179445522320556_dp, 0.0178318837305014_dp, 0.0177429844595629_dp, 0.0176742470657558_dp, & + & 0.0176223247106897_dp, 0.0175841533828809_dp, 0.0175569719680091_dp, 0.0175383384439840_dp, & + & 0.0175261405497054_dp, 0.0175185994219973_dp, 0.0175142649868469_dp, 0.0175120023008297_dp, & + & 0.0175109685247783_dp, 0.0175105807300184_dp, 0.0175104752414228_dp, 0.0175104596715592_dp, & + & 0.0175104584354351_dp, 0.0175104357818476_dp, 0.0175102823010285_dp, 0.0175097180976067_dp, & + & 0.0175082142020528_dp, 0.0175049232864097_dp, 0.0174986220267606_dp, 0.0174876679552654_dp, & + & 0.0174699736559170_dp, 0.0174430011421123_dp, 0.0174037791362203_dp, 0.0173489456650486_dp, & + & 0.0172748177906996_dp, 0.0171774893289935_dp, 0.0170529560119661_dp, 0.0168972657231379_dp, & + & 0.0167066892450229_dp, 0.0164779045617287_dp, 0.0162081853970619_dp, 0.0158955826496694_dp, & + & 0.0155390860587907_dp, 0.0151387531254805_dp, 0.0146957932774683_dp, 0.0142125976093794_dp, & + & 0.0136927081738918_dp, 0.0131407254482276_dp, 0.0125621577673378_dp, 0.0119632215829419_dp, & + & 0.0113506057324493_dp, 0.0107312159270734_dp, 0.0101119170226838_dp, 0.0094992901853566_dp, & + & 0.0088994199169186_dp, 0.0083177223876341_dp, 0.0077588221328497_dp, 0.0072264795106669_dp, & + & 0.0067235670010000_dp, 0.0062520889434694_dp, 0.0058132369279278_dp, 0.0054074717876631_dp, & + & 0.0050346228633487_dp, 0.0046939957230805_dp, 0.0043844806725630_dp, 0.0041046559838271_dp, & + & 0.0038528815641179_dp, 0.0036273804962441_dp, 0.0034263072941911_dp, 0.0032478027668219_dp, & + & 0.0030900361323738_dp, 0.0029512355708761_dp, 0.0028297087804248_dp, 0.0027238553025768_dp, & + & 0.0026321723919800_dp, 0.0025532560648536_dp, 0.0024857987478804_dp, 0.0024285847321437_dp, & + & 0.0023804844462028_dp, 0.0023404483905232_dp, 0.0023075014039762_dp, 0.0022807377526561_dp, & + & 0.0022593173468231_dp, 0.0022424632139142_dp, 0.0022294601956396_dp, 0.0022196546989157_dp, & + & 0.0022124552196310_dp, 0.0022073332753543_dp, 0.0022038243339821_dp, 0.0022015283113212_dp, & + & 0.0022001092342769_dp, 0.0021992937248818_dp, 0.0021988680480014_dp, 0.0021986735738331_dp, & + & 0.0021986006232808_dp, 0.0021985807792824_dp, 0.0021985778503613_dp, 0.0021985776156974_dp, & + & 0.0021985732883465_dp, 0.0021985439700814_dp, 0.0021984361957763_dp, 0.0021981489300273_dp, & + & 0.0021975203624081_dp, 0.0021963169879804_dp, 0.0021942255853169_dp, 0.0021908487450020_dp, & + & 0.0021857046384994_dp, 0.0021782317252565_dp, 0.0021677990465960_dp, 0.0021537226145405_dp, & + & 0.0021352881442773_dp, 0.0021117799808081_dp, 0.0020825155353137_dp, 0.0020468839006220_dp, & + & 0.0020043866176351_dp, 0.0019546779027273_dp, 0.0018976011325336_dp, 0.0018332181340846_dp, & + & 0.0017618279500127_dp, 0.0016839723055533_dp, 0.0016004260005822_dp, 0.0015121718112745_dp, & + & 0.0014203610552528_dp, 0.0013262625335209_dp, 0.0012312038677820_dp, 0.0011365100875054_dp, & + & 0.0010434445455729_dp, 0.0009531568356032_dp, 0.0008666414233396_dp, 0.0007847093188182_dp, & + & 0.0007079735239977_dp, 0.0006368475386758_dp, 0.0005715551419065_dp, 0.0005121490377604_dp, & + & 0.0004585358126903_dp, 0.0004105046625043_dp, 0.0003677570757787_dp, 0.0003299348412789_dp, & + & 0.0002966445965278_dp, 0.0002674777392038_dp, 0.0002420258099924_dp, 0.0002198926731829_dp, & + & 0.0002007036694138_dp, 0.0001841116317500_dp, 0.0001698009262263_dp, 0.0001574892335157_dp, & + & 0.0001469259435574_dp, 0.0001378890416852_dp, 0.0001301829585856_dp, 0.0001236364565464_dp, & + & 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9.0213702502950395e-05_dp, & + & 8.8703204863094202e-05_dp, 8.6835374453642103e-05_dp, 8.4580142196699599e-05_dp, 8.1918059859020800e-05_dp, & + & 7.8843255842286894e-05_dp, 7.5365786099013094e-05_dp, 7.1512829453723698e-05_dp, 6.7328289070189799e-05_dp, & + & 6.2870957862060095e-05_dp, 5.8212015861869297e-05_dp, 5.3432155549870699e-05_dp, 4.8617446402943201e-05_dp, & + & 4.3853675606442300e-05_dp, 3.9221200054839803e-05_dp, 3.4791743960482797e-05_dp, 3.0625542947859699e-05_dp, & + & 2.6768267801458000e-05_dp, 2.3250088677428901e-05_dp, 2.0086187785040000e-05_dp, 1.7275466358768199e-05_dp, & + & 1.4800250951907399e-05_dp, 1.2630126278168101e-05_dp, 1.0727236066543399e-05_dp, 9.0547842681587604e-06_dp, & + & 7.5896022551091804e-06_dp, 6.3249016264421698e-06_dp, 5.2541780704018501e-06_dp, 4.3704168142255597e-06_dp, & + & 3.6681149495621000e-06_dp, 3.0351456636879001e-06_dp, 2.4273484662273901e-06_dp, 2.1130328811125301e-06_dp, & + & 1.7893055215267901e-06_dp, 1.4435051234329400e-06_dp, 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0.0333137220305488_dp, 0.0333059818049293_dp, & + & 0.0333019411522173_dp, 0.0333000950456963_dp, 0.0332994025237454_dp, 0.0332992141425308_dp, & + & 0.0332991863379135_dp, 0.0332991841498185_dp, 0.0332991442940838_dp, 0.0332988742665066_dp, & + & 0.0332978816293448_dp, 0.0332952357213046_dp, 0.0332894457145230_dp, 0.0332783590680208_dp, & + & 0.0332590852703021_dp, 0.0332279497241217_dp, 0.0331804825336590_dp, 0.0331114466988822_dp, & + & 0.0330149096632937_dp, 0.0328843611514600_dp, 0.0327128786380939_dp, 0.0324933395258498_dp, & + & 0.0322186761697196_dp, 0.0318821663766755_dp, 0.0314777481633257_dp, 0.0310003437359825_dp, & + & 0.0304461743374347_dp, 0.0298130453138796_dp, 0.0291005800070465_dp, 0.0283103822777662_dp, & + & 0.0274461108237816_dp, 0.0265134538976852_dp, 0.0255200001784388_dp, 0.0244750097245188_dp, & + & 0.0233890972411004_dp, 0.0222738473377930_dp, 0.0211413871110082_dp, 0.0200039445463673_dp, & + & 0.0188734215312465_dp, 0.0177610077245234_dp, 0.0166768565693545_dp, 0.0156298380912219_dp, & + & 0.0146273757077040_dp, 0.0136753670209231_dp, 0.0127781822582804_dp, 0.0119387292208657_dp, & + & 0.0111585705514656_dp, 0.0104380778485620_dp, 0.0097766074309789_dp, 0.0091726840670603_dp, & + & 0.0086241813177423_dp, 0.0081284898796739_dp, 0.0076826680762352_dp, 0.0072835711497063_dp, & + & 0.0069279581010946_dp, 0.0066125764525324_dp, 0.0063342264867998_dp, 0.0060898072932147_dp, & + & 0.0058763473752847_dp, 0.0056910227172295_dp, 0.0055311651367873_dp, 0.0053942635413122_dp, & + & 0.0052779604139346_dp, 0.0051800455269628_dp, 0.0050984485343903_dp, 0.0050312317445176_dp, & + & 0.0049765840257052_dp, 0.0049328164556570_dp, 0.0048983599970924_dp, 0.0048717651770787_dp, & + & 0.0048517034745856_dp, 0.0048369698933470_dp, 0.0048264860263103_dp, 0.0048193028155481_dp, & + & 0.0048146021827335_dp, 0.0048116967536629_dp, 0.0048100270176619_dp, 0.0048091554381884_dp, & + & 0.0048087572458755_dp, 0.0048086078765905_dp, 0.0048085672451137_dp, 0.0048085612480264_dp, & + & 0.0048085607718988_dp, 0.0048085520463417_dp, 0.0048084929297829_dp, 0.0048082756160142_dp, & + & 0.0048076963754369_dp, 0.0048064289151739_dp, 0.0048040023187923_dp, 0.0047997847673500_dp, & + & 0.0047929743083941_dp, 0.0047825979946978_dp, 0.0047675207179765_dp, 0.0047464649606042_dp, & + & 0.0047180424214304_dp, 0.0046807979883709_dp, 0.0046332657952561_dp, 0.0045740361137234_dp, & + & 0.0045018306380626_dp, 0.0044155824223822_dp, 0.0043145154840900_dp, 0.0041982180936913_dp, & + & 0.0040667032466715_dp, 0.0039204499511172_dp, 0.0037604198909520_dp, 0.0035880457499289_dp, & + & 0.0034051898852780_dp, 0.0032140748618232_dp, 0.0030171902356813_dp, 0.0028171825017722_dp, & + & 0.0026167369052956_dp, 0.0024184605751429_dp, 0.0022247760361935_dp, 0.0020378326705384_dp, & + & 0.0018594413922983_dp, 0.0016910350911488_dp, 0.0015336547297977_dp, 0.0013879587091950_dp, & + & 0.0012542514427025_dp, 0.0011325260655681_dp, 0.0010225158346202_dp, 0.0009237490131326_dp, & + & 0.0008356028107031_dp, 0.0007573530911600_dp, 0.0006882178030736_dp, 0.0006273931603147_dp, & + & 0.0005740823627036_dp, 0.0005275171315731_dp, 0.0004869726665646_dp, 0.0004517768973713_dp, & + & 0.0004213150968795_dp, 0.0003950309799734_dp, 0.0003724253146871_dp, 0.0003530528749209_dp, & + & 0.0003365183517516_dp, 0.0003224716784374_dp, 0.0003106031217115_dp, 0.0003006384231625_dp, & + & 0.0002923342114087_dp, 0.0002854738386091_dp, 0.0002798637331054_dp, 0.0002753303091367_dp, & + & 0.0002717174378191_dp, 0.0002688844568581_dp, 0.0002667046746083_dp, 0.0002650643057507_dp, & + & 0.0002638617596205_dp, 0.0002630071892256_dp, 0.0002624222013310_dp, 0.0002620396264206_dp, & + & 0.0002618032529895_dp, 0.0002616674426505_dp, 0.0002615965608754_dp, 0.0002615641797661_dp, & + & 0.0002615520333578_dp, 0.0002615487293198_dp, 0.0002615482416530_dp, 0.0002615482025874_dp, & + & 0.0002615474820900_dp, 0.0002615426006614_dp, 0.0002615246566862_dp, 0.0002614768298912_dp, & + & 0.0002613721886462_dp, 0.0002611718898535_dp, 0.0002608238865776_dp, 0.0002602622736489_dp, & + & 0.0002594074144540_dp, 0.0002581669992736_dp, 0.0002564381771961_dp, 0.0002541108729091_dp, & + & 0.0002510723372566_dp, 0.0002472128835649_dp, 0.0002424326300456_dp, 0.0002366489115957_dp, & + & 0.0002298038594972_dp, 0.0002218715001874_dp, 0.0002128636267571_dp, 0.0002028336783155_dp, & + & 0.0001918779509467_dp, 0.0001801336729628_dp, 0.0001677738015360_dp, 0.0001549988014133_dp, & + & 0.0001420260791463_dp, 0.0001290780818692_dp, 0.0001163702529183_dp, 0.0001041000033624_dp, & + & 9.2437604095607599e-05_dp, 8.1519574393951202e-05_dp, 7.1444914574669797e-05_dp, 6.2274297128794801e-05_dp, & + & 5.4032003355075597e-05_dp, 4.6710253144510703e-05_dp, 4.0275343742734997e-05_dp, 3.4674353258878903e-05_dp, & + & 2.9841424762366801e-05_dp, 2.5703346004490898e-05_dp, 2.2183623663352099e-05_dp, 1.9205493906326899e-05_dp, & + & 1.6695410494094200e-05_dp, 1.4585727079463600e-05_dp, 1.2816070658061600e-05_dp, 1.1334892079162300e-05_dp, & + & 1.0098730420793301e-05_dp, 9.0689995815296192e-06_dp, 8.2116171853385805e-06_dp, 7.4982964619607603e-06_dp, & + & 6.9044463799627903e-06_dp, 6.4074605745645402e-06_dp, 5.9897829274291300e-06_dp, 5.6407941926295297e-06_dp, & + & 5.3526931225178504e-06_dp, 5.1159005494127996e-06_dp, 4.9198528060401301e-06_dp, 4.7564225837959401e-06_dp, & + & 4.6209552166942600e-06_dp, 4.5106411974415997e-06_dp, 4.4227061408719203e-06_dp, 4.3538722707125999e-06_dp, & + & 4.3007542629425197e-06_dp, 4.2603266692253800e-06_dp, 4.2300821263552297e-06_dp, 4.2079659081650797e-06_dp, & + & 4.1922617128875598e-06_dp, 4.1815124802724296e-06_dp, 4.1744818162214903e-06_dp, 4.1701373945102196e-06_dp, & + & 4.1676410589275301e-06_dp, 4.1663381011858300e-06_dp, 4.1657428511143701e-06_dp, 4.1655195630596600e-06_dp, & + & 4.1654588258666098e-06_dp, 4.1654498588172803e-06_dp, 4.1654491482745496e-06_dp, 4.1654359890230799e-06_dp, & + & 4.1653468656477301e-06_dp, 4.1650192486031301e-06_dp, 4.1641460626351503e-06_dp, 4.1622358040172003e-06_dp, & + & 4.1585800119037197e-06_dp, 4.1522306588603897e-06_dp, 4.1419902387929099e-06_dp, 4.1264179984068497e-06_dp, & + & 4.1038559928097104e-06_dp, 4.0724784113876896e-06_dp, 4.0303654529338903e-06_dp, 3.9755993554990701e-06_dp, & + & 3.9063770529423900e-06_dp, 3.8211418100786398e-06_dp, 3.7187684469586202e-06_dp, 3.5988756010851800e-06_dp, & + & 3.4622865854316800e-06_dp, 3.3113767514692002e-06_dp, 3.1496333008362900e-06_dp, 2.9799611453995601e-06_dp, & + & 2.8028877565588998e-06_dp, 2.6173104785698300e-06_dp, 2.4241613303388502e-06_dp, 2.2287576868507101e-06_dp, & + & 2.0387054391335398e-06_dp, 1.8614447654385900e-06_dp, 1.7050028091603100e-06_dp, 1.5752607041008600e-06_dp, & + & 1.4660001212973801e-06_dp, 1.3587309766194300e-06_dp, 1.2375079805337899e-06_dp, 1.0929953049298999e-06_dp, & + & 9.1169712135297200e-07_dp, 9.0660159202116098e-07_dp, 8.5362299984126398e-07_dp, 7.0065943447161803e-07_dp, & + & 6.8155881649545304e-07_dp, 6.4657001530576995e-07_dp, 5.4913345337581600e-07_dp, 4.4077548011500798e-07_dp, & + & 4.4345539862433698e-07_dp, -1.4210854715202001e-14_dp, -1.4210854715202001e-14_dp, 7.7227706896110196e-07_dp, & + & 1.1088044189477799e-06_dp, 1.2591339455525500e-06_dp, 1.2084589968708300e-06_dp, 9.8865730535635500e-07_dp, & + & 6.6239528706546501e-07_dp, -1.4210854715202001e-14_dp, -1.4210854715202001e-14_dp, -1.4210854715202001e-14_dp, & + & -1.4210854715202001e-14_dp, -1.4210854715202001e-14_dp, -1.4210854715202001e-14_dp, -1.4210854715202001e-14_dp, & + & -1.4210854715202001e-14_dp, -1.4210854715202001e-14_dp, -1.4210854715202001e-14_dp, -1.4210854715202001e-14_dp, & + & -1.4210854715202001e-14_dp, -1.4210854715202001e-14_dp, -1.4210854715202001e-14_dp, -1.4210854715202001e-14_dp, & + & -1.4210854715202001e-14_dp, -1.4210854715202001e-14_dp, -1.4210854715202001e-14_dp, -1.4210854715202001e-14_dp, & + & 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33.6090383606011969_dp, 33.5672435198702033_dp, 33.5239421163011002_dp, 33.4794026791526989_dp, & + & 33.4339155536877968_dp, 33.3877878551718013_dp, 33.3413379825087972_dp, 33.2948898475383004_dp, & + & 33.2487669847279008_dp, 33.2032867070101005_dp, 33.1587544672627033_dp, 33.1154585723874035_dp, & + & 33.0736653794569975_dp, 33.0336150824637969_dp, 32.9955181753141034_dp, 32.9595526532121994_dp, & + & 32.9258619915327984_dp, 32.8945539194794989_dp, 32.8656999857550005_dp, 32.8393358953449024_dp, & + & 32.8154625803866011_dp, 32.7940479538540970_dp, 32.7750292822962024_dp, 32.7583161029837981_dp, & + & 32.7437936014410980_dp, 32.7313263574459015_dp, 32.7207623612449012_dp, 32.7119371970741994_dp, & + & 32.7046782882989007_dp, 32.6988090978147028_dp, 32.6941531789971975_dp, 32.6905379766201989_dp, & + & 32.6877982838908991_dp, 32.6857792710737982_dp, 32.6843390129810984_dp, 32.6833504566629003_dp, & + & 32.6827027865941986_dp, 32.6823021620676997_dp, 32.6820718198447011_dp, 32.6819515538012979_dp, & + & 32.6818966017356018_dp, 32.6818759870730986_dp, 32.6818703793618965_dp, 32.6818695516747013_dp, & + & 32.6818694430996004_dp, 32.6818669134294026_dp, 32.6818497745250980_dp, 32.6817867698476974_dp, & + & 32.6816188205716003_dp, 32.6812512578532974_dp, 32.6805472935918999_dp, 32.6793229759364010_dp, & + & 32.6773438366882019_dp, 32.6743233932267003_dp, 32.6699236185546980_dp, 32.6637574404894977_dp, & + & 32.6553932760295993_dp, 32.6443615506998981_dp, 32.6301630964831020_dp, 32.6122792669019006_dp, & + & 32.5901835547913024_dp, 32.5633544477035031_dp, 32.5312892077184017_dp, 32.4935182164349001_dp, & + & 32.4496194821049997_dp, 32.3992328651808990_dp, 32.3420735435863023_dp, 32.2779442145448030_dp, & + & 32.2067455226465000_dp, 32.1284842220361995_dp, 32.0432786317439025_dp, 31.9513610321414987_dp, & + & 31.8530767772965007_dp, 31.7488800562876001_dp, 31.6393264135217009_dp, 31.5250623159737984_dp, & + & 31.4068122142528985_dp, 31.2853636663570995_dp, 31.1615511650304988_dp, 31.0362393265546004_dp, & + & 30.9103060637018991_dp, 30.7846262887997995_dp, 30.6600565893414014_dp, 30.5374212046836995_dp, & + & 30.4174995227436007_dp, 30.3010152209740014_dp, 30.1886271021447001_dp, 30.0809216236974990_dp, & + & 29.9784070872130997_dp, 29.8815094371845014_dp, 29.7905696105584994_dp, 29.7058423755565997_dp, & + & 29.6274965964650008_dp, 29.5556168580488006_dp, 29.4902063778603001_dp, 29.4311911266933990_dp, & + & 29.3784250670044997_dp, 29.3316964067177999_dp, 29.2907347519307990_dp, 29.2552190271164996_dp, & + & 29.2247860159587987_dp, 29.1990393605228995_dp, 29.1775588417635987_dp, 29.1599097512810985_dp, & + & 29.1456521537879993_dp, 29.1343498331066009_dp, 29.1255787128139012_dp, 29.1189345469689016_dp, & + & 29.1140396874930012_dp, 29.1105487532299989_dp, 29.1081530515073013_dp, 29.1065836357308001_dp, & + & 29.1056129212038002_dp, 29.1050548245979002_dp, 29.1047634385474012_dp, 29.1046302997247004_dp, & + & 29.1045803544113006_dp, 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-7.1054273576010003e-15_dp, -7.1054273576010003e-15_dp, -7.1054273576010003e-15_dp, & + & -7.1054273576010003e-15_dp, -7.1054273576010003e-15_dp, -7.1054273576010003e-15_dp, -7.1054273576010003e-15_dp, & + & -7.1054273576010003e-15_dp, -7.1054273576010003e-15_dp, -7.1054273576010003e-15_dp, -7.1054273576010003e-15_dp, & + & -7.1054273576010003e-15_dp, -7.1054273576010003e-15_dp, -7.1054273576010003e-15_dp, -7.1054273576010003e-15_dp, & + & -7.1054273576010003e-15_dp & + &] + case (36) + out = [& + & 36.0000000000000000_dp, 35.9999999710689025_dp, 35.9999990764622027_dp, 35.9999930153608005_dp, & + & 35.9999707339678992_dp, 35.9999113388581975_dp, 35.9997813485471028_dp, 35.9995323802195983_dp, & + & 35.9990993554543977_dp, 35.9983992930622989_dp, 35.9973307393538988_dp, 35.9957738668830984_dp, & + & 35.9935912527007034_dp, 35.9906293271582030_dp, 35.9867204650916008_dp, 35.9816856734824029_dp, & + & 35.9753378140339990_dp, 35.9674852858927991_dp, 35.9579360831735997_dp, 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0.1421887853144670_dp, & + & 0.1371692203669850_dp, 0.1323161731578040_dp, 0.1276560111492060_dp, 0.1232105689100320_dp, & + & 0.1189971539132270_dp, 0.1150286838494810_dp, 0.1113139284999110_dp, 0.1078578282792580_dp, & + & 0.1046618626562430_dp, 0.1017244443202970_dp, 0.0990413186929544_dp, 0.0966059526903464_dp, & + & 0.0944099011017485_dp, 0.0924431432110282_dp, 0.0906943860986544_dp, 0.0891513342534367_dp, & + & 0.0878009276066507_dp, 0.0866295518452915_dp, 0.0856232258859677_dp, 0.0847677717455895_dp, & + & 0.0840489718070074_dp, 0.0834527177409541_dp, 0.0829651542195080_dp, 0.0825728191636443_dp, & + & 0.0822627807395335_dp, 0.0820227697924238_dp, 0.0818413050179458_dp, 0.0817078070442463_dp, & + & 0.0816126968375315_dp, 0.0815474735216668_dp, 0.0815047668546924_dp, 0.0814783602200748_dp, & + & 0.0814631810173196_dp, 0.0814552566827942_dp, 0.0814516361207254_dp, 0.0814502779442066_dp, & + & 0.0814499084892830_dp, 0.0814498539585813_dp, 0.0814498497034677_dp, 0.0814497726574572_dp, & + & 0.0814492506605546_dp, 0.0814473317614954_dp, 0.0814422168098972_dp, 0.0814310235169913_dp, & + & 0.0814095895263733_dp, 0.0813723234735448_dp, 0.0813121126645342_dp, 0.0812202955410086_dp, & + & 0.0810867063709892_dp, 0.0808997984200772_dp, 0.0806468500147588_dp, 0.0803142552287710_dp, & + & 0.0798878972954142_dp, 0.0793535982718794_dp, 0.0786976331032818_dp, 0.0779072903721030_dp, & + & 0.0769714561630153_dp, 0.0758811922577749_dp, 0.0746302760189792_dp, 0.0732156675379727_dp, & + & 0.0716378705071747_dp, 0.0699011571941810_dp, 0.0680136348779712_dp, 0.0659871407954853_dp, & + & 0.0638369642867787_dp, 0.0615814073329801_dp, 0.0592412067652930_dp, 0.0568388517681697_dp, & + & 0.0543978377534486_dp, 0.0519419014309435_dp, 0.0494942815946757_dp, 0.0470770459436309_dp, & + & 0.0447105167969895_dp, 0.0424128188430188_dp, 0.0401995612717059_dp, 0.0380836559921462_dp, & + & 0.0360752641783080_dp, 0.0341818558946017_dp, 0.0324083624537010_dp, 0.0307573985387748_dp, & + & 0.0292295307691717_dp, 0.0278235708930765_dp, 0.0265368746259966_dp, 0.0253656307828578_dp, & + & 0.0243051292796110_dp, 0.0233500004105807_dp, 0.0224944212557077_dp, 0.0217322879678505_dp, & + & 0.0210573549634319_dp, 0.0204633436965338_dp, 0.0199440247904406_dp, 0.0194932779118986_dp, & + & 0.0191051339894344_dp, 0.0187738042817358_dp, 0.0184937004671113_dp, 0.0182594494132218_dp, & + & 0.0180659056452726_dp, 0.0179081638052523_dp, 0.0177815726204287_dp, 0.0176817511149352_dp, & + & 0.0176046070437508_dp, 0.0175463568438303_dp, 0.0175035458250861_dp, 0.0174730669016014_dp, & + & 0.0174521759206385_dp, 0.0174385016000826_dp, 0.0174300482341465_dp, 0.0174251896545883_dp, & + & 0.0174226534055464_dp, 0.0174214946562827_dp, 0.0174210599830005_dp, 0.0174209417426141_dp, & + & 0.0174209242906187_dp, 0.0174209229172249_dp, 0.0174208979011681_dp, 0.0174207284144856_dp, & + & 0.0174201053738514_dp, 0.0174184446560162_dp, 0.0174148106202452_dp, 0.0174078525572199_dp, & + & 0.0173957572773418_dp, 0.0173762211069075_dp, 0.0173464445854066_dp, 0.0173031530637004_dp, & + & 0.0172426460785076_dp, 0.0171608777028709_dp, 0.0170535689383158_dp, 0.0169163515497459_dp, & + & 0.0167449405476390_dp, 0.0165353298771294_dp, 0.0162840029762350_dp, 0.0159881470168202_dp, & + & 0.0156458572318243_dp, 0.0152563161958099_dp, 0.0148199326714789_dp, 0.0143384259686741_dp, & + & 0.0138148448030577_dp, 0.0132535142659265_dp, 0.0126599103285372_dp, 0.0120404676761439_dp, & + & 0.0114023328107393_dp, 0.0107530794625745_dp, 0.0101004067067905_dp, 0.0094518413364924_dp, & + & 0.0088144648700208_dp, 0.0081946822974430_dp, 0.0075980448250093_dp, 0.0070291331818808_dp, & + & 0.0064915022868632_dp, 0.0059876829386809_dp, 0.0055192322111353_dp, 0.0050868216979296_dp, & + & 0.0046903517032248_dp, 0.0043290797526794_dp, 0.0040017530921119_dp, 0.0037067367717967_dp, & + & 0.0034421311186534_dp, 0.0032058745812478_dp, 0.0029958298891799_dp, 0.0028098530796328_dp, & + & 0.0026458461578898_dp, 0.0025017949752808_dp, 0.0023757943688736_dp, 0.0022660627815014_dp, & + & 0.0021709485516439_dp, 0.0020889299050637_dp, 0.0020186104547264_dp, 0.0019587117597695_dp, & + & 0.0019080642343567_dp, 0.0018655974463187_dp, 0.0018303306130889_dp, 0.0018013638913814_dp, & + & 0.0017778708684091_dp, 0.0017590924913549_dp, 0.0017443325185269_dp, 0.0017329544362639_dp, & + & 0.0017243796636848_dp, 0.0017180867653295_dp, 0.0017136113146989_dp, 0.0017105460047233_dp, & + & 0.0017085405877708_dp, 0.0017073012496738_dp, 0.0017065890760151_dp, 0.0017062173507725_dp, & + & 0.0017060475277901_dp, 0.0017059838247917_dp, 0.0017059664963597_dp, 0.0017059639387256_dp, & + & 0.0017059637356809_dp, 0.0017059600144265_dp, 0.0017059348025654_dp, 0.0017058421237479_dp, & + & 0.0017055950964320_dp, 0.0017050545865942_dp, 0.0017040198417249_dp, 0.0017022216507669_dp, & + & 0.0016993186202967_dp, 0.0016948971988810_dp, 0.0016884760967457_dp, 0.0016795157064919_dp, & + & 0.0016674330020194_dp, 0.0016516221465466_dp, 0.0016314806604640_dp, 0.0016064404840535_dp, & + & 0.0015760026483278_dp, 0.0015397735975071_dp, 0.0014975005798590_dp, 0.0014491030538295_dp, & + & 0.0013946968639900_dp, 0.0013346081288717_dp, 0.0012693744076557_dp, 0.0011997317629096_dp, & + & 0.0011265877157740_dp, 0.0010509816221713_dp, 0.0009740354529768_dp, 0.0008968990956717_dp, & + & 0.0008206949131804_dp, 0.0007464662940606_dp, 0.0006751343219733_dp, 0.0006074656023856_dp, & + & 0.0005440529015743_dp, 0.0004853087892727_dp, 0.0004314711306890_dp, 0.0003826182227940_dp, & + & 0.0003386907448970_dp, 0.0002995175524774_dp, 0.0002648426328022_dp, 0.0002343510972267_dp, & + & 0.0002076927065175_dp, 0.0001845019700255_dp, 0.0001644143016861_dp, 0.0001470781091157_dp, & + & 1.3216306653873701e-04_dp, 1.1936513271848500e-04_dp, 1.0840903473052800e-04_dp, 9.9048913099863994e-05_dp, & + & 9.1067673800182506e-05_dp, 8.4275430161540003e-05_dp, 7.8507319273057901e-05_dp, 7.3620946132280096e-05_dp, & + & 6.9493692336663999e-05_dp, 6.6020086009643806e-05_dp, 6.3109361953195303e-05_dp, 6.0683271854600200e-05_dp, & + & 5.8674156797167102e-05_dp, 5.7023274017353702e-05_dp, 5.5679366234073802e-05_dp, 5.4597463162053800e-05_dp, & + & 5.3737903364492501e-05_dp, 5.3065559839637899e-05_dp, 5.2549247747890597e-05_dp, 5.2161288067509297e-05_dp, & + & 5.1877198401939502e-05_dp, 5.1675481032020798e-05_dp, 5.1537477489205203e-05_dp, 5.1447260219106297e-05_dp, & + & 5.1391533588684999e-05_dp, 5.1359520227833902e-05_dp, 5.1342813300436801e-05_dp, 5.1335181353806500e-05_dp, & + & 5.1332318605545899e-05_dp, 5.1331539893340098e-05_dp, 5.1331424955947100e-05_dp, 5.1331415747313299e-05_dp, & + & 5.1331245956021101e-05_dp, 5.1330095523383099e-05_dp, 5.1325866657236902e-05_dp, 5.1314595573614999e-05_dp, & + & 5.1289936791931703e-05_dp, 5.1242741861301497e-05_dp, 5.1160762026825102e-05_dp, 5.1028508991635101e-05_dp, & + & 5.0827312328749499e-05_dp, 5.0535614725788498e-05_dp, 5.0129544099775103e-05_dp, 4.9583793078511503e-05_dp, & + & 4.8872818233292003e-05_dp, 4.7972341924662501e-05_dp, 4.6861100365447301e-05_dp, 4.5522732854408298e-05_dp, & + & 4.3947658099341397e-05_dp, 4.2134742393784597e-05_dp, 4.0092545113168399e-05_dp, 3.7839941434469899e-05_dp, & + & 3.5405976149149899e-05_dp, 3.2828889395375400e-05_dp, 3.0154355386002900e-05_dp, 2.7433062385284801e-05_dp, & + & 2.4717818909891799e-05_dp, 2.2060404432977500e-05_dp, 1.9508422553826700e-05_dp, 1.7102483084841000e-05_dp, & + & 1.4874109503182401e-05_dp, 1.2844745548079600e-05_dp, 1.1026016494497500e-05_dp, 9.4209971166492306e-06_dp, & + & 8.0258587900061701e-06_dp, 6.8312258818537000e-06_dp, 5.8230030219874598e-06_dp, 4.9830819648377698e-06_dp, & + & 4.2906587438551503e-06_dp, 3.7244299946337399e-06_dp, 3.2649443610921501e-06_dp, 2.8958995699213098e-06_dp, & + & 2.6037247380372702e-06_dp, 2.3759234935028000e-06_dp, 2.1998131387590501e-06_dp, 2.0629969270658000e-06_dp, & + & 1.9548003891145501e-06_dp, 1.8673096988663899e-06_dp, 1.7957972886506500e-06_dp, 1.7380913988063199e-06_dp, & + & 1.6927152728385400e-06_dp, 1.6576154706626801e-06_dp, 1.6306750296735101e-06_dp, 1.6103606412798399e-06_dp, & + & 1.5952168297417300e-06_dp, 1.5833901017003901e-06_dp, 1.5731991780398900e-06_dp, 1.5638997226119500e-06_dp, & + & 1.5556324797216801e-06_dp, 1.5487708253658600e-06_dp, 1.5434236644296100e-06_dp, 1.5393908512351101e-06_dp, & + & 1.5363572032356400e-06_dp, 1.5340533678909200e-06_dp, 1.5323004944889400e-06_dp, 1.5309859264789300e-06_dp, & + & 1.5300288751518601e-06_dp, 1.5293602615429300e-06_dp, 1.5289163997067600e-06_dp, 1.5286393875158000e-06_dp, & + & 1.5284792382885800e-06_dp, 1.5283953658240501e-06_dp, 1.5283569823054700e-06_dp, 1.5283425796042100e-06_dp, & + & 1.5283386574083101e-06_dp, 1.5283380747632700e-06_dp, 1.5283380321307001e-06_dp, 1.5283371723739900e-06_dp, & + & 1.5283313743452700e-06_dp, 1.5283100438523400e-06_dp, 1.5282532430660501e-06_dp, 1.5281291609881001e-06_dp, & + & 1.5278923939376901e-06_dp, 1.5274832279033001e-06_dp, 1.5268284556668700e-06_dp, 1.5258434871157099e-06_dp, & + & 1.5244350635157399e-06_dp, 1.5225018330511401e-06_dp, 1.5199288228018300e-06_dp, 1.5165719986498499e-06_dp, & + & 1.5122347747365001e-06_dp, 1.5066506762195801e-06_dp, 1.4995009181006899e-06_dp, 1.4904963663298100e-06_dp, & + & 1.4795180476312499e-06_dp, 1.4667399526047099e-06_dp, 1.4526228255817801e-06_dp, 1.4377756372141399e-06_dp, & + & 1.4228766005430800e-06_dp, 1.4087434081488901e-06_dp, 1.3960953566538600e-06_dp, 1.3845338528994899e-06_dp, & + & 1.3716701730004401e-06_dp, 1.3541052936716401e-06_dp, 1.3296987191324701e-06_dp, 1.2985950732513600e-06_dp, & + & 1.2626507270852000e-06_dp, 1.2246058460618799e-06_dp, 1.1859701274374901e-06_dp, 1.1438573253030901e-06_dp, & + & 1.0914920736127000e-06_dp, 1.0218754908919400e-06_dp, 9.2973265708451404e-07_dp, 8.1457602618684198e-07_dp, & + & 6.8508528272559499e-07_dp, 5.5307501156676196e-07_dp, 4.2325080329419501e-07_dp, -2.1316282072802999e-14_dp, & + & -2.1316282072802999e-14_dp, -2.1316282072802999e-14_dp, -2.1316282072802999e-14_dp, 4.4906728646765302e-07_dp, & + & 6.0029903892200299e-07_dp, 6.5639444812859395e-07_dp, 6.1149945196348199e-07_dp, 4.8442458933095601e-07_dp, & + & -2.1316282072802999e-14_dp, -2.1316282072802999e-14_dp, -2.1316282072802999e-14_dp, -2.1316282072802999e-14_dp, & + & -2.1316282072802999e-14_dp, -2.1316282072802999e-14_dp, -2.1316282072802999e-14_dp, -2.1316282072802999e-14_dp, & + & -2.1316282072802999e-14_dp, -2.1316282072802999e-14_dp, -2.1316282072802999e-14_dp, -2.1316282072802999e-14_dp, & + & -2.1316282072802999e-14_dp, -2.1316282072802999e-14_dp, -2.1316282072802999e-14_dp, -2.1316282072802999e-14_dp, & + & -2.1316282072802999e-14_dp, -2.1316282072802999e-14_dp, -2.1316282072802999e-14_dp, -2.1316282072802999e-14_dp, & + & -2.1316282072802999e-14_dp, -2.1316282072802999e-14_dp, -2.1316282072802999e-14_dp, -2.1316282072802999e-14_dp, & + & 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0.1807281413325580_dp, 0.1779524526558520_dp, 0.1750240264378250_dp, 0.1719623050032690_dp, & + & 0.1687888984545580_dp, 0.1655270449179650_dp, 0.1622010512463280_dp, 0.1588357377713690_dp, & + & 0.1554559074822710_dp, 0.1520858560335440_dp, 0.1487489347165580_dp, 0.1454671743352450_dp, & + & 0.1422609741103780_dp, 0.1391488565299990_dp, 0.1361472865262240_dp, 0.1332705514470760_dp, & + & 0.1305306968394430_dp, 0.1279375119981200_dp, 0.1254985585365920_dp, 0.1232192349636560_dp, & + & 0.1211028703974580_dp, 0.1191508410302120_dp, 0.1173627036216940_dp, 0.1157363411036700_dp, & + & 0.1142681161845540_dp, 0.1129530297961590_dp, 0.1117848821055600_dp, 0.1107564347006900_dp, & + & 0.1098595731922810_dp, 0.1090854699543370_dp, 0.1084247468292080_dp, 0.1078676375985740_dp, & + & 0.1074041497062050_dp, 0.1070242242830660_dp, 0.1067178930021480_dp, 0.1064754296636960_dp, & + & 0.1062874938492800_dp, 0.1061452635034570_dp, 0.1060405529536300_dp, 0.1059659127856420_dp, & + & 0.1059147080976790_dp, 0.1058811720975680_dp, 0.1058604325961810_dp, 0.1058485098536510_dp, & + & 0.1058422852264660_dp, 0.1058394411704950_dp, 0.1058383742708600_dp, 0.1058380840492110_dp, & + & 0.1058380412130190_dp, 0.1058380378422330_dp, 0.1058379764397870_dp, 0.1058375604312540_dp, & + & 0.1058360311437310_dp, 0.1058319546622140_dp, 0.1058230335725770_dp, 0.1058059493475480_dp, & + & 0.1057762420175690_dp, 0.1057282331984980_dp, 0.1056549978704740_dp, 0.1055483894520320_dp, & + & 0.1053991216288490_dp, 0.1051969089817600_dp, 0.1049306666491960_dp, 0.1045887670359780_dp, & + & 0.1041593489464960_dp, 0.1036306715429870_dp, 0.1029915023812290_dp, 0.1022315257296920_dp, & + & 0.1013417545966180_dp, 0.1003149278729650_dp, 0.0991458729062416_dp, 0.0978318139976437_dp, & + & 0.0963726089032448_dp, 0.0947708983522162_dp, 0.0930321578675262_dp, 0.0911646463646250_dp, & + & 0.0891792517847705_dp, 0.0870892399780772_dp, 0.0849099185699203_dp, 0.0826582323892637_dp, & + & 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0.1679996585125210_dp, 0.1679996517631680_dp, 0.1679995295547060_dp, & + & 0.1679987015755560_dp, 0.1679956578525220_dp, 0.1679875445268170_dp, 0.1679697893331350_dp, & + & 0.1679357883934500_dp, 0.1678766679232520_dp, 0.1677811335283150_dp, 0.1676354186494820_dp, & + & 0.1674233422294760_dp, 0.1671264836277540_dp, 0.1667244799801470_dp, 0.1661954474061820_dp, & + & 0.1655165226025520_dp, 0.1646645154404500_dp, 0.1636166563905230_dp, 0.1623514152928180_dp, & + & 0.1608493607220750_dp, 0.1590940226706220_dp, 0.1570727162753510_dp, 0.1547772816402140_dp, & + & 0.1522046951252850_dp, 0.1493575112305550_dp, 0.1462441015094170_dp, 0.1428786675209960_dp, & + & 0.1392810179845370_dp, 0.1354761149902760_dp, 0.1314934090567520_dp, 0.1273659966134280_dp, & + & 0.1231296448133890_dp, 0.1188217363686230_dp, 0.1144801906539000_dp, 0.1101424164153710_dp, & + & 0.1058443462959960_dp, 0.1016195947430990_dp, 0.0974987697132050_dp, 0.0935089561485540_dp, & + & 0.0896733767092002_dp, 0.0860112238245136_dp, 0.0825376476526998_dp, 0.0792638775608978_dp, & + & 0.0761974504742113_dp, 0.0733425177976699_dp, 0.0707002032548232_dp, 0.0682689864292101_dp, & + & 0.0660450904822909_dp, 0.0640228569120183_dp, 0.0621950948195575_dp, 0.0605533965819518_dp, & + & 0.0590884158031102_dp, 0.0577901067661841_dp, 0.0566479272509284_dp, 0.0556510085004973_dp, & + & 0.0547882973533547_dp, 0.0540486761604484_dp, 0.0534210661628620_dp, 0.0528945195951565_dp, & + & 0.0524583049941540_dp, 0.0521019891235923_dp, 0.0518155176682882_dp, 0.0515892955053019_dp, & + & 0.0514142660285302_dp, 0.0512819877879167_dp, 0.0511847057007131_dp, 0.0511154133826963_dp, & + & 0.0510679027901233_dp, 0.0510367973875105_dp, 0.0510175654597447_dp, 0.0510065109258520_dp, & + & 0.0510007400183881_dp, 0.0509981033699276_dp, 0.0509971142925920_dp, 0.0509968452415066_dp, & + & 0.0509968055302039_dp, 0.0509968024050949_dp, 0.0509967454820597_dp, 0.0509963598212053_dp, & + & 0.0509949421073443_dp, 0.0509911631274491_dp, 0.0509828935552719_dp, 0.0509670587603779_dp, & + & 0.0509395295074881_dp, 0.0508950552867304_dp, 0.0508272468112594_dp, 0.0507286137957550_dp, & + & 0.0505906633074744_dp, 0.0504040625723761_dp, 0.0501588679509766_dp, 0.0498448187659690_dp, & + & 0.0494516907601934_dp, 0.0489696993220861_dp, 0.0483899375330026_dp, 0.0477048290248021_dp, & + & 0.0469085711846517_dp, 0.0459975410791884_dp, 0.0449706352539749_dp, 0.0438295158291737_dp, & + & 0.0425787393576371_dp, 0.0412257516961745_dp, 0.0397807412407545_dp, 0.0382563534898495_dp, & + & 0.0366672809268422_dp, 0.0350297524005967_dp, 0.0333609543134301_dp, 0.0316784210087704_dp, & + & 0.0299994331930478_dp, 0.0283404609320428_dp, 0.0267166821397993_dp, 0.0251415993572053_dp, & + & 0.0236267680959230_dp, 0.0221816402770685_dp, 0.0208135173992829_dp, 0.0195276008677183_dp, & + & 0.0183271219151209_dp, 0.0172135309078953_dp, 0.0161867253924513_dp, 0.0152452975960529_dp, & + & 0.0143867847252750_dp, 0.0136079087594680_dp, 0.0129047960391020_dp, 0.0122731704215653_dp, & + & 0.0117085168589739_dp, 0.0112062147828595_dp, 0.0107616425999097_dp, 0.0103702559278958_dp, & + & 0.0100276430068433_dp, 0.0097295611080526_dp, 0.0094719578353519_dp, 0.0092509810579742_dp, & + & 0.0090629809032166_dp, 0.0089045068245355_dp, 0.0087723022849104_dp, 0.0086632990855193_dp, & + & 0.0085746128456918_dp, 0.0085035406156422_dp, 0.0084475610947905_dp, 0.0084043374489084_dp, & + & 0.0083717222900432_dp, 0.0083477640227656_dp, 0.0083307134916808_dp, 0.0083190297031734_dp, & + & 0.0083113833528188_dp, 0.0083066569672567_dp, 0.0083039406572851_dp, 0.0083025227575106_dp, & + & 0.0083018749664987_dp, 0.0083016319672780_dp, 0.0083015658664962_dp, 0.0083015561101973_dp, & + & 0.0083015553356276_dp, 0.0083015411405611_dp, 0.0083014449674579_dp, 0.0083010914323935_dp, & + & 0.0083001490949997_dp, 0.0082980871033698_dp, 0.0082941392564777_dp, 0.0082872774018270_dp, & + & 0.0082761961704989_dp, 0.0082593111201561_dp, 0.0082347723464977_dp, 0.0082004954524280_dp, & + & 0.0081542113472182_dp, 0.0080935356033862_dp, 0.0080160569797130_dp, 0.0079194432188459_dp, & + & 0.0078015604172137_dp, 0.0076606002878066_dp, 0.0074952077239274_dp, 0.0073045995155638_dp, & + & 0.0070886641913290_dp, 0.0068480330495575_dp, 0.0065841137020328_dp, 0.0062990799282829_dp, & + & 0.0059958151733497_dp, 0.0056778112581739_dp, 0.0053490282828150_dp, 0.0050137256716738_dp, & + & 0.0046762772505034_dp, 0.0043409847106304_dp, 0.0040119036000163_dp, 0.0036926941511766_dp, & + & 0.0033865061342198_dp, 0.0030959030077327_dp, 0.0028228265119239_dp, 0.0025685990692281_dp, & + & 0.0023339583750470_dp, 0.0021191166567434_dp, 0.0019238363238259_dp, 0.0017475139924059_dp, & + & 0.0015892658712886_dp, 0.0014480089355260_dp, 0.0013225339055936_dp, 0.0012115676004427_dp, & + & 0.0011138236162509_dp, 0.0010280413993229_dp, 0.0009530145934349_dp, 0.0008876100530770_dp, & + & 0.0008307791073179_dp, 0.0007815626270187_dp, 0.0007390913725445_dp, 0.0007025829692111_dp, & + & 0.0006713365965894_dp, 0.0006447262416103_dp, 0.0006221932632826_dp, 0.0006032388938024_dp, & + & 0.0005874170741436_dp, 0.0005743278415480_dp, 0.0005636114330585_dp, 0.0005549432442820_dp, & + & 0.0005480297133147_dp, 0.0005426051115691_dp, 0.0005384291648909_dp, 0.0005352853951734_dp, & + & 0.0005329800475380_dp, 0.0005313414444075_dp, 0.0005302195889243_dp, 0.0005294858362532_dp, & + & 0.0005290324591698_dp, 0.0005287719575975_dp, 0.0005286359943995_dp, 0.0005285738813043_dp, & + & 0.0005285505820893_dp, 0.0005285442442897_dp, 0.0005285433088531_dp, 0.0005285432338979_dp, & + & 0.0005285418518781_dp, 0.0005285324885307_dp, 0.0005284980690945_dp, 0.0005284063289324_dp, & + & 0.0005282056055478_dp, 0.0005278213790589_dp, 0.0005271537777318_dp, 0.0005260762899155_dp, & + & 0.0005244359474759_dp, 0.0005220552563472_dp, 0.0005187361352483_dp, 0.0005142660678175_dp, & + & 0.0005084265638189_dp, 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1.3326357610310400e-05_dp, 1.3326324371121200e-05_dp, 1.3326321692375099e-05_dp, 1.3326272068070500e-05_dp, & + & 1.3325935903196800e-05_dp, 1.3324700162797901e-05_dp, 1.3321406576949400e-05_dp, 1.3314200806746600e-05_dp, & + & 1.3300409264616100e-05_dp, 1.3276451888089000e-05_dp, 1.3237801255172600e-05_dp, 1.3178999950014299e-05_dp, & + & 1.3093750645509801e-05_dp, 1.2975096048251099e-05_dp, 1.2815707393087900e-05_dp, 1.2608297431882001e-05_dp, & + & 1.2346156218257001e-05_dp, 1.2023761783552800e-05_dp, 1.1637344663029100e-05_dp, 1.1185248489198301e-05_dp, & + & 1.0668071354302800e-05_dp, 1.0088922849149601e-05_dp, 9.4541902839750896e-06_dp, 8.7741947041308793e-06_dp, & + & 8.0618048059477604e-06_dp, 7.3287902964125402e-06_dp, 6.5843921746022699e-06_dp, 5.8395044248982197e-06_dp, & + & 5.1130590605907898e-06_dp, 4.4344652607719598e-06_dp, 3.8194779037326001e-06_dp, 3.2563871315005599e-06_dp, & + & 2.7882987367888699e-06_dp, 2.3805124484965698e-06_dp, 1.9996247857534399e-06_dp, 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32.9452463125731967_dp, 32.6663372428102008_dp, & + & 32.3914037682034035_dp, 32.1221941660012007_dp, 31.8603287809931999_dp, 31.6072794096561012_dp, & + & 31.3643530222259983_dp, 31.1326798371607012_dp, 30.9132056126469017_dp, 30.7066878901494000_dp, & + & 30.5136958294995004_dp, 30.3346132215202999_dp, 30.1696442522504995_dp, 30.0188216148156997_dp, & + & 29.8820166090061008_dp, 29.7589509218955008_dp, 29.6492098343846990_dp, 29.5522566404806994_dp, & + & 29.4674480938710985_dp, 29.3940507082282991_dp, 29.3312577341431009_dp, 29.2782066186466992_dp, & + & 29.2339967259943982_dp, 29.1977070645443995_dp, 29.1684137284926983_dp, 29.1452067295027000_dp, & + & 29.1272058665042017_dp, 29.1135752664428011_dp, 29.1035362281762993_dp, 29.0963780187081014_dp, & + & 29.0914663068496999_dp, 29.0882489740986010_dp, 29.0862591143054985_dp, 29.0851151194620989_dp, & + & 29.0845178443670989_dp, 29.0842449429156993_dp, 29.0841425679126004_dp, 29.0841147194062017_dp, & + & 29.0841106090242008_dp, 29.0841102919920012_dp, 29.0841045991109013_dp, 29.0840660290018000_dp, & + & 29.0839242411651000_dp, 29.0835462865786987_dp, 29.0827191408333015_dp, 29.0811350524999987_dp, & + & 29.0783802930815014_dp, 29.0739278251571989_dp, 29.0671343243563989_dp, 29.0572418965504013_dp, & + & 29.0433847212990983_dp, 29.0246007231344016_dp, 28.9998482214816988_dp, 28.9680273373950001_dp, & + & 28.9280057429281001_dp, 28.8786481324187996_dp, 28.8188485835721018_dp, 28.7475647731446990_dp, & + & 28.6638528335382006_dp, 28.5669015008920013_dp, 28.4560641305195006_dp, 28.3308871576351997_dp, & + & 28.1911336712216993_dp, 28.0368009500909992_dp, 27.8681310767389014_dp, 27.6856140800290014_dp, & + & 27.4899834357908013_dp, 27.2822041416029002_dp, 27.0634539425916998_dp, 26.8350985871784005_dp, & + & 26.5986622136495008_dp, 26.3557941025127001_dp, 26.1082330821042987_dp, 25.8577708616558013_dp, & + & 25.6062155054631013_dp, 25.3553561683283988_dp, 25.1069300930475983_dp, 24.8625927259058983_dp, & + & 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0.4356653246121030_dp, 0.4258695010516720_dp, & + & 0.4164342803045640_dp, 0.4074031258038100_dp, 0.3988122940368870_dp, 0.3906908618527820_dp, & + & 0.3830608828582240_dp, 0.3759376487733870_dp, 0.3693300328859340_dp, 0.3632408948094510_dp, & + & 0.3576675284183750_dp, 0.3526021378905850_dp, 0.3480323300254820_dp, 0.3439416142020950_dp, & + & 0.3403099042885030_dp, 0.3371140193204100_dp, 0.3343281816818330_dp, 0.3319245127375440_dp, & + & 0.3298735263360300_dp, 0.3281446203329490_dp, 0.3267065653491200_dp, 0.3255279885000770_dp, & + & 0.3245778479911220_dp, 0.3238258924718810_dp, 0.3232430971181510_dp, 0.3228020667839570_dp, & + & 0.3224773954546620_dp, 0.3222459707975820_dp, 0.3220872129623520_dp, 0.3219832379652560_dp, & + & 0.3219189379639720_dp, 0.3218819733795830_dp, 0.3218626749794920_dp, 0.3218538574825440_dp, & + & 0.3218505497514390_dp, 0.3218496499699270_dp, 0.3218495171641180_dp, 0.3218495068843980_dp, & + & 0.3218493218210410_dp, 0.3218480679905720_dp, 0.3218434587925500_dp, 0.3218311724815020_dp, & + & 0.3218042847919950_dp, 0.3217527939557810_dp, 0.3216632581752280_dp, 0.3215185639244000_dp, & + & 0.3212978414270400_dp, 0.3209765411298020_dp, 0.3205266817097650_dp, 0.3199172758813300_dp, & + & 0.3191149347872370_dp, 0.3180846449622760_dp, 0.3167907037917170_dp, 0.3151977903029890_dp, & + & 0.3132721385145700_dp, 0.3109827711384480_dp, 0.3083027430943870_dp, 0.3052103380467700_dp, & + & 0.3016901579918070_dp, 0.2977340465999210_dp, 0.2933417920291820_dp, 0.2885215643050640_dp, & + & 0.2832900556485000_dp, 0.2776723083923610_dp, 0.2717012330443470_dp, 0.2654168371040700_dp, & + & 0.2588652018739880_dp, 0.2520972583351270_dp, 0.2451674231205630_dp, 0.2381321610618630_dp, & + & 0.2310485415009750_dp, 0.2239728517836210_dp, 0.2169593236835540_dp, 0.2100590178351570_dp, & + & 0.2033188986351250_dp, 0.1967811186289050_dp, 0.1904825181998360_dp, 0.1844543343671890_dp, & + & 0.1787221024237620_dp, 0.1733057265051700_dp, 0.1682196902226420_dp, 0.1634733761809880_dp, & + & 0.1590714632942180_dp, 0.1550143728808850_dp, 0.1512987380645190_dp, 0.1479178754917210_dp, & + & 0.1448622433123750_dp, 0.1421198743143390_dp, 0.1396767777155360_dp, 0.1375173071319790_dp, & + & 0.1356244954882090_dp, 0.1339803600244100_dp, 0.1325661820592860_dp, 0.1313627668183770_dp, & + & 0.1303506885103540_dp, 0.1295105250365150_dp, 0.1288230853904930_dp, 0.1282696311075570_dp, & + & 0.1278320912325840_dp, 0.1274932683819050_dp, 0.1272370317575240_dp, 0.1270484916032760_dp, & + & 0.1269141487087570_dp, 0.1268220122637230_dp, 0.1267616796861550_dp, 0.1267243729756870_dp, & + & 0.1267029276070770_dp, 0.1266917318549620_dp, 0.1266866165747440_dp, 0.1266846976810290_dp, & + & 0.1266841756977190_dp, 0.1266840986541670_dp, 0.1266840926423360_dp, 0.1266839837880770_dp, & + & 0.1266832462857860_dp, 0.1266805351691570_dp, 0.1266733084795670_dp, 0.1266574938173330_dp, & + & 0.1266272098023290_dp, 0.1265745548936650_dp, 0.1264894753918140_dp, 0.1263597236515390_dp, & + & 0.1261709163867620_dp, 0.1259067012168840_dp, 0.1255490370403860_dp, 0.1250785902130360_dp, & + & 0.1244752437221590_dp, 0.1237187105913620_dp, 0.1227892358066640_dp, 0.1216683635190850_dp, & + & 0.1203397387513120_dp, 0.1187899060937670_dp, 0.1170090627987580_dp, 0.1149917211452450_dp, & + & 0.1127372356955830_dp, 0.1102501555718830_dp, 0.1075403702307510_dp, 0.1046230290377890_dp, & + & 0.1015182293910120_dp, 0.0982504839591485_dp, 0.0948479932551365_dp, 0.0913417636404787_dp, & + & 0.0877646214826271_dp, 0.0841501804538112_dp, 0.0805318202845910_dp, 0.0769417316869507_dp, & + & 0.0734100742273824_dp, 0.0699642826987201_dp, 0.0666285443396646_dp, 0.0634234555289268_dp, & + & 0.0603658537270064_dp, 0.0574688096136740_dp, 0.0547417563505448_dp, 0.0521907279960701_dp, & + & 0.0498186771855202_dp, 0.0476258428219083_dp, 0.0456101411213865_dp, 0.0437675573091312_dp, & + & 0.0420925199916553_dp, 0.0405782452088843_dp, 0.0392170419373841_dp, 0.0380005750327896_dp, & + & 0.0369200850699727_dp, 0.0359665672060601_dp, 0.0351309130946618_dp, 0.0344040211017003_dp, & + & 0.0337768807098726_dp, 0.0332406371389453_dp, 0.0327866419401843_dp, 0.0324064947277378_dp, & + & 0.0320920803667448_dp, 0.0318356049195856_dp, 0.0316296325272347_dp, 0.0314671242399100_dp, & + & 0.0313414786790887_dp, 0.0312465733824752_dp, 0.0311768048249021_dp, 0.0311271244797595_dp, & + & 0.0310930679382011_dp, 0.0310707740569711_dp, 0.0310569913640393_dp, 0.0310490694802823_dp, & + & 0.0310449340639991_dp, 0.0310430446770980_dp, 0.0310423359220806_dp, 0.0310421431253545_dp, & + & 0.0310421146690203_dp, 0.0310421124296383_dp, 0.0310420716397388_dp, 0.0310417952831870_dp, & + & 0.0310407793821668_dp, 0.0310380714772549_dp, 0.0310321458732616_dp, 0.0310207998538559_dp, & + & 0.0310010759802921_dp, 0.0309692156102344_dp, 0.0309206487406470_dp, 0.0308500250693697_dp, & + & 0.0307512906198468_dp, 0.0306178132112009_dp, 0.0304425583277848_dp, 0.0302183144462944_dp, & + & 0.0299379636110473_dp, 0.0295947891284527_dp, 0.0291828079525587_dp, 0.0286971110822520_dp, & + & 0.0281341916349547_dp, 0.0274922378212352_dp, 0.0267713674050398_dp, 0.0259737818530539_dp, & + & 0.0251038224556126_dp, 0.0241679171235347_dp, 0.0231744148441990_dp, 0.0221333140973528_dp, & + & 0.0210559008221693_dp, 0.0199543196196075_dp, 0.0188411076812258_dp, 0.0177287236513735_dp, & + & 0.0166291029219323_dp, 0.0155532669520184_dp, 0.0145110078215183_dp, 0.0135106613721021_dp, & + & 0.0125589739850867_dp, 0.0116610601624458_dp, 0.0108204413215560_dp, 0.0100391511855946_dp, & + & 0.0093178903075923_dp, 0.0086562117489777_dp, 0.0080527213972133_dp, 0.0075052790967334_dp, & + & 0.0070111898502319_dp, 0.0065673772931447_dp, 0.0061705343296907_dp, 0.0058172483150401_dp, & + & 0.0055041004554752_dp, 0.0052277409708168_dp, 0.0049849427940245_dp, 0.0047726371240131_dp, & + & 0.0045879341748858_dp, 0.0044281322472202_dp, 0.0042907179729710_dp, 0.0041733603183403_dp, & + & 0.0040739006387440_dp, 0.0039903407420638_dp, 0.0039208305385472_dp, 0.0038636564715162_dp, & + & 0.0038172315611220_dp, 0.0037800875684937_dp, 0.0037508694926061_dp, 0.0037283323472366_dp, & + & 0.0037113399283868_dp, 0.0036988650821286_dp, 0.0036899908311270_dp, 0.0036839116244352_dp, & + & 0.0036799339479146_dp, 0.0036774755732551_dp, 0.0036760628264290_dp, 0.0036753254118835_dp, & + & 0.0036749885191227_dp, 0.0036748621451750_dp, 0.0036748277689824_dp, 0.0036748226951460_dp, & + & 0.0036748222923393_dp, 0.0036748149100632_dp, 0.0036747648944413_dp, 0.0036745810364991_dp, & + & 0.0036740909752027_dp, 0.0036730186732115_dp, 0.0036709657959477_dp, 0.0036673980440014_dp, & + & 0.0036616375616134_dp, 0.0036528626096697_dp, 0.0036401157083574_dp, 0.0036223213706919_dp, & + & 0.0035983143075740_dp, 0.0035668785360485_dp, 0.0035267971347324_dp, 0.0034769114632880_dp, & + & 0.0034161875447865_dp, 0.0033437860995349_dp, 0.0032591315692017_dp, 0.0031619745716256_dp, & + & 0.0030524417833178_dp, 0.0029310674468093_dp, 0.0027988016713820_dp, 0.0026569924679052_dp, & + & 0.0025073409132048_dp, 0.0023518316860276_dp, 0.0021926440028395_dp, 0.0020320501833737_dp, & + & 0.0018723102697820_dp, 0.0017155711580088_dp, 0.0015637777664352_dp, 0.0014186022545886_dp, & + & 0.0012813955118176_dp, 0.0011531630787829_dp, 0.0010345651943950_dp, 0.0009259378833804_dp, & + & 0.0008273295722461_dp, 0.0007385466227205_dp, 0.0006592019354414_dp, 0.0005887628649788_dp, & + & 0.0005265966988475_dp, 0.0004720126924198_dp, 0.0004242991314385_dp, 0.0003827532925982_dp, & + & 0.0003467027006749_dp, 0.0003155178252428_dp, 0.0002886182328297_dp, 0.0002654749688276_dp, & + & 0.0002456112664149_dp, 0.0002286023146780_dp, 0.0002140738237415_dp, 0.0002016990011739_dp, & + & 0.0001911940416264_dp, 0.0001823127530471_dp, 0.0001748411129583_dp, 0.0001685923454460_dp, & + & 0.0001634027584458_dp, 0.0001591283091358_dp, 0.0001556417595481_dp, 0.0001528302992924_dp, & + & 0.0001505935663957_dp, 0.0001488420364666_dp, 0.0001474957623913_dp, 0.0001464834374048_dp, & + & 0.0001457417368087_dp, 0.0001452148775840_dp, 0.0001448543249793_dp, 0.0001446185733087_dp, & + & 0.0001444729322344_dp, 0.0001443892590771_dp, 0.0001443455903853_dp, 0.0001443256415072_dp, & + & 0.0001443181585827_dp, 0.0001443161231052_dp, 0.0001443158226806_dp, 0.0001443157986145_dp, & + & 0.0001443153551719_dp, 0.0001443123507627_dp, 0.0001443013067046_dp, 0.0001442718708446_dp, & + & 0.0001442074691624_dp, 0.0001440842011817_dp, 0.0001438700528027_dp, 0.0001435245109960_dp, & + & 0.0001429986752299_dp, 0.0001422359671892_dp, 0.0001411735387862_dp, 0.0001397444613929_dp, & + & 0.0001378807402972_dp, 0.0001355171288679_dp, 0.0001325956117597_dp, 0.0001290702850767_dp, & + & 0.0001249122032334_dp, 0.0001201136292579_dp, 0.0001146910860612_dp, 0.0001086867306128_dp, & + & 1.0216787521955000e-04_dp, 9.5224870591437098e-05_dp, 8.7967834268454199e-05_dp, 8.0522622710077499e-05_dp, & + & 7.3025928926995193e-05_dp, 6.5618742397077794e-05_dp, 5.8437337344230400e-05_dp, 5.1602133936512500e-05_dp, & + & 4.5206987344670297e-05_dp, 3.9313161032339401e-05_dp, 3.3951463876746897e-05_dp, 2.9132079269800202e-05_dp, & + & 2.4856290551156201e-05_dp, 2.1121789679057201e-05_dp, 1.7917281567747499e-05_dp, 1.5211059185560299e-05_dp, & + & 1.2945018411869599e-05_dp, 1.1043913026753700e-05_dp, 9.4381951427635596e-06_dp, 8.0850086305872503e-06_dp, & + & 6.9710956722701701e-06_dp, 6.0950747169386002e-06_dp, 5.4403720852747003e-06_dp, 4.9601739533500197e-06_dp, & + & 4.5905141448088199e-06_dp, 4.2767538985799496e-06_dp, 3.9894502705806198e-06_dp, 3.7271560273666199e-06_dp, & + & 3.5073823667630698e-06_dp, 3.3454226908702401e-06_dp, 3.2387728197136299e-06_dp, 3.1739073733660899e-06_dp, & + & 3.1393927670819700e-06_dp, 3.1266063160728701e-06_dp, 3.1255951427056099e-06_dp, 3.1266739668467402e-06_dp, & + & 3.1244855378531598e-06_dp, 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0.3479360309982910_dp, & + & 0.3472781552120450_dp, 0.3467579245307350_dp, 0.3463549815650640_dp, 0.3460502033170980_dp, & + & 0.3458259179823030_dp, 0.3456660905237500_dp, 0.3455564689288980_dp, 0.3454846836415650_dp, & + & 0.3454402938965020_dp, 0.3454147764907130_dp, 0.3454014547694230_dp, 0.3453953681165840_dp, & + & 0.3453930848274990_dp, 0.3453924637198330_dp, 0.3453923720457150_dp, 0.3453923649497670_dp, & + & 0.3453922372029790_dp, 0.3453913717009910_dp, 0.3453881900436930_dp, 0.3453797090636780_dp, & + & 0.3453611494085250_dp, 0.3453256083689310_dp, 0.3452638113406150_dp, 0.3451639554432550_dp, & + & 0.3450116577447420_dp, 0.3447900190585000_dp, 0.3444798121454580_dp, 0.3440598000982720_dp, & + & 0.3435071864785970_dp, 0.3427981932856600_dp, 0.3419087560721720_dp, 0.3408153177186290_dp, & + & 0.3394956939998650_dp, 0.3379299758367300_dp, 0.3361014259348560_dp, 0.3339973223858410_dp, & + & 0.3316096997322480_dp, 0.3289359397643070_dp, 0.3259791703443900_dp, 0.3227484407632630_dp, & + & 0.3192586558666410_dp, 0.3155302672529740_dp, 0.3115887366303340_dp, 0.3074638021358990_dp, & + & 0.3031885913649570_dp, 0.2987986336794320_dp, 0.2943308282902350_dp, 0.2898224235156520_dp, & + & 0.2853100570379400_dp, 0.2808288979398770_dp, 0.2764119201278130_dp, 0.2720893248176640_dp, & + & 0.2678881183081360_dp, 0.2638318412356280_dp, 0.2599404374955650_dp, 0.2562302452911570_dp, & + & 0.2527140893269790_dp, 0.2494014517963880_dp, 0.2462987001868480_dp, 0.2434093516452980_dp, & + & 0.2407343562889110_dp, 0.2382723850213680_dp, 0.2360201107825050_dp, 0.2339724754517150_dp, & + & 0.2321229376460680_dp, 0.2304636992689380_dp, 0.2289859107995510_dp, 0.2276798569310610_dp, & + & 0.2265351252714470_dp, 0.2255407614434970_dp, 0.2246854141045420_dp, 0.2239574732086780_dp, & + & 0.2233452043148250_dp, 0.2228368809696450_dp, 0.2224209162336450_dp, 0.2220859933480880_dp, & + & 0.2218211944406720_dp, 0.2216161251221320_dp, 0.2214610319205410_dp, 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0.1995263500212230_dp, & + & 0.1972963352693000_dp, 0.1950290539037880_dp, 0.1927430739182160_dp, 0.1904564886252090_dp, & + & 0.1881865067074740_dp, 0.1859491213742710_dp, 0.1837588647230110_dp, 0.1816286465015220_dp, & + & 0.1795696706948820_dp, 0.1775914191640030_dp, 0.1757016891264200_dp, 0.1739066705050620_dp, & + & 0.1722110497785610_dp, 0.1706181285485190_dp, 0.1691299472046740_dp, 0.1677474064956210_dp, & + & 0.1664703822455070_dp, 0.1652978306872090_dp, 0.1642278837422570_dp, 0.1632579349692160_dp, & + & 0.1623847178058070_dp, 0.1616043782008490_dp, 0.1609125438612150_dp, 0.1603043922163180_dp, & + & 0.1597747189013030_dp, 0.1593180081356990_dp, 0.1589285058706550_dp, 0.1586002960348690_dp, & + & 0.1583273796609750_dp, 0.1581037561469570_dp, 0.1579235054221610_dp, 0.1577808693632720_dp, & + & 0.1576703304590270_dp, 0.1575866854726370_dp, 0.1575251117156710_dp, 0.1574812235426750_dp, & + & 0.1574511168131990_dp, 0.1574313993484040_dp, 0.1574192058259600_dp, 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0.2663349715266320_dp, 0.2619428146605070_dp, 0.2574865446324210_dp, & + & 0.2529979164565650_dp, 0.2485082919980210_dp, 0.2440481069094820_dp, 0.2396464083197860_dp, & + & 0.2353304654083670_dp, 0.2311254513656560_dp, 0.2270541928713780_dp, 0.2231369819516830_dp, & + & 0.2193914446301260_dp, 0.2158324608720650_dp, 0.2124721306769000_dp, 0.2093197816063960_dp, & + & 0.2063820134425070_dp, 0.2036627760057710_dp, 0.2011634764512000_dp, 0.1988831126190080_dp, & + & 0.1968184292864310_dp, 0.1949640944452180_dp, 0.1933128930108980_dp, 0.1918559356146330_dp, & + & 0.1905828803066360_dp, 0.1894821650624860_dp, 0.1885412489107380_dp, 0.1877468592676620_dp, & + & 0.1870852426887310_dp, 0.1865424157508290_dp, 0.1861044122139360_dp, 0.1857575220445180_dp, & + & 0.1854885173876820_dp, 0.1852848602274340_dp, 0.1851348863421760_dp, 0.1850279603001040_dp, & + & 0.1849545966758090_dp, 0.1849065434143570_dp, 0.1848768242967790_dp, 0.1848597387295430_dp, & + & 0.1848508185162170_dp, 0.1848467427953650_dp, 0.1848452138514890_dp, 0.1848447979416580_dp, & + & 0.1848447365542330_dp, 0.1848447317232880_dp, 0.1848446437291930_dp, 0.1848440475564030_dp, & + & 0.1848418559644570_dp, 0.1848360140025560_dp, 0.1848232291009990_dp, 0.1847987448269630_dp, & + & 0.1847561675385950_dp, 0.1846873541929670_dp, 0.1845823684135300_dp, 0.1844295105570030_dp, & + & 0.1842154258639040_dp, 0.1839252927601150_dp, 0.1835430909413060_dp, 0.1830519459966240_dp, & + & 0.1824345440412780_dp, 0.1816736062394990_dp, 0.1807524093901730_dp, 0.1796553351842010_dp, & + & 0.1783684276464830_dp, 0.1768799359967730_dp, 0.1751808190348430_dp, 0.1732651874261180_dp, & + & 0.1711306620745750_dp, 0.1687786300791460_dp, 0.1662143843957440_dp, 0.1634471389003380_dp, & + & 0.1604899166512580_dp, 0.1573593152813970_dp, 0.1540751591998560_dp, 0.1506600532933580_dp, & + & 0.1471388568570190_dp, 0.1435380994123320_dp, 0.1398853618276950_dp, 0.1362086467393550_dp, & + & 0.1325357617022220_dp, 0.1288937368743030_dp, 0.1253082964094790_dp, 0.1218033992605850_dp, & + & 0.1184008608891030_dp, 0.1151200627142760_dp, 0.1119777513102700_dp, 0.1089879248025410_dp, & + & 0.1061617999885410_dp, 0.1035078506825610_dp, 0.1010319057828040_dp, 0.0987372945827047_dp, & + & 0.0966250267935465_dp, 0.0946939955383712_dp, 0.0929411930354789_dp, 0.0913619305971309_dp, & + & 0.0899500567052911_dp, 0.0886981690039548_dp, 0.0875978179024273_dp, 0.0866397010158906_dp, & + & 0.0858138487283355_dp, 0.0851098018637160_dp, 0.0845167826578148_dp, 0.0840238600962024_dp, & + & 0.0836201101985168_dp, 0.0832947710996237_dp, 0.0830373919705991_dp, 0.0828379738740921_dp, & + & 0.0826870999274973_dp, 0.0825760515051499_dp, 0.0824969068405608_dp, 0.0824426183910134_dp, & + & 0.0824070655467040_dp, 0.0823850799016412_dp, 0.0823724411645870_dp, 0.0823658428436644_dp, & + & 0.0823628280717372_dp, 0.0823616971353189_dp, 0.0823613894944941_dp, 0.0823613440865714_dp, & + & 0.0823613404819881_dp, 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32.9891618572179013_dp, & + & 32.8198829733952024_dp, 32.6330101715953020_dp, 32.4288604738031978_dp, 32.2080547875206022_dp, & + & 31.9715118870667006_dp, 31.7204328882415005_dp, 31.4562768255174987_dp, 31.1807283840683986_dp, & + & 30.8956592253042999_dp, 30.6030846457916006_dp, 30.3051174997621011_dp, 30.0039213750346008_dp, & + & 29.7016649316171986_dp, 29.4004790967798009_dp, 29.1024184822523999_dp, 28.8094279862282008_dp, & + & 28.5233151129264009_dp, 28.2457281351695997_dp, 27.9781398829841983_dp, 27.7218366915215988_dp, & + & 27.4779118947648016_dp, 27.2472632008907993_dp, 27.0305933116414998_dp, 26.8284132260277985_dp, & + & 26.6410477721234003_dp, 26.4686430176465990_dp, 26.3111753050548991_dp, 26.1684617313724992_dp, & + & 26.0401719440612993_dp, 25.9258411529071005_dp, 25.8248842671007992_dp, 25.7366110600242983_dp, & + & 25.6602422450303997_dp, 25.5949263165771015_dp, 25.5397569749470001_dp, 25.4937909118910007_dp, & + & 25.4560656915972991_dp, 25.4256174195424016_dp, 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34.9835779423550974_dp, 34.7504061111864999_dp, 34.4981920820505010_dp, & + & 34.2279735732165022_dp, 33.9411062958030030_dp, 33.6392354172563017_dp, 33.3242584583958035_dp, & + & 32.9982814636795965_dp, 32.6635705813319035_dp, 32.3225013129234000_dp, 31.9775076300235988_dp, & + & 31.6310329221163009_dp, 31.2854843726005996_dp, 30.9431919141118996_dp, 30.6063724541164000_dp, & + & 30.2770996455105994_dp, 29.9572791477155995_dp, 29.6486291019309007_dp, 29.3526654272246006_dp, & + & 29.0706915115016002_dp, 28.8037918932907999_dp, 28.5528295767093994_dp, 28.3184466696570993_dp, & + & 28.1010680711117011_dp, 27.9009079538938991_dp, 27.7179787976956007_dp, 27.5521027294959993_dp, & + & 27.4029249300503999_dp, 27.2699288685963985_dp, 27.1524531329026999_dp, 27.0497096256413982_dp, & + & 26.9608028972260989_dp, 26.8847503765647993_dp, 26.8205032428667991_dp, 26.7669676538634995_dp, & + & 26.7230260106478994_dp, 26.6875579005802983_dp, 26.6594603223152014_dp, 26.6376667665128011_dp, & + & 26.6211647076940991_dp, 26.6090110618080011_dp, 26.6003451839936993_dp, 26.5943990237154004_dp, & + & 26.5905041199867007_dp, 26.5880952058844002_dp, 26.5867102952363012_dp, 26.5859872400346013_dp, & + & 26.5856568685349011_dp, 26.5855329345198008_dp, 26.5854992214382015_dp, 26.5854942454570988_dp, & + & 26.5854938686908007_dp, 26.5854871943136999_dp, 26.5854419744239010_dp, 26.5852757412813006_dp, & + & 26.5848326244151991_dp, 26.5838628722639996_dp, 26.5820056742605999_dp, 26.5787759706324991_dp, & + & 26.5735558553190998_dp, 26.5655910823648007_dp, 26.5539930755687017_dp, 26.5377467117493993_dp, & + & 26.5157239962747013_dp, 26.4867035729625009_dp, 26.4493958085970000_dp, 26.4024729677616996_dp, & + & 26.3446037531725992_dp, 26.2744912413401011_dp, 26.1909130086303996_dp, 26.0927620373533991_dp, & + & 25.9790868355747016_dp, 25.8491291172217998_dp, 25.7023573863293002_dp, 25.5384948604821993_dp, & + & 25.3575403555234011_dp, 25.1597810303921996_dp, 24.9457962447724988_dp, 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0.1072308323506660_dp, 0.1061185095046260_dp, 0.1051713909377840_dp, 0.1043744542161850_dp, & + & 0.1037126073300100_dp, 0.1031708814090280_dp, 0.1027346173850530_dp, 0.1023896460530690_dp, & + & 0.1021224595650240_dp, 0.1019203711053220_dp, 0.1017716584737230_dp, 0.1016656866526940_dp, & + & 0.1015930042344730_dp, 0.1015454088597210_dp, 0.1015159775627270_dp, 0.1014990590679900_dp, & + & 0.1014902265470000_dp, 0.1014861909997650_dp, 0.1014846771436170_dp, 0.1014842653396220_dp, & + & 0.1014842045582610_dp, 0.1014841997750580_dp, 0.1014841126497290_dp, 0.1014835223639210_dp, & + & 0.1014813524253670_dp, 0.1014755682774360_dp, 0.1014629103773220_dp, 0.1014386711539000_dp, & + & 0.1013965257307630_dp, 0.1013284257544740_dp, 0.1012245649866660_dp, 0.1010734243645710_dp, & + & 0.1008619028389010_dp, 0.1005755382763740_dp, 0.1001988199117530_dp, 0.0997155901549434_dp, & + & 0.0991095290072082_dp, 0.0983647090486528_dp, 0.0974662032118232_dp, 0.0964007217831977_dp, & + & 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39.6764888355327017_dp, & + & 39.4529687603532011_dp, 39.2062126506006976_dp, 38.9366239595499977_dp, 38.6449991040912977_dp, & + & 38.3325183064668025_dp, 38.0007246854992999_dp, 37.6514927631220004_dp, 37.2869880421188995_dp, & + & 36.9096196331684965_dp, 36.5219880441523017_dp, 36.1268302048794965_dp, 35.7269636279001972_dp, & + & 35.3252313610789983_dp, 34.9244491309245007_dp, 34.5273558507088012_dp, 34.1365684880039026_dp, & + & 33.7545421361204987_dp, 33.3835359784836996_dp, 33.0255856410250033_dp, 32.6824821817611024_dp, & + & 32.3557576837475978_dp, 32.0466771354166013_dp, 31.7562360462662987_dp, 31.4851630909972009_dp, & + & 31.2339270149307993_dp, 31.0027470584946983_dp, 30.7916062436367994_dp, 30.6002669798647986_dp, & + & 30.4282885653184003_dp, 30.2750462600869987_dp, 30.1397516847837004_dp, 30.0214743439496985_dp, & + & 29.9191640922623989_dp, 29.8316743550983006_dp, 29.7577858881446993_dp, 29.6962308184113013_dp, & + & 29.6457166566047015_dp, 29.6049499143993984_dp, 29.5726589060921015_dp, 29.5476152691130984_dp, & + & 29.5286537082807001_dp, 29.5146894601062009_dp, 29.5047329901100994_dp, 29.4979014803162016_dp, & + & 29.4934267359849009_dp, 29.4906592380014985_dp, 29.4890681857477013_dp, 29.4882375085215998_dp, & + & 29.4878579641943013_dp, 29.4877155838452012_dp, 29.4876768529220996_dp, 29.4876711363184008_dp, & + & 29.4876707034744996_dp, 29.4876630356866016_dp, 29.4876110852973987_dp, 29.4874201102015014_dp, & + & 29.4869110409443991_dp, 29.4857969565047000_dp, 29.4836633560372015_dp, 29.4799530210514007_dp, & + & 29.4739561712535014_dp, 29.4648065110872999_dp, 29.4514836395875008_dp, 29.4328221490091018_dp, & + & 29.4075275630987996_dp, 29.3741990602178014_dp, 29.3313586887051017_dp, 29.2774865147028009_dp, & + & 29.2110608540534002_dp, 29.1306024434210009_dp, 29.0347211207698983_dp, 28.9221633357004002_dp, & + & 28.7918586225265010_dp, 28.6429630696989008_dp, 28.4748978304476985_dp, 28.2873808552905999_dp, & + & 28.0804502891259986_dp, 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0.7202788843696770_dp, 0.7200039288439229_dp, & + & 0.7198238598697630_dp, 0.7197125048276261_dp, 0.7196484903687830_dp, 0.7196150701058740_dp, & + & 0.7195998003522990_dp, 0.7195940721794610_dp, 0.7195925139812400_dp, 0.7195922839945870_dp, & + & 0.7195922663275240_dp, 0.7195919500129550_dp, 0.7195898069375770_dp, 0.7195819287980210_dp, & + & 0.7195609288190919_dp, 0.7195149721405020_dp, 0.7194269644370760_dp, 0.7192739334261660_dp, & + & 0.7190266352199470_dp, 0.7186494142225540_dp, 0.7181003410816940_dp, 0.7173316475991810_dp, & + & 0.7162904699719090_dp, 0.7149199018309100_dp, 0.7131603460262710_dp, 0.7109511390482910_dp, & + & 0.7082324048934940_dp, 0.7049470771032990_dp, 0.7010430101484389_dp, 0.6964750862399000_dp, & + & 0.6912072131602121_dp, 0.6852141048618420_dp, 0.6784827409590261_dp, 0.6710134145996850_dp, & + & 0.6628203002098730_dp, 0.6539315017053871_dp, 0.6443885753034380_dp, 0.6342455555997190_dp, & + & 0.6235675453906990_dp, 0.6124289554212080_dp, 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0.2589265075614830_dp, 0.2510675458363490_dp, & + & 0.2433809229266050_dp, 0.2359149194638950_dp, 0.2287120574866460_dp, 0.2218087339528130_dp, & + & 0.2152350630975520_dp, 0.2090149042151950_dp, 0.2031660458695090_dp, 0.1977005146084140_dp, & + & 0.1926249757929670_dp, 0.1879411957870190_dp, 0.1836465380293650_dp, 0.1797344699074590_dp, & + & 0.1761950623561010_dp, 0.1730154692499470_dp, 0.1701803785508960_dp, 0.1676724315076260_dp, & + & 0.1654726097731190_dp, 0.1635605929811280_dp, 0.1619150910509430_dp, 0.1605141562903610_dp, & + & 0.1593354803015360_dp, 0.1583566798785090_dp, 0.1575555746705390_dp, 0.1569104575478660_dp, & + & 0.1564003565515860_dp, 0.1560052852466920_dp, 0.1557064764360380_dp, 0.1554865927244860_dp, & + & 0.1553299065016060_dp, 0.1552224416461030_dp, 0.1551520696905160_dp, 0.1551085543031120_dp, & + & 0.1550835396592450_dp, 0.1550704804520960_dp, 0.1550645137503470_dp, 0.1550622754600400_dp, & + & 0.1550616665932270_dp, 0.1550615767258560_dp, 0.1550615697133540_dp, 0.1550614427404180_dp, & + & 0.1550605824814400_dp, 0.1550574200994820_dp, 0.1550489905113470_dp, 0.1550305433816280_dp, & + & 0.1549952180547220_dp, 0.1549337968204870_dp, 0.1548345501052070_dp, 0.1546831861770530_dp, & + & 0.1544629165515090_dp, 0.1541546462295860_dp, 0.1537372949294140_dp, 0.1531882513524320_dp, & + & 0.1524839571189890_dp, 0.1516006103228590_dp, 0.1505149708974330_dp, 0.1492052415908920_dp, & + & 0.1476519899655100_dp, 0.1458390693202180_dp, 0.1437544907358020_dp, 0.1413911955188920_dp, & + & 0.1387476779833320_dp, 0.1358284132821410_dp, 0.1326440539992430_dp, 0.1292113720484740_dp, & + & 0.1255529382107880_dp, 0.1216965490466180_dp, 0.1176744283100390_dp, 0.1135222456428120_dp, & + & 0.1092780076362770_dp, 0.1049808840710260_dp, 0.1006700345472350_dp, 0.0963834976942195_dp, & + & 0.0921571972096586_dp, 0.0880241071807006_dp, 0.0840136049065023_dp, 0.0801510243586563_dp, & + & 0.0764574090011365_dp, 0.0729494502098902_dp, 0.0696395878642306_dp, 0.0665362432763317_dp, & + & 0.0636441515163710_dp, 0.0609647600667387_dp, 0.0584966630461281_dp, 0.0562360442907845_dp, & + & 0.0541771076634490_dp, 0.0523124784312188_dp, 0.0506335648994707_dp, 0.0491308743355745_dp, & + & 0.0477942813402450_dp, 0.0466132501148877_dp, 0.0455770145160699_dp, 0.0446747214286205_dp, & + & 0.0438955439136919_dp, 0.0432287708930374_dp, 0.0426638799276589_dp, 0.0421905990295102_dp, & + & 0.0417989625082100_dp, 0.0414793646821749_dp, 0.0412226139653313_dp, 0.0410199884607749_dp, & + & 0.0408632928423600_dp, 0.0407449150737875_dp, 0.0406578804906559_dp, 0.0405959000284639_dp, & + & 0.0405534089751711_dp, 0.0405255925923171_dp, 0.0405083952793461_dp, 0.0404985106149525_dp, & + & 0.0404933505334952_dp, 0.0404909929875998_dp, 0.0404901086130565_dp, 0.0404898680438492_dp, & + & 0.0404898325364229_dp, 0.0404898297421283_dp, 0.0404897788450285_dp, 0.0404894340107660_dp, & + & 0.0404881663808823_dp, 0.0404847874783485_dp, 0.0404773935090645_dp, 0.0404632357643919_dp, & + & 0.0404386234350511_dp, 0.0403988651297453_dp, 0.0403382553124629_dp, 0.0402501115735134_dp, & + & 0.0401268679518978_dp, 0.0399602282213039_dp, 0.0397413809638465_dp, 0.0394612752672714_dp, & + & 0.0391109519836874_dp, 0.0386819208252263_dp, 0.0381665684572567_dp, 0.0375585776754406_dp, & + & 0.0368533333578398_dp, 0.0360482878823234_dp, 0.0351432577872970_dp, 0.0341406251735492_dp, & + & 0.0330454219662784_dp, 0.0318652825708057_dp, 0.0306102601260676_dp, 0.0292925125470305_dp, & + & 0.0279258756182941_dp, 0.0265253502039542_dp, 0.0251065379319186_dp, 0.0236850635609471_dp, & + & 0.0222760221956833_dp, 0.0208934856701575_dp, 0.0195500953922760_dp, 0.0182567597524326_dp, & + & 0.0170224641059775_dp, 0.0158541916130588_dp, 0.0147569449363232_dp, 0.0137338526869542_dp, & + & 0.0127863408754365_dp, 0.0119143483862700_dp, 0.0111165663063275_dp, 0.0103906832853369_dp, & + & 0.0097336224474560_dp, 0.0091417591574725_dp, 0.0086111126991710_dp, 0.0081375082761213_dp, & + & 0.0077167084780996_dp, 0.0073445154012859_dp, 0.0070168460051434_dp, 0.0067297841351177_dp, & + & 0.0064796130461531_dp, 0.0062628323287583_dp, 0.0060761629643906_dp, 0.0059165438999287_dp, & + & 0.0057811231054217_dp, 0.0056672456178433_dp, 0.0055724406055475_dp, 0.0054944090331048_dp, & + & 0.0054310130667972_dp, 0.0053802679421580_dp, 0.0053403366191986_dp, 0.0053095271849202_dp, & + & 0.0052862926377770_dp, 0.0052692324163246_dp, 0.0052570948298154_dp, 0.0052487794242353_dp, & + & 0.0052433382809909_dp, 0.0052399753012935_dp, 0.0052380426663632_dp, 0.0052370338726462_dp, & + & 0.0052365729957700_dp, 0.0052364001129064_dp, 0.0052363530853512_dp, 0.0052363461442013_dp, & + & 0.0052363455931470_dp, 0.0052363354940326_dp, 0.0052362670715809_dp, 0.0052360155495279_dp, & + & 0.0052353451314673_dp, 0.0052338781783163_dp, 0.0052310697084152_dp, 0.0052261886364704_dp, & + & 0.0052183072562144_dp, 0.0052063005509524_dp, 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0.0627082538526338_dp, 0.0626910051890803_dp, & + & 0.0626803372495885_dp, 0.0626742041321648_dp, 0.0626710020598011_dp, 0.0626695389990886_dp, & + & 0.0626689901533268_dp, 0.0626688408538598_dp, 0.0626688188175564_dp, 0.0626688170520424_dp, & + & 0.0626687844948464_dp, 0.0626685639151816_dp, 0.0626677530410973_dp, 0.0626655915499015_dp, & + & 0.0626608611863020_dp, 0.0626518020010565_dp, 0.0626360480865173_dp, 0.0626105858011243_dp, & + & 0.0625717370276817_dp, 0.0625151694888046_dp, 0.0624359355302033_dp, 0.0623285400585729_dp, & + & 0.0621870374775852_dp, 0.0620051564963831_dp, 0.0617764506018403_dp, 0.0614944708200653_dp, & + & 0.0611529561864046_dp, 0.0607460361648293_dp, 0.0602684381811684_dp, 0.0597156925483091_dp, & + & 0.0590843264527479_dp, 0.0583720384197761_dp, 0.0575778448489928_dp, 0.0567021908559155_dp, & + & 0.0557470187868887_dp, 0.0547157893799550_dp, 0.0536134525690812_dp, 0.0524463672855546_dp, & + & 0.0512221721700143_dp, 0.0499496117081435_dp, 0.0486383247578885_dp, 0.0472986045478763_dp, & + & 0.0459411408082531_dp, 0.0445767555920895_dp, 0.0432161444576593_dp, 0.0418696339868490_dp, & + & 0.0405469651688293_dp, 0.0392571101243533_dp, 0.0380081271855772_dp, 0.0368070567214289_dp, & + & 0.0356598575514511_dp, 0.0345713815370630_dp, 0.0335453821419662_dp, 0.0325845515104959_dp, & + & 0.0316905799535476_dp, 0.0308642316220897_dp, 0.0301054305066657_dp, 0.0294133516127175_dp, & + & 0.0287865131012950_dp, 0.0282228662268267_dp, 0.0277198809443178_dp, 0.0272746260086478_dp, & + & 0.0268838431912855_dp, 0.0265440158545687_dp, 0.0262514325383734_dp, 0.0260022464296412_dp, & + & 0.0257925316175545_dp, 0.0256183369160112_dp, 0.0254757377905435_dp, 0.0253608866004242_dp, & + & 0.0252700609964194_dp, 0.0251997099439478_dp, 0.0251464965063377_dp, 0.0251073362601346_dp, & + & 0.0250794300498143_dp, 0.0250602897426688_dp, 0.0250477557223121_dp, 0.0250400050573631_dp, & + & 0.0250355495861783_dp, 0.0250332235422945_dp, 0.0250321607795740_dp, 0.0250317621047600_dp, & + & 0.0250316536559581_dp, 0.0250316376491497_dp, 0.0250316363546261_dp, 0.0250316123321284_dp, & + & 0.0250314495764030_dp, 0.0250308512733426_dp, 0.0250292564488888_dp, 0.0250257663761175_dp, & + & 0.0250190830882673_dp, 0.0250074627319776_dp, 0.0249886863491184_dp, 0.0249600504929361_dp, & + & 0.0249183798258912_dp, 0.0248600634630805_dp, 0.0247811162676896_dp, 0.0246772655244882_dp, & + & 0.0245440623908877_dp, 0.0243770162477404_dp, 0.0241717485822619_dp, 0.0239241614089138_dp, & + & 0.0236306135887929_dp, 0.0232880969011120_dp, 0.0228944025285358_dp, 0.0224482679304714_dp, & + & 0.0219494940627527_dp, 0.0213990236831165_dp, 0.0207989731236893_dp, 0.0201526123739768_dp, & + & 0.0194642914794656_dp, 0.0187393148812021_dp, 0.0179837690931350_dp, 0.0172043126698327_dp, & + & 0.0164079403829760_dp, 0.0156017355750038_dp, 0.0147926255529711_dp, 0.0139871545193984_dp, & + & 0.0131912869670288_dp, 0.0124102518774976_dp, 0.0116484347664567_dp, 0.0109093209468796_dp, & + & 0.0101954896834684_dp, 0.0095086554800474_dp, 0.0088497498386460_dp, 0.0082190346360136_dp, & + & 0.0076162368991390_dp, 0.0070406942338934_dp, 0.0064915004124373_dp, 0.0059676415473149_dp, & + & 0.0054681147693003_dp, 0.0049920232759604_dp, 0.0045386439063435_dp, 0.0041074658433900_dp, & + & 0.0036982014251947_dp, 0.0033107721221199_dp, 0.0029452743180514_dp, 0.0026019305077227_dp, & + & 0.0022810318696571_dp, 0.0019828779415860_dp, 0.0017077184239867_dp, 0.0014557011051011_dp, & + & 0.0012268286975967_dp, 0.0010209261605496_dp, 0.0008376189856136_dp, 0.0006763220480366_dp, & + & 0.0005362380141491_dp, 0.0004163639536330_dp, 0.0003155047008647_dp, 0.0002322915842257_dp, & + & 1.6520533675645801e-04_dp, 1.1260226074227801e-04_dp, 7.2743001339858906e-05_dp, 4.3823576064028202e-05_dp, & + & 2.4008617486970299e-05_dp, 1.1467179859892000e-05_dp, 4.4120893676335999e-06_dp, 1.1451217716285100e-06_dp, & + & -1.4210854715202001e-14_dp & + &] 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87.6100224243112962_dp, 87.6099562360700048_dp, 87.6097129208946939_dp, & + & 87.6090643304428056_dp, 87.6076448983494060_dp, 87.6049264863681003_dp, 87.6001990521144052_dp, & + & 87.5925580117122990_dp, 87.5808990263997060_dp, 87.5639207755490929_dp, 87.5401360856364050_dp, & + & 87.5078915611919967_dp, 87.4653956064004063_dp, 87.4107544338397986_dp, 87.3420153327977999_dp, & + & 87.2572161218816973_dp, 87.1544393541911973_dp, 87.0318695009309948_dp, 86.8878510421934038_dp, & + & 86.7209451802559954_dp, 86.5299828030825040_dp, 86.3141114012422008_dp, 86.0728339011080976_dp, & + & 85.8060378116412039_dp, 85.5140136417549996_dp, 85.1974621414034061_dp, 84.8574904425847052_dp, & + & 84.4955975323827033_dp, 84.1136496457154976_dp, 83.7138461825692985_dp, 83.2986767882845953_dp, & + & 82.8708704763790962_dp, 82.4333382383852040_dp, 81.9891114043757057_dp, 81.5412787985277987_dp, & + & 81.0929260705036938_dp, 80.6470801897547034_dp, 80.2066610110741038_dp, 79.7744404470203960_dp, & + & 79.3530086353429027_dp, 78.9447459203418020_dp, 78.5517995079288056_dp, 78.1760640780448028_dp, & + & 77.8191661437940070_dp, 77.4824523162658068_dp, 77.1669817883335014_dp, 76.8735233189423042_dp, & + & 76.6025568585077963_dp, 76.3542797817012939_dp, 76.1286175367300046_dp, 75.9252384027657001_dp, & + & 75.7435719710992004_dp, 75.5828309212766953_dp, 75.4420356377563053_dp, 75.3200411936494021_dp, & + & 75.2155662075835068_dp, 75.1272230534614067_dp, 75.0535488704324933_dp, 74.9930367842166987_dp, & + & 74.9441667155301019_dp, 74.9054351224286989_dp, 74.8753830069232009_dp, 74.8526215179029037_dp, & + & 74.8358545068999064_dp, 74.8238974437000053_dp, 74.8156921765175014_dp, 74.8103171255687016_dp, & + & 74.8069926264246021_dp, 74.8050812856096030_dp, 74.8040833691027984_dp, 74.8036274072485980_dp, & + & 74.8034563593159021_dp, 74.8034098300459931_dp, 74.8034029624201935_dp, 74.8034023561395003_dp, & + & 74.8033904763689037_dp, 74.8033099891618036_dp, 74.8030141094805998_dp, 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63.4955983916268991_dp, 63.0773353304567976_dp, & + & 62.6836218062059984_dp, 62.3155582664043024_dp, 61.9738954841842968_dp, 61.6590442499651985_dp, & + & 61.3710895595816979_dp, 61.1098086789647965_dp, 60.8746925582347984_dp, 60.6649701538527992_dp, & + & 60.4796352811680009_dp, 60.3174756544179971_dp, 60.1771037762296004_dp, 60.0569893170114995_dp, & + & 59.9554925814830000_dp, 59.8708986012566982_dp, 59.8014513258957976_dp, 59.7453873177411978_dp, & + & 59.7009682958914993_dp, 59.6665118298608022_dp, 59.6404194609209028_dp, 59.6212015351490976_dp, & + & 59.6074980711729978_dp, 59.5980950596633008_dp, 59.5919357002550996_dp, 59.5881262214911018_dp, & + & 59.5859360946756027_dp, 59.5847926352002020_dp, 59.5842701754906017_dp, 59.5840741822286972_dp, & + & 59.5840208672538978_dp, 59.5840129980732982_dp, 59.5840123668676966_dp, 59.5840007179224003_dp, & + & 59.5839217946002009_dp, 59.5836316640641996_dp, 59.5828582821555983_dp, 59.5811657526262977_dp, & + & 59.5779243479005984_dp, 59.5722874922174981_dp, 59.5631767658572997_dp, 59.5492758239739999_dp, & + & 59.5290339309776968_dp, 59.5006795853179966_dp, 59.4622444434710005_dp, 59.4115974410597971_dp, & + & 59.3464886520872028_dp, 59.2646020286628996_dp, 59.1636157351810965_dp, 59.0412683528520006_dp, & + & 58.8954288113181974_dp, 58.7241675392078974_dp, 58.5258260542342015_dp, 58.2990820746593030_dp, & + & 58.0430072601929012_dp, 57.7571149017173013_dp, 57.4413952771520968_dp, 57.0963369542443999_dp, & + & 56.7229330061134007_dp, 56.3226718500770005_dp, 55.8975131554880988_dp, 55.4498499301543006_dp, & + & 54.9824584462191979_dp, 54.4984380910556965_dp, 54.0011435349940996_dp, 53.4941118119252010_dp, & + & 52.9809870188240026_dp, 52.4654453462111974_dp, 51.9511230300109972_dp, 51.4415495443966009_dp, & + & 50.9400879334031984_dp, 50.4498836360460032_dp, 49.9738225547369979_dp, 49.5144985250079017_dp, & + & 49.0741898371655978_dp, 48.6548440876697015_dp, 48.2580704196734018_dp, 47.8851381386403006_dp, & + & 47.5369807292032007_dp, 47.2142044126529967_dp, 46.9171005307822000_dp, 46.6456611895767992_dp, & + & 46.3995977248299027_dp, 46.1783616508210031_dp, 45.9811678200864975_dp, 45.8070195587063012_dp, & + & 45.6547355510012025_dp, 45.5229782339078994_dp, 45.4102834282086008_dp, 45.3150908848380993_dp, & + & 45.2357753636905997_dp, 45.1706777945889968_dp, 45.1181360012707984_dp, 45.0765144062431986_dp, & + & 45.0442320845098010_dp, 45.0197885047258026_dp, 45.0017862936814979_dp, 44.9889503889459021_dp, & + & 44.9801430076012991_dp, 44.9743739561724993_dp, 44.9708059352284977_dp, 44.9687546461275005_dp, & + & 44.9676836792524028_dp, 44.9671943435635981_dp, 44.9670107765167018_dp, 44.9669608417974018_dp, & + & 44.9669534715363000_dp, 44.9669529030707977_dp, 44.9669426952559022_dp, 44.9668735358084035_dp, & + & 44.9666192983712989_dp, 44.9659415947670027_dp, 44.9644584573064989_dp, 44.9616180727930015_dp, & + & 44.9566786238845992_dp, 44.9486951708438980_dp, 44.9365143639962028_dp, 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2.6001207231729499e-06_dp, 2.3376768183425199e-06_dp, & + & 1.7815207655758101e-06_dp, 1.0730115747037399e-06_dp, 1.4210854715202001e-14_dp, 5.3843007208342897e-07_dp, & + & 6.6701876733077402e-07_dp, 6.2314985882494501e-07_dp, 5.2431524011353801e-07_dp, 4.3734611665513501e-07_dp, & + & 3.8817508141164602e-07_dp, 1.4210854715202001e-14_dp, 1.4210854715202001e-14_dp, 2.8421709430404001e-14_dp, & + & 1.4210854715202001e-14_dp, 1.4210854715202001e-14_dp, 1.4210854715202001e-14_dp, 1.4210854715202001e-14_dp, & + & 1.4210854715202001e-14_dp, 1.4210854715202001e-14_dp, 1.4210854715202001e-14_dp, 1.4210854715202001e-14_dp, & + & 1.4210854715202001e-14_dp, 1.4210854715202001e-14_dp, 1.4210854715202001e-14_dp, 1.4210854715202001e-14_dp, & + & 2.8421709430404001e-14_dp & + &] + case (101) + out = [& + & 101.0000000000000000_dp, 100.9999998732159980_dp, 100.9999959527920055_dp, 100.9999693912990040_dp, & + & 100.9998717477400021_dp, 100.9996114604820008_dp, 100.9990418008789987_dp, 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47.4515451919387985_dp, 47.3121368689674995_dp, & + & 47.1484770545551015_dp, 46.9590070701171030_dp, 46.7424971551397022_dp, 46.4981024851740017_dp, & + & 46.2254093274138995_dp, 45.9244689992152999_dp, 45.5958177960520032_dp, 45.2404816890769013_dp, & + & 44.8599653238673994_dp, 44.4562256407468013_dp, 44.0316312380687975_dp, 43.5889093600872002_dp, & + & 43.1310830460111987_dp, 42.6614014521435010_dp, 42.1832665832047979_dp, 41.7001595985120019_dp, & + & 41.2155695041319987_dp, 40.7329264789755996_dp, 40.2555414341819997_dp, 39.7865528001070032_dp, & + & 39.3288810629744034_dp, 38.8851912578777004_dp, 38.4578634320068034_dp, 38.0489709595616006_dp, & + & 37.6602664626935990_dp, 37.2931749447992971_dp, 36.9487935791174991_dp, 36.6278974426876971_dp, & + & 36.3309503732501966_dp, 36.0581200756704021_dp, 35.8092966210654993_dp, 35.5841135576107988_dp, & + & 35.3819709686301991_dp, 35.2020599484721970_dp, 35.0433880982007011_dp, 34.9048057539195966_dp, & + & 34.7850327391434035_dp, 34.6826854736375978_dp, 34.5963042745984026_dp, 34.5243806562503011_dp, & + & 34.4653843784331997_dp, 34.4177899231135029_dp, 34.3801020007073035_dp, 34.3508796165900989_dp, & + & 34.3287581725156983_dp, 34.3124690467816009_dp, 34.3008560976302022_dp, 34.2928885705482003_dp, & + & 34.2876699626906003_dp, 34.2844425042109009_dp, 34.2825870513950974_dp, 34.2816183422568983_dp, & + & 34.2811757320664015_dp, 34.2810096938676026_dp, 34.2809645274672974_dp, 34.2809578610018022_dp, & + & 34.2809573562371028_dp, 34.2809484143822019_dp, 34.2808878320171004_dp, 34.2806651250949983_dp, & + & 34.2800714722091016_dp, 34.2787722875456993_dp, 34.2762842324189023_dp, 34.2719576055261967_dp, & + & 34.2649649535172998_dp, 34.2542966281231003_dp, 34.2387638786671005_dp, 34.2170099022699006_dp, & + & 34.1875290711443967_dp, 34.1486943111632968_dp, 34.0987923158392974_dp, 34.0360659475772991_dp, & + & 33.9587628127721004_dp, 33.8651886155845006_dp, 33.7537635208828988_dp, 33.6230794197426022_dp, & + & 33.4719557246815995_dp, 33.2994911606489978_dp, 33.1051089925517985_dp, 32.8885932644448005_dp, & + & 32.6501139321041975_dp, 32.3902392483123975_dp, 32.1099343914538977_dp, 31.8105460785004013_dp, & + & 31.4937737217974991_dp, 31.1616285091629983_dp, 30.8163825325368990_dp, 30.4605106835252002_dp, & + & 30.0966284053269000_dp, 29.7274284920129013_dp, 29.3556199433761016_dp, 28.9838714418834016_dp, & + & 28.6147613816125990_dp, 28.2507356399004017_dp, 27.8940735443847991_dp, 27.5468618456823009_dp, & + & 27.2109760268868008_dp, 26.8880679960719995_dp, 26.5795591098337987_dp, 26.2866375274809982_dp, & + & 26.0102590432829004_dp, 25.7511507329279006_dp, 25.5098169347971009_dp, 25.2865472380346006_dp, & + & 25.0814262561721009_dp, 24.8943450293375008_dp, 24.7250139297434011_dp, 24.5729769561615008_dp, & + & 24.4376273032975995_dp, 24.3182240871504014_dp, 24.2139100992767986_dp, 24.1237304502617995_dp, & + & 24.0466519433501986_dp, 23.9815829912899012_dp, 23.9273938525476986_dp, 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0.3770352395466570_dp, & + & 0.3768495302081900_dp, 0.3765791882360220_dp, 0.3762006576332060_dp, 0.3756878421549890_dp, & + & 0.3750126076091790_dp, 0.3741454271250720_dp, 0.3730561571611450_dp, 0.3717149244235570_dp, & + & 0.3700930958733720_dp, 0.3681642962364720_dp, 0.3659054306847340_dp, 0.3632976655021450_dp, & + & 0.3603273174131090_dp, 0.3569866034946900_dp, 0.3532742085615150_dp, 0.3491956355344430_dp, & + & 0.3447633160488830_dp, 0.3399964724681300_dp, 0.3349207372720000_dp, 0.3295675500910700_dp, & + & 0.3239733651211760_dp, 0.3181787112111610_dp, 0.3122271528782930_dp, 0.3061642026195700_dp, & + & 0.3000362333259400_dp, 0.2938894349049260_dp, 0.2877688521594310_dp, 0.2817175324678800_dp, & + & 0.2757758027407820_dp, 0.2699806862529500_dp, 0.2643654618383660_dp, 0.2589593609927480_dp, & + & 0.2537873929117470_dp, 0.2488702835354250_dp, 0.2442245122555850_dp, 0.2398624289471630_dp, & + & 0.2357924341683880_dp, 0.2320192064847930_dp, 0.2285439626514720_dp, 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0.0981639011601345_dp, & + & 0.0972064282615293_dp, 0.0963821228873627_dp, 0.0956801048871512_dp, 0.0950892923613793_dp, & + & 0.0945985448318538_dp, 0.0941968037951000_dp, 0.0938732306031511_dp, 0.0936173406500416_dp, & + & 0.0934191318944073_dp, 0.0932692049102712_dp, 0.0931588710138556_dp, 0.0930802446346064_dp, & + & 0.0930263160359885_dp, 0.0929910007625097_dp, 0.0929691627854083_dp, 0.0929566091979410_dp, & + & 0.0929500554074849_dp, 0.0929470609981138_dp, 0.0929459377033481_dp, 0.0929456321410385_dp, & + & 0.0929455870407025_dp, 0.0929455834915416_dp, 0.0929455188438055_dp, 0.0929450808466470_dp, & + & 0.0929434707328625_dp, 0.0929391788380656_dp, 0.0929297865244649_dp, 0.0929118006265526_dp, & + & 0.0928805277126656_dp, 0.0928299950241467_dp, 0.0927529244201111_dp, 0.0926407649169505_dp, & + & 0.0924837883440262_dp, 0.0922712511071495_dp, 0.0919916229444908_dp, 0.0916328808038998_dp, & + & 0.0911828625768436_dp, 0.0906296714990305_dp, 0.0899621178002405_dp, 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51.1286657438207968_dp, 51.1284504152295014_dp, 51.1283918406082023_dp, & + & 51.1283831951159016_dp, 51.1283825282923985_dp, 51.1283705542820002_dp, 51.1282894286069975_dp, & + & 51.1279912021497012_dp, 51.1271962407220002_dp, 51.1254564912093983_dp, 51.1221246785838019_dp, & + & 51.1163306779899003_dp, 51.1069661656718992_dp, 51.0926784888829033_dp, 51.0718745026143992_dp, & + & 51.0427348924997020_dp, 51.0032392307489033_dp, 50.9512016893668971_dp, 50.8843169601354006_dp, & + & 50.8002155081037969_dp, 50.6965268268632983_dp, 50.5709488909003966_dp, 50.4213215428680002_dp, & + & 50.2457011488370000_dp, 50.0424335438179000_dp, 49.8102221141881003_dp, 49.5481878591749023_dp, & + & 49.2559184660926022_dp, 48.9335038347750029_dp, 48.5815560882288011_dp, 48.2012128801149018_dp, & + & 47.7941237030876991_dp, 47.3624198402226995_dp, 46.9086694920411986_dp, 46.4358203562748031_dp, & + & 45.9471324543606983_dp, 45.4461042445803969_dp, 44.9363950486055970_dp, 44.4217466103216978_dp, & + & 43.9059062955985979_dp, 43.3925541128411965_dp, 42.8852354306699013_dp, 42.3873009861978005_dp, & + & 41.9018554777724006_dp, 41.4317156800847997_dp, 40.9793785923523970_dp, 40.5469996531022971_dp, & + & 40.1363805783220968_dp, 39.7489659645377031_dp, 39.3858474963671981_dp, 39.0477744376580986_dp, & + & 38.7351690672193030_dp, 38.4481458217707015_dp, 38.1865330930245008_dp, 37.9498968514241000_dp, & + & 37.7375654984204019_dp, 37.5486555534204030_dp, 37.3820979422981026_dp, 37.2366647629917011_dp, & + & 37.1109964594064010_dp, 37.0036293422124984_dp, 36.9130233621412032_dp, 36.8375899777832032_dp, & + & 36.7757198762259989_dp, 36.7258102118546006_dp, 36.6862909368518970_dp, 36.6556497164531976_dp, & + & 36.6324548620328017_dp, 36.6153756834579980_dp, 36.6031996647180975_dp, 36.5948459069949976_dp, & + & 36.5893743615161000_dp, 36.5859904880430022_dp, 36.5840451179791017_dp, 36.5830294656256996_dp, & + & 36.5825654070783983_dp, 36.5823913229229021_dp, 36.5823439678330971_dp, 36.5823369783217984_dp, & + & 36.5823364490970988_dp, 36.5823270739349979_dp, 36.5822635558526983_dp, 36.5820300569701971_dp, & + & 36.5814076370381969_dp, 36.5800454982128969_dp, 36.5774368852838023_dp, 36.5729006290650034_dp, & + & 36.5655692184182968_dp, 36.5543841663938025_dp, 36.5380992922927987_dp, 36.5152923660954016_dp, & + & 36.4843853462243999_dp, 36.4436731791179014_dp, 36.3913608162888025_dp, 36.3256077440943983_dp, & + & 36.2445789235720000_dp, 36.1465006215074993_dp, 36.0297192073204968_dp, 35.8927606289532974_dp, & + & 35.7343880053332015_dp, 35.5536546246444018_dp, 35.3499496538740985_dp, 35.1230340730170028_dp, & + & 34.8730647580089013_dp, 34.6006052397602986_dp, 34.3066224278729024_dp, 33.9924694470058029_dp, & + & 33.6598556103155033_dp, 33.3108053538479965_dp, 32.9476085843215003_dp, 32.5727652731222008_dp, & + & 32.1889272173191969_dp, 31.7988396852681987_dp, 31.4052852200793993_dp, 31.0110312801960006_dp, & + & 30.6187827660798000_dp, 30.2311399252366009_dp, 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0.0734682038760752_dp, 0.0711257803042145_dp, 0.0689635358153851_dp, & + & 0.0669795106552726_dp, 0.0651700182364436_dp, 0.0635299194359931_dp, 0.0620528761388641_dp, & + & 0.0607315800806276_dp, 0.0595579555849355_dp, 0.0585233368425122_dp, 0.0576186219361432_dp, & + & 0.0568344068798154_dp, 0.0561611035239338_dp, 0.0555890453108390_dp, 0.0551085846036443_dp, & + & 0.0547101847247973_dp, 0.0543845090095232_dp, 0.0541225081835819_dp, 0.0539155063016494_dp, & + & 0.0537552844183722_dp, 0.0536341601979444_dp, 0.0535450608808503_dp, 0.0534815864898377_dp, & + & 0.0534380599192161_dp, 0.0534095606384994_dp, 0.0533919391446176_dp, 0.0533818099834065_dp, & + & 0.0533765220684757_dp, 0.0533741060723543_dp, 0.0533731997643088_dp, 0.0533729532280347_dp, & + & 0.0533729168398480_dp, 0.0533729139762471_dp, 0.0533728618166549_dp, 0.0533725084285095_dp, & + & 0.0533712093488532_dp, 0.0533677465757023_dp, 0.0533601688700998_dp, 0.0533456585296648_dp, & + & 0.0533204307847939_dp, 0.0532796717709232_dp, 0.0532175207605263_dp, 0.0531271018788573_dp, & + & 0.0530006097392715_dp, 0.0528294521668755_dp, 0.0526044512985209_dp, 0.0523161017719502_dp, & + & 0.0519548814426116_dp, 0.0515116062072281_dp, 0.0509778163004171_dp, 0.0503461772411526_dp, & + & 0.0496108749068895_dp, 0.0487679815491617_dp, 0.0478157684525939_dp, 0.0467549418097661_dp, & + & 0.0455887814720484_dp, 0.0443231675338183_dp, 0.0429664869078010_dp, 0.0415294205695886_dp, & + & 0.0400246211561068_dp, 0.0384662991075970_dp, 0.0368697425314224_dp, 0.0352508005878889_dp, & + & 0.0336253619499729_dp, 0.0320088587268259_dp, 0.0304158225438869_dp, 0.0288595138530923_dp, & + & 0.0273516386512966_dp, 0.0259021592391377_dp, 0.0245191981371562_dp, 0.0232090276229542_dp, & + & 0.0219761323922398_dp, 0.0208233300699874_dp, 0.0197519335819436_dp, 0.0187619401046959_dp, & + & 0.0178522327255308_dp, 0.0170207827028293_dp, 0.0162648423377902_dp, 0.0155811210394177_dp, & + & 0.0149659400032505_dp, 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0.4946833469891630_dp, 0.4942896932839600_dp, & + & 0.4939998146904830_dp, 0.4937931463780100_dp, 0.4936513503115380_dp, 0.4935584747171480_dp, & + & 0.4935010350817630_dp, 0.4934680130808860_dp, 0.4934507726452320_dp, 0.4934428953534250_dp, & + & 0.4934399403102250_dp, 0.4934391364669040_dp, 0.4934390178213310_dp, 0.4934390086376650_dp, & + & 0.4934388433063930_dp, 0.4934377231629700_dp, 0.4934336054018470_dp, 0.4934226289973220_dp, & + & 0.4933986075807870_dp, 0.4933526043699460_dp, 0.4932726065126190_dp, 0.4931433143716080_dp, & + & 0.4929460591178980_dp, 0.4926588594152290_dp, 0.4922566248248190_dp, 0.4917115096834270_dp, & + & 0.4909934164854230_dp, 0.4900706421772160_dp, 0.4889106543134430_dp, 0.4874809769521850_dp, & + & 0.4857501588782040_dp, 0.4836887898261890_dp, 0.4812705245410170_dp, 0.4784730705399770_dp, & + & 0.4752790940510750_dp, 0.4716770003191750_dp, 0.4676615495123140_dp, 0.4632342776245930_dp, & + & 0.4584037024408620_dp, 0.4531853068080100_dp, 0.4476013039341210_dp, 0.4416802009608600_dp, & + & 0.4354561865544750_dp, 0.4289683750071590_dp, 0.4222599430452620_dp, 0.4153771963494250_dp, & + & 0.4083686012020710_dp, 0.4012838133819800_dp, 0.3941727321580400_dp, 0.3870846026202770_dp, & + & 0.3800671850733150_dp, 0.3731660060336420_dp, 0.3664237015843950_dp, 0.3598794603931590_dp, & + & 0.3535685705107880_dp, 0.3475220710770940_dp, 0.3417665072641540_dp, 0.3363237842467580_dp, & + & 0.3312111138057930_dp, 0.3264410454569600_dp, 0.3220215728414930_dp, 0.3179563055619640_dp, & + & 0.3142446966697180_dp, 0.3108823165331240_dp, 0.3078611647036950_dp, 0.3051700124860160_dp, & + & 0.3027947700422970_dp, 0.3007188728552280_dp, 0.2989236831129030_dp, 0.2973889019758790_dp, & + & 0.2960929887038760_dp, 0.2950135822745780_dp, 0.2941279204798240_dp, 0.2934132506388210_dp, & + & 0.2928472251537780_dp, 0.2924082742928530_dp, 0.2920759479628710_dp, 0.2918312179552490_dp, & + & 0.2916567323107270_dp, 0.2915370141086560_dp, 0.2914585981589400_dp, 0.2914101007204270_dp, & + & 0.2913822194150270_dp, 0.2913676628336500_dp, 0.2913610118051790_dp, 0.2913585167737550_dp, & + & 0.2913578380646410_dp, 0.2913577378885750_dp, 0.2913577300716810_dp, 0.2913575885336430_dp, & + & 0.2913566295928550_dp, 0.2913531044280550_dp, 0.2913437076557410_dp, 0.2913231431651300_dp, & + & 0.2912837601488430_dp, 0.2912152741415350_dp, 0.2911045862772000_dp, 0.2909357121103400_dp, & + & 0.2906898291349900_dp, 0.2903454494835960_dp, 0.2898787210900480_dp, 0.2892638567779500_dp, & + & 0.2884736862552440_dp, 0.2874803209133030_dp, 0.2862559157845370_dp, 0.2847735072725750_dp, & + & 0.2830078996912560_dp, 0.2809365686842260_dp, 0.2785405457349550_dp, 0.2758052456973130_dp, & + & 0.2727211989851530_dp, 0.2692846520223070_dp, 0.2654980038608130_dp, 0.2613700533952820_dp, & + & 0.2569160400083630_dp, 0.2521574702626170_dp, 0.2471217337775760_dp, 0.2418415219923280_dp, & + & 0.2363540734118600_dp, 0.2307002775062020_dp, 0.2249236761084600_dp, 0.2190694054944370_dp, & + & 0.2131831240343160_dp, 0.2073099692833720_dp, 0.2014935847269190_dp, 0.1957752504315950_dp, & + & 0.1901931440930160_dp, 0.1847817500758140_dp, 0.1795714247611930_dp, 0.1745881176016440_dp, & + & 0.1698532393949250_dp, 0.1653836629457570_dp, 0.1611918368019900_dp, 0.1572859902353090_dp, & + & 0.1536704069962410_dp, 0.1503457463529260_dp, 0.1473093921708820_dp, 0.1445558138962750_dp, & + & 0.1420769268650730_dp, 0.1398624430076300_dp, 0.1379002064431920_dp, 0.1361765114297950_dp, & + & 0.1346764024904990_dp, 0.1333839581882760_dp, 0.1322825609496760_dp, 0.1313551555675050_dp, & + & 0.1305844986323020_dp, 0.1299534002568520_dp, 0.1294449582224640_dp, 0.1290427832415590_dp, & + & 0.1287312125764690_dp, 0.1284955079408690_dp, 0.1283220325887560_dp, 0.1281984018857680_dp, & + & 0.1281136015399510_dp, 0.1280580680745800_dp, 0.1280237270401590_dp, 0.1280039858157100_dp, & + & 0.1279936795411200_dp, 0.1279889706158740_dp, 0.1279872041510970_dp, 0.1279867236313240_dp, & + & 0.1279866527076620_dp, 0.1279866471262780_dp, 0.1279865454627610_dp, 0.1279858566783640_dp, & + & 0.1279833246481270_dp, 0.1279765752928770_dp, 0.1279618050410390_dp, 0.1279335203379620_dp, & + & 0.1278843395623570_dp, 0.1278048679718320_dp, 0.1276836553981720_dp, 0.1275072452122430_dp, & + & 0.1272603214016210_dp, 0.1269259582727500_dp, 0.1264859741469590_dp, 0.1259213863698390_dp, & + & 0.1252129600136270_dp, 0.1243418369541870_dp, 0.1232902258468580_dp, 0.1220421273447980_dp, & + & 0.1205840632701300_dp, 0.1189057740100590_dp, 0.1170008458332600_dp, 0.1148672296945820_dp, & + & 0.1125076158498930_dp, 0.1099296344205950_dp, 0.1071458607904250_dp, 0.1041736159130410_dp, & + & 0.1010345644366450_dp, 0.0977541269322586_dp, 0.0943607351985349_dp, 0.0908849703507286_dp, & + & 0.0873586310818126_dp, 0.0838137833085142_dp, 0.0802818420077784_dp, 0.0767927315197454_dp, & + & 0.0733741625286939_dp, 0.0700510533035299_dp, 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0.0816539126980729_dp, 0.0815894643072994_dp, 0.0814911921415131_dp, 0.0813482262540930_dp, & + & 0.0811482290570069_dp, 0.0808776223083214_dp, 0.0805219068968057_dp, 0.0800660734428931_dp, & + & 0.0794950965177890_dp, 0.0787944991208605_dp, 0.0779509673245542_dp, 0.0769529882787765_dp, & + & 0.0757914788231773_dp, 0.0744603676379825_dp, 0.0729570920183704_dp, 0.0712829716782011_dp, & + & 0.0694434268824011_dp, 0.0674480166695872_dp, 0.0653102844738385_dp, 0.0630474121327040_dp, & + & 0.0606796977333914_dp, 0.0582298864422199_dp, 0.0557223948259349_dp, 0.0531824768968505_dp, & + & 0.0506353833258544_dp, 0.0481055636937526_dp, 0.0456159556293159_dp, 0.0431873951110475_dp, & + & 0.0408381703748972_dp, 0.0385837292391926_dp, 0.0364365376390623_dp, 0.0344060769196801_dp, & + & 0.0324989597493186_dp, 0.0307191397359219_dp, 0.0290681879216237_dp, 0.0275456099246441_dp, & + & 0.0261491800333147_dp, 0.0248752723771872_dp, 0.0237191737633253_dp, 0.0226753673262294_dp, & + & 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0.0080533968558427_dp, 0.0080505749138524_dp, 0.0080491018997435_dp, & + & 0.0080484289345577_dp, 0.0080481764929488_dp, 0.0080481078237398_dp, 0.0080480976883308_dp, & + & 0.0080480968836838_dp, 0.0080480821370372_dp, 0.0080479822269979_dp, 0.0080476149555580_dp, & + & 0.0080466360094533_dp, 0.0080444939383142_dp, 0.0080403928743067_dp, 0.0080332650263557_dp, & + & 0.0080217550928268_dp, 0.0080042188311324_dp, 0.0079787380295215_dp, 0.0079431539548125_dp, & + & 0.0078951208984393_dp, 0.0078321806261386_dp, 0.0077518572922628_dp, 0.0076517707099555_dp, & + & 0.0075297638485381_dp, 0.0073840382297590_dp, 0.0072132887825092_dp, 0.0070168280252147_dp, & + & 0.0067946885440051_dp, 0.0065476929519264_dp, 0.0062774820624440_dp, 0.0059864949218849_dp, & + & 0.0056778984210837_dp, 0.0053554690170898_dp, 0.0050234340225046_dp, 0.0046862842535233_dp, & + & 0.0043485728852772_dp, 0.0040147166347850_dp, 0.0036888146710083_dp, 0.0033744980943737_dp, & + & 0.0030748189413004_dp, 0.0027921831551083_dp, 0.0025283275093671_dp, 0.0022843365823775_dp, & + & 0.0020606928516145_dp, 0.0018573509866400_dp, 0.0016738266410101_dp, 0.0015092905712493_dp, & + & 0.0013626605789341_dp, 0.0012326860407370_dp, 0.0011180219377849_dp, 0.0010172908176998_dp, & + & 0.0009291320317999_dp, 0.0008522382739216_dp, 0.0007853802518554_dp, 0.0007274212006081_dp, & + & 0.0006773235405007_dp, 0.0006341499962588_dp, 0.0005970610046688_dp, 0.0005653095989828_dp, & + & 0.0005382345021445_dp, 0.0005152520147362_dp, 0.0004958473225827_dp, 0.0004795658556986_dp, & + & 0.0004660052021990_dp, 0.0004548078817237_dp, 0.0004456551030501_dp, 0.0004382615206708_dp, & + & 0.0004323709487579_dp, 0.0004277529687897_dp, 0.0004242003530379_dp, 0.0004215272078199_dp, & + & 0.0004195677141468_dp, 0.0004181753184724_dp, 0.0004172222083554_dp, 0.0004165989036125_dp, & + & 0.0004162138024100_dp, 0.0004159925416189_dp, 0.0004158770624372_dp, 0.0004158243079218_dp, & + & 0.0004158045193350_dp, 0.0004157991364764_dp, 0.0004157983419901_dp, 0.0004157982783397_dp, & + & 0.0004157971046652_dp, 0.0004157891527967_dp, 0.0004157599220207_dp, 0.0004156820122461_dp, & + & 0.0004155115527027_dp, 0.0004151852713790_dp, 0.0004146183941032_dp, 0.0004137035877818_dp, & + & 0.0004123111837089_dp, 0.0004102909304180_dp, 0.0004074755108263_dp, 0.0004036860101166_dp, & + & 0.0003987394161697_dp, 0.0003924580753960_dp, 0.0003846808042880_dp, 0.0003752750925230_dp, & + & 0.0003641495492275_dp, 0.0003512654927960_dp, 0.0003366464225252_dp, 0.0003203840973072_dp, & + & 0.0003026401220296_dp, 0.0002836423257975_dp, 0.0002636758003121_dp, 0.0002430691812094_dp, & + & 0.0002221774092277_dp, 0.0002013625749271_dp, 0.0001809744956773_dp, 0.0001613325775054_dp, & + & 1.4271033923307600e-04_dp, 1.2532373756357599e-04_dp, 1.0932445911748800e-04_dp, 9.4799449001925495e-05_dp, & + & 8.1776764162100294e-05_dp, 7.0235678037988705e-05_dp, 6.0118260506669699e-05_dp, 5.1339648010184599e-05_dp, & + & 4.3794148609776999e-05_dp, 3.7359074056553302e-05_dp, 3.1902498278668598e-05_dp, 2.7293611793766100e-05_dp, & + & 2.3410731571971199e-05_dp, 2.0149972542071700e-05_dp, 1.7429172388005999e-05_dp, 1.5176281422668601e-05_dp, & + & 1.3317730974904400e-05_dp, 1.1781596001014800e-05_dp, 1.0502495157993499e-05_dp, 9.4285481537781396e-06_dp, & + & 8.5301809633619996e-06_dp, 7.7842551178264296e-06_dp, 7.1519236399808497e-06_dp, 6.6005488861264902e-06_dp, & + & 6.1385887448750501e-06_dp, 5.7955440411205902e-06_dp, 5.5673049956794801e-06_dp, 5.4071538642119802e-06_dp, & + & 5.2677798976219501e-06_dp, 5.1300781649388202e-06_dp, 4.9978841332176697e-06_dp, 4.8813713533490997e-06_dp, & + & 4.7867697645642701e-06_dp, 4.7145970825113198e-06_dp, 4.6619015137139303e-06_dp, 4.6246624521018004e-06_dp, & + & 4.5990956039077000e-06_dp, 4.5820822691666797e-06_dp, 4.5711878300380704e-06_dp, 4.5645530235560702e-06_dp, & + & 4.5607752099385800e-06_dp, 4.5588136146079697e-06_dp, 4.5579198229006596e-06_dp, 4.5575849298984403e-06_dp, & + & 4.5574938809522800e-06_dp, 4.5574804232728596e-06_dp, 4.5574792437719199e-06_dp, 4.5574561937655702e-06_dp, & + & 4.5573001301590904e-06_dp, 4.5567263668999700e-06_dp, 4.5551969520829499e-06_dp, 4.5518501536889702e-06_dp, & + & 4.5454416977008796e-06_dp, 4.5343025334432199e-06_dp, 4.5163210415921597e-06_dp, 4.4889735448805402e-06_dp, & + & 4.4494676103568096e-06_dp, 4.3951478687631598e-06_dp, 4.3244283176591100e-06_dp, 4.2384553324836799e-06_dp, & + & 4.1429034780549003e-06_dp, 4.0471667261954297e-06_dp, 3.9564359326504902e-06_dp, 3.8575094123416403e-06_dp, & + & 3.7140923865308701e-06_dp, 3.4921709755053598e-06_dp, 3.2124948745604300e-06_dp, 2.9734900692801598e-06_dp, & + & 2.8251042465399202e-06_dp, 2.6167984117364502e-06_dp, 2.1888084944521299e-06_dp, 1.7964081422405800e-06_dp, & + & 1.9742465582339702e-06_dp, 2.0688949433633799e-06_dp, 1.5728956697103100e-06_dp, 1.2307683476819900e-06_dp, & + & 1.8897238760473600e-06_dp, 1.8324535062674800e-06_dp, 7.2753263680169798e-07_dp, 1.5793180949685799e-06_dp, & + & 1.8671008348292200e-06_dp, 9.2016907160541503e-07_dp, 3.5389784613926201e-06_dp, 5.7552407213279400e-06_dp, & + & 7.1537430699208901e-06_dp, 7.5274118103152398e-06_dp, 6.9220295983995996e-06_dp, 5.6231859844047003e-06_dp, & + & 4.0863298806925698e-06_dp, 2.7797161408216202e-06_dp, 1.7815217177030701e-06_dp, 1.5360869980440801e-06_dp, & + & 2.5673725048136501e-06_dp, 3.3070146940872300e-06_dp, 3.4797437962197402e-06_dp, 3.1092310734948102e-06_dp, & + & 2.3404976587926302e-06_dp, 1.3581478555124700e-06_dp, 0.0000000000000000e+00_dp, 8.6837428625585702e-07_dp, & + & 1.0437429835974401e-06_dp, 1.0020755780715301e-06_dp, 8.8057399239005505e-07_dp, 7.4956402329462403e-07_dp, & + & 6.4143900146973497e-07_dp, 5.7111610374249700e-07_dp, 5.3126963450722500e-07_dp, 4.9713416672148004e-07_dp, & + & 4.5119374192381698e-07_dp, 0.0000000000000000e+00_dp, 0.0000000000000000e+00_dp, 0.0000000000000000e+00_dp, & + & 0.0000000000000000_dp, 0.0000000000000000_dp, 0.0000000000000000_dp, 0.0000000000000000_dp, & + & 0.0000000000000000_dp, 0.0000000000000000_dp, 0.0000000000000000_dp, 0.0000000000000000_dp, & + & 0.0000000000000000_dp & + &] + + case default + call error("Bad atomic number supplied!") + end select + + end subroutine get_sap_data + +end module sap + diff --git a/slateratom/lib/utilities.f90 b/slateratom/lib/utilities.f90 index 1b1f8a66..86116852 100644 --- a/slateratom/lib/utilities.f90 +++ b/slateratom/lib/utilities.f90 @@ -6,7 +6,7 @@ module utilities implicit none private - public :: check_convergence, check_electron_number + public :: check_electron_number, check_convergence_energy, check_convergence_orbgrad public :: vector_length, fak, zeroOutCpotOfEmptyDensitySpinChannels @@ -33,8 +33,8 @@ end subroutine zeroOutCpotOfEmptyDensitySpinChannels !> Checks SCF convergence by comparing new and old potential. - pure subroutine check_convergence(pot_old, pot_new, max_l, problemsize, scftol, iScf, change_max,& - & tConverged) + pure subroutine check_convergence_pot(pot_old, pot_new, max_l, problemsize, scftol, iScf, change_max,& + & tConverged) !> old and new potential to compare real(dp), intent(in) :: pot_old(:,0:,:,:), pot_new(:,0:,:,:) @@ -82,7 +82,134 @@ pure subroutine check_convergence(pot_old, pot_new, max_l, problemsize, scftol, tConverged = .false. end if - end subroutine check_convergence + end subroutine check_convergence_pot + + !> Checks SCF convergence by computing the occupied-virtual orbital gradient norm + pure subroutine check_convergence_orbgrad(max_l, num_alpha, poly_order, fock, coef, occ, & + & scftol, iScf, gradnorm, tConverged) + + !> maximum angular momentum + integer, intent(in) :: max_l + + !> number of exponents in each shell + integer, intent(in) :: num_alpha(0:) + + !> highest polynomial order + l in each shell + integer, intent(in) :: poly_order(0:) + + !> Fock matrix + real(dp), intent(in) :: fock(:, 0:, :, :) + + !> MO coefficients supervector + real(dp), intent(in) :: coef(:, 0:, :, :) + + !> occupations + real(dp), intent(in) :: occ(:, 0:, :) + + !> scf tolerance, i.e. convergence criteria + real(dp), intent(in) :: scftol + + !> current SCF step + integer, intent(in) :: iScf + + !> orbital gradient norm value + real(dp), intent(out) :: gradnorm + + !> true, if SCF converged + logical, intent(out) :: tConverged + + !> auxilliary variables + integer :: iSpin, ll, diagsize, ii, aa + real(dp) :: occ_ii, occ_aa + + !> Partial Fock matrix in MO basis + real(dp), allocatable :: fock_mo(:, :) + + ! doi.org/10.3390/molecules25051218 + ! eq. (46) + + gradnorm = 0.0_dp + + if (iScf < 3) then + tConverged = .false. + end if + + do iSpin = 1, 2 + do ll = 0, max_l + diagsize = num_alpha(ll) * poly_order(ll) + allocate(fock_mo(diagsize, diagsize)) + fock_mo = 0.0_dp + + ! Compute Fock matrix in MO basis + fock_mo = matmul(fock(iSpin, ll, :, :), coef(iSpin, ll, :, :)) + fock_mo = matmul(transpose(coef(iSpin, ll, :, :)), fock_mo) + + ! Compute orbital gradient norm + do ii = 1, diagsize + + aa = 1 + do while (aa <= ii) + aa = aa + 1 + end do + + do while (aa < diagsize) + ! Only occupied-virtual block contributes + occ_ii = abs(occ(iSpin, ll, ii)) + occ_aa = abs(occ(iSpin, ll, aa)) + if (occ_ii < 1e-16 .neqv. occ_aa < 1e-16) then + gradnorm = gradnorm + (-2.0_dp * fock_mo(ii, aa))**2 + end if + aa = aa + 1 + end do + end do + + deallocate(fock_mo) + end do + end do + + gradnorm = sqrt(gradnorm) + + if (gradnorm < scftol) then + tConverged = .true. + else + tConverged = .false. + end if + + end subroutine check_convergence_orbgrad + + !> Checks convergence by computing energy change from the last SCF iteration + pure subroutine check_convergence_energy(energy_old, energy_new, scftol, iScf, change, tConverged) + + !> old and new potential to compare + real(dp), intent(in) :: energy_new, energy_old + + !> scf tolerance, i.e. convergence criteria + real(dp), intent(in) :: scftol + + !> current SCF step + integer, intent(in) :: iScf + + !> obtained maximum change in potential + real(dp), intent(out) :: change + + !> true, if SCF converged + logical, intent(out) :: tConverged + + change = 0.0_dp + + if (iScf < 3) then + tConverged = .false. + end if + + change = abs(energy_new - energy_old) + + if (change < scftol) then + tConverged = .true. + else + tConverged = .false. + end if + + end subroutine check_convergence_energy !> Checks conservation of electron number during SCF. If this fluctuates you are in deep trouble. diff --git a/slateratom/lib/xcfunctionals.f90 b/slateratom/lib/xcfunctionals.f90 index cb20cd34..75eed5b0 100644 --- a/slateratom/lib/xcfunctionals.f90 +++ b/slateratom/lib/xcfunctionals.f90 @@ -6,9 +6,11 @@ module xcfunctionals use common_constants, only : rec4pi use utilities, only : zeroOutCpotOfEmptyDensitySpinChannels use xc_f03_lib_m, only : xc_f03_func_t, xc_f03_func_init, xc_f03_func_end, xc_f03_lda_exc_vxc,& - & xc_f03_gga_exc_vxc, xc_f03_func_set_ext_params, XC_LDA_X, XC_LDA_X_YUKAWA, XC_LDA_C_PW,& - & XC_GGA_X_PBE, XC_GGA_X_B88, XC_GGA_X_SFAT_PBE, XC_HYB_GGA_XC_B3LYP,& - & XC_HYB_GGA_XC_CAMY_B3LYP, XC_GGA_C_PBE, XC_GGA_C_LYP, XC_POLARIZED + & xc_f03_gga_exc_vxc, xc_f03_mgga_exc_vxc, xc_f03_func_set_ext_params, XC_LDA_X, XC_LDA_X_YUKAWA,& + & XC_LDA_C_PW, XC_GGA_X_PBE, XC_GGA_X_B88, XC_GGA_X_SFAT_PBE, XC_HYB_GGA_XC_B3LYP,& + & XC_HYB_GGA_XC_CAMY_B3LYP, XC_GGA_C_PBE, XC_GGA_C_LYP, XC_MGGA_X_SCAN, XC_MGGA_X_R4SCAN,& + & XC_MGGA_C_SCAN, XC_MGGA_X_TASK, XC_MGGA_X_R2SCAN, XC_MGGA_C_R2SCAN, XC_MGGA_X_TPSS,& + & XC_MGGA_C_TPSS, XC_MGGA_C_CC, XC_POLARIZED implicit none private @@ -19,6 +21,9 @@ module xcfunctionals public :: getExcVxc_LCY_PBE96, getExcVxc_LCY_BNL public :: getExcVxc_HYB_B3LYP, getExcVxc_HYB_PBE0 public :: getExcVxc_CAMY_B3LYP, getExcVxc_CAMY_PBEh + public :: getExcVxc_MGGA_TPSS, getExcVxc_MGGA_SCAN,& + & getExcVxc_MGGA_r2SCAN, getExcVxc_MGGA_r4SCAN,& + & getExcVxc_MGGA_TASK, getExcVxc_MGGA_TASK_CC interface libxcVxcToInternalVxc @@ -64,10 +69,29 @@ module xcfunctionals !> CAMY-PBEh integer :: CAMY_PBEh = 10 + !> MGGA-TPSS + integer :: MGGA_TPSS = 11 + + !> MGGA-SCAN + integer :: MGGA_SCAN = 12 + + !> MGGA-r2SCAN + integer :: MGGA_r2SCAN = 13 + + !> MGGA-r4SCAN + integer :: MGGA_r4SCAN = 14 + + !> MGGA-TASK + integer :: MGGA_TASK = 15 + + !> MGGA-TASK+CC + integer :: MGGA_TASK_CC = 16 + contains procedure :: isLDA => TXcFunctionalsEnum_isLDA procedure :: isGGA => TXcFunctionalsEnum_isGGA + procedure :: isMGGA => TXcFunctionalsEnum_isMGGA procedure :: isGlobalHybrid => TXcFunctionalsEnum_isGlobalHybrid procedure :: isLongRangeCorrected => TXcFunctionalsEnum_isLongRangeCorrected procedure :: isCAMY => TXcFunctionalsEnum_isCAMY @@ -117,6 +141,24 @@ pure function TXcFunctionalsEnum_isGGA(this, xcnr) result(isGGA) end function TXcFunctionalsEnum_isGGA + pure function TXcFunctionalsEnum_isMGGA(this, xcnr) result(isMGGA) + + !> Class instance + class(TXcFunctionalsEnum), intent(in) :: this + + !> identifier of exchange-correlation type + integer, intent(in) :: xcnr + + !> True, if xc-functional index corresponds to a GGA functional + logical :: isMGGA + + isMGGA = .false. + if (xcnr == this%MGGA_SCAN .or. xcnr == this%MGGA_r2SCAN & + & .or. xcnr == this%MGGA_TASK .or. xcnr == this%MGGA_r4SCAN & + & .or. xcnr == this%MGGA_TPSS .or. xcnr == this%MGGA_TASK_CC) & + & isMGGA = .true. + + end function TXcFunctionalsEnum_isMGGA pure function TXcFunctionalsEnum_isLongRangeCorrected(this, xcnr) result(isLongRangeCorrected) @@ -191,7 +233,7 @@ pure function TXcFunctionalsEnum_isNotImplemented(this, xcnr) result(isNotImplem isNotImplemented = .false. - if (xcnr < 0 .or. xcnr > 10) then + if (xcnr < 0 .or. xcnr > 16) then isNotImplemented = .true. end if @@ -342,7 +384,6 @@ subroutine getExcVxc_GGA_PBE96(abcissa, dz, dzdr, rho, drho, sigma, exc, vxc) end subroutine getExcVxc_GGA_PBE96 - !> Calculates exc and vxc for the GGA-BLYP xc-functional. subroutine getExcVxc_GGA_BLYP(abcissa, dz, dzdr, rho, drho, sigma, exc, vxc) @@ -431,6 +472,772 @@ subroutine getExcVxc_GGA_BLYP(abcissa, dz, dzdr, rho, drho, sigma, exc, vxc) end subroutine getExcVxc_GGA_BLYP + !> Calculates exc, vxc, and vtau for the MGGA-TPSS xc-functional. + subroutine getExcVxc_MGGA_TPSS(abcissa, dz, dzdr, rho, drho, sigma, tau, exc, vxc, vtau) + + !> numerical integration abcissas + real(dp), intent(in) :: abcissa(:) + + !> step width in linear coordinates + real(dp), intent(in) :: dz + + !> dz/dr + real(dp), intent(in) :: dzdr(:) + + !> density on grid + real(dp), intent(in) :: rho(:,:) + + !> 1st deriv. of density on grid + real(dp), intent(in) :: drho(:,:) + + !> contracted gradients of the density + real(dp), intent(in), allocatable :: sigma(:,:) + + !> Kinetic energy density + real(dp), intent(in):: tau(:,:) + + !> exc energy density on grid + real(dp), intent(out) :: exc(:) + + !> xc potential on grid + real(dp), intent(out) :: vxc(:,:) + + !> orbital-dependent tau potential on grid + real(dp), intent(out) :: vtau(:, :) + + !! density in libxc compatible format, i.e. rho/(4pi) + real(dp), allocatable :: rhor(:,:) + + !! Kinetic energy density (in libxc compatible format) + real(dp), allocatable :: tau_libxc(:,:) + + !! libxc related objects + type(xc_f03_func_t) :: xcfunc_x, xcfunc_c + + !! number of density grid points + integer(c_size_t) :: nn + + !! exchange and correlation energy on grid + real(dp), allocatable :: ex(:), ec(:) + + !! exchange and correlation potential on grid + real(dp), allocatable :: vx(:,:), vc(:,:) + + !! first partial derivative of the energy per unit volume in terms of sigma (exchange) + real(dp), allocatable :: vxsigma(:,:) + + !! first partial derivative of the energy per unit volume in terms of sigma (correlation) + real(dp), allocatable :: vcsigma(:,:) + + !! first partial derivative of the energy per unit volume in terms of tau (exchange) + real(dp), allocatable :: vxtau(:,:) + + !! first partial derivative of the energy per unit volume in terms of tau (correlation) + real(dp), allocatable :: vctau(:,:) + + !! laplacian for libxc (dummy) + real(dp), allocatable :: lapl(:,:) + + !! first partial derivative of the energy per unit volume in terms of laplacian (exchange) (dummy) + real(dp), allocatable :: vxlapl(:,:) + + !! first partial derivative of the energy per unit volume in terms of laplacian (correlation) (dummy) + real(dp), allocatable :: vclapl(:,:) + + nn = size(rho, dim=1) + ! divide by 4*pi to catch different normalization of spherical harmonics + allocate(rhor(2, nn)) + rhor(:,:) = transpose(rho) * rec4pi + + allocate(tau_libxc(2, nn)) + tau_libxc(:,:) = transpose(tau) * rec4pi + + allocate(ex(nn)) + ex(:) = 0.0_dp + allocate(ec(nn)) + ec(:) = 0.0_dp + allocate(vx(2, nn)) + vx(:,:) = 0.0_dp + allocate(vc(2, nn)) + vc(:,:) = 0.0_dp + + allocate(vxsigma(3, nn)) + vxsigma(:,:) = 0.0_dp + allocate(vcsigma(3, nn)) + vcsigma(:,:) = 0.0_dp + + allocate(vxtau(2, nn)) + vxtau(:,:) = 0.0_dp + allocate(vctau(2, nn)) + vctau(:,:) = 0.0_dp + + allocate(lapl(2, nn)) + lapl(:, :) = 0.0_dp + allocate(vxlapl(2, nn)) + vxlapl(:,:) = 0.0_dp + allocate(vclapl(2, nn)) + vclapl(:,:) = 0.0_dp + + call xc_f03_func_init(xcfunc_x, XC_MGGA_X_TPSS, XC_POLARIZED) + call xc_f03_func_init(xcfunc_c, XC_MGGA_C_TPSS, XC_POLARIZED) + + ! Exchange energy and potential + call xc_f03_mgga_exc_vxc(xcfunc_x, nn, rhor(1, 1), sigma(1, 1), lapl(1, 1), tau_libxc(1, 1),& + & ex(1), vx(1, 1), vxsigma(1, 1), vxlapl(1, 1), vxtau(1, 1)) + ! Correlation energy and potential + call xc_f03_mgga_exc_vxc(xcfunc_c, nn, rhor(1, 1), sigma(1, 1), lapl(1, 1), tau_libxc(1, 1),& + & ec(1), vc(1, 1), vcsigma(1, 1), vclapl(1, 1), vctau(1, 1)) + + call zeroOutCpotOfEmptyDensitySpinChannels(rho, vc) + + exc(:) = ex + ec + vxc(:,:) = transpose(vx + vc) + vtau(:, :) = transpose(vxtau + vctau) + + call libxcVxcToInternalVxc(abcissa, dz, dzdr, drho, vxsigma, vcsigma, vxc) + + ! finalize libxc objects + call xc_f03_func_end(xcfunc_x) + call xc_f03_func_end(xcfunc_c) + + end subroutine getExcVxc_MGGA_TPSS + + !> Calculates exc, vxc, and vtau for the MGGA-SCAN xc-functional. + subroutine getExcVxc_MGGA_SCAN(abcissa, dz, dzdr, rho, drho, sigma, tau, exc, vxc, vtau) + + !> numerical integration abcissas + real(dp), intent(in) :: abcissa(:) + + !> step width in linear coordinates + real(dp), intent(in) :: dz + + !> dz/dr + real(dp), intent(in) :: dzdr(:) + + !> density on grid + real(dp), intent(in) :: rho(:,:) + + !> 1st deriv. of density on grid + real(dp), intent(in) :: drho(:,:) + + !> contracted gradients of the density + real(dp), intent(in), allocatable :: sigma(:,:) + + !> Kinetic energy density + real(dp), intent(in):: tau(:,:) + + !> exc energy density on grid + real(dp), intent(out) :: exc(:) + + !> xc potential on grid + real(dp), intent(out) :: vxc(:,:) + + !> orbital-dependent tau potential on grid + real(dp), intent(out) :: vtau(:, :) + + !! density in libxc compatible format, i.e. rho/(4pi) + real(dp), allocatable :: rhor(:,:) + + !! Kinetic energy density (in libxc compatible format) + real(dp), allocatable :: tau_libxc(:,:) + + !! libxc related objects + type(xc_f03_func_t) :: xcfunc_x, xcfunc_c + + !! number of density grid points + integer(c_size_t) :: nn + + !! exchange and correlation energy on grid + real(dp), allocatable :: ex(:), ec(:) + + !! exchange and correlation potential on grid + real(dp), allocatable :: vx(:,:), vc(:,:) + + !! first partial derivative of the energy per unit volume in terms of sigma (exchange) + real(dp), allocatable :: vxsigma(:,:) + + !! first partial derivative of the energy per unit volume in terms of sigma (correlation) + real(dp), allocatable :: vcsigma(:,:) + + !! first partial derivative of the energy per unit volume in terms of tau (exchange) + real(dp), allocatable :: vxtau(:,:) + + !! first partial derivative of the energy per unit volume in terms of tau (correlation) + real(dp), allocatable :: vctau(:,:) + + !! laplacian for libxc (dummy) + real(dp), allocatable :: lapl(:,:) + + !! first partial derivative of the energy per unit volume in terms of laplacian (exchange) (dummy) + real(dp), allocatable :: vxlapl(:,:) + + !! first partial derivative of the energy per unit volume in terms of laplacian (correlation) (dummy) + real(dp), allocatable :: vclapl(:,:) + + nn = size(rho, dim=1) + ! divide by 4*pi to catch different normalization of spherical harmonics + allocate(rhor(2, nn)) + rhor(:,:) = transpose(rho) * rec4pi + + allocate(tau_libxc(2, nn)) + tau_libxc(:,:) = transpose(tau) * rec4pi + + allocate(ex(nn)) + ex(:) = 0.0_dp + allocate(ec(nn)) + ec(:) = 0.0_dp + allocate(vx(2, nn)) + vx(:,:) = 0.0_dp + allocate(vc(2, nn)) + vc(:,:) = 0.0_dp + + allocate(vxsigma(3, nn)) + vxsigma(:,:) = 0.0_dp + allocate(vcsigma(3, nn)) + vcsigma(:,:) = 0.0_dp + + allocate(vxtau(2, nn)) + vxtau(:,:) = 0.0_dp + allocate(vctau(2, nn)) + vctau(:,:) = 0.0_dp + + allocate(lapl(2, nn)) + lapl(:, :) = 0.0_dp + allocate(vxlapl(2, nn)) + vxlapl(:,:) = 0.0_dp + allocate(vclapl(2, nn)) + vclapl(:,:) = 0.0_dp + + call xc_f03_func_init(xcfunc_x, XC_MGGA_X_SCAN, XC_POLARIZED) + call xc_f03_func_init(xcfunc_c, XC_MGGA_C_SCAN, XC_POLARIZED) + + ! Exchange energy and potential + call xc_f03_mgga_exc_vxc(xcfunc_x, nn, rhor(1, 1), sigma(1, 1), lapl(1, 1), tau_libxc(1, 1),& + & ex(1), vx(1, 1), vxsigma(1, 1), vxlapl(1, 1), vxtau(1, 1)) + ! Correlation energy and potential + call xc_f03_mgga_exc_vxc(xcfunc_c, nn, rhor(1, 1), sigma(1, 1), lapl(1, 1), tau_libxc(1, 1),& + & ec(1), vc(1, 1), vcsigma(1, 1), vclapl(1, 1), vctau(1, 1)) + + call zeroOutCpotOfEmptyDensitySpinChannels(rho, vc) + + exc(:) = ex + ec + vxc(:,:) = transpose(vx + vc) + vtau(:, :) = transpose(vxtau + vctau) + + call libxcVxcToInternalVxc(abcissa, dz, dzdr, drho, vxsigma, vcsigma, vxc) + + ! finalize libxc objects + call xc_f03_func_end(xcfunc_x) + call xc_f03_func_end(xcfunc_c) + + end subroutine getExcVxc_MGGA_SCAN + + !> Calculates exc, vxc, and vtau for the MGGA-r2SCAN xc-functional. + subroutine getExcVxc_MGGA_r2SCAN(abcissa, dz, dzdr, rho, drho, sigma, tau, exc, vxc, vtau) + + !> numerical integration abcissas + real(dp), intent(in) :: abcissa(:) + + !> step width in linear coordinates + real(dp), intent(in) :: dz + + !> dz/dr + real(dp), intent(in) :: dzdr(:) + + !> density on grid + real(dp), intent(in) :: rho(:,:) + + !> 1st deriv. of density on grid + real(dp), intent(in) :: drho(:,:) + + !> contracted gradients of the density + real(dp), intent(in), allocatable :: sigma(:,:) + + !> Kinetic energy density + real(dp), intent(in):: tau(:,:) + + !> exc energy density on grid + real(dp), intent(out) :: exc(:) + + !> xc potential on grid + real(dp), intent(out) :: vxc(:,:) + + !> orbital-dependent tau potential on grid + real(dp), intent(out) :: vtau(:, :) + + !! density in libxc compatible format, i.e. rho/(4pi) + real(dp), allocatable :: rhor(:,:) + + !! Kinetic energy density (in libxc compatible format) + real(dp), allocatable :: tau_libxc(:,:) + + !! libxc related objects + type(xc_f03_func_t) :: xcfunc_x, xcfunc_c + + !! number of density grid points + integer(c_size_t) :: nn + + !! exchange and correlation energy on grid + real(dp), allocatable :: ex(:), ec(:) + + !! exchange and correlation potential on grid + real(dp), allocatable :: vx(:,:), vc(:,:) + + !! first partial derivative of the energy per unit volume in terms of sigma (exchange) + real(dp), allocatable :: vxsigma(:,:) + + !! first partial derivative of the energy per unit volume in terms of sigma (correlation) + real(dp), allocatable :: vcsigma(:,:) + + !! first partial derivative of the energy per unit volume in terms of tau (exchange) + real(dp), allocatable :: vxtau(:,:) + + !! first partial derivative of the energy per unit volume in terms of tau (correlation) + real(dp), allocatable :: vctau(:,:) + + !! laplacian for libxc (dummy) + real(dp), allocatable :: lapl(:,:) + + !! first partial derivative of the energy per unit volume in terms of laplacian (exchange) (dummy) + real(dp), allocatable :: vxlapl(:,:) + + !! first partial derivative of the energy per unit volume in terms of laplacian (correlation) (dummy) + real(dp), allocatable :: vclapl(:,:) + + nn = size(rho, dim=1) + ! divide by 4*pi to catch different normalization of spherical harmonics + allocate(rhor(2, nn)) + rhor(:,:) = transpose(rho) * rec4pi + + allocate(tau_libxc(2, nn)) + tau_libxc(:,:) = transpose(tau) * rec4pi + + allocate(ex(nn)) + ex(:) = 0.0_dp + allocate(ec(nn)) + ec(:) = 0.0_dp + allocate(vx(2, nn)) + vx(:,:) = 0.0_dp + allocate(vc(2, nn)) + vc(:,:) = 0.0_dp + + allocate(vxsigma(3, nn)) + vxsigma(:,:) = 0.0_dp + allocate(vcsigma(3, nn)) + vcsigma(:,:) = 0.0_dp + + allocate(vxtau(2, nn)) + vxtau(:,:) = 0.0_dp + allocate(vctau(2, nn)) + vctau(:,:) = 0.0_dp + + allocate(lapl(2, nn)) + lapl(:, :) = 0.0_dp + allocate(vxlapl(2, nn)) + vxlapl(:,:) = 0.0_dp + allocate(vclapl(2, nn)) + vclapl(:,:) = 0.0_dp + + call xc_f03_func_init(xcfunc_x, XC_MGGA_X_R2SCAN, XC_POLARIZED) + call xc_f03_func_init(xcfunc_c, XC_MGGA_C_R2SCAN, XC_POLARIZED) + + ! Exchange energy and potential + call xc_f03_mgga_exc_vxc(xcfunc_x, nn, rhor(1, 1), sigma(1, 1), lapl(1, 1), tau_libxc(1, 1),& + & ex(1), vx(1, 1), vxsigma(1, 1), vxlapl(1, 1), vxtau(1, 1)) + ! Correlation energy and potential + call xc_f03_mgga_exc_vxc(xcfunc_c, nn, rhor(1, 1), sigma(1, 1), lapl(1, 1), tau_libxc(1, 1),& + & ec(1), vc(1, 1), vcsigma(1, 1), vclapl(1, 1), vctau(1, 1)) + + call zeroOutCpotOfEmptyDensitySpinChannels(rho, vc) + + exc(:) = ex + ec + vxc(:,:) = transpose(vx + vc) + vtau(:, :) = transpose(vxtau + vctau) + + call libxcVxcToInternalVxc(abcissa, dz, dzdr, drho, vxsigma, vcsigma, vxc) + + ! finalize libxc objects + call xc_f03_func_end(xcfunc_x) + call xc_f03_func_end(xcfunc_c) + + end subroutine getExcVxc_MGGA_r2SCAN + + !> Calculates exc, vxc, and vtau for the MGGA-r4SCAN xc-functional. + subroutine getExcVxc_MGGA_r4SCAN(abcissa, dz, dzdr, rho, drho, sigma, tau, exc, vxc, vtau) + + !> numerical integration abcissas + real(dp), intent(in) :: abcissa(:) + + !> step width in linear coordinates + real(dp), intent(in) :: dz + + !> dz/dr + real(dp), intent(in) :: dzdr(:) + + !> density on grid + real(dp), intent(in) :: rho(:,:) + + !> 1st deriv. of density on grid + real(dp), intent(in) :: drho(:,:) + + !> contracted gradients of the density + real(dp), intent(in), allocatable :: sigma(:,:) + + !> Kinetic energy density + real(dp), intent(in):: tau(:,:) + + !> exc energy density on grid + real(dp), intent(out) :: exc(:) + + !> xc potential on grid + real(dp), intent(out) :: vxc(:,:) + + !> orbital-dependent tau potential on grid + real(dp), intent(out) :: vtau(:, :) + + !! density in libxc compatible format, i.e. rho/(4pi) + real(dp), allocatable :: rhor(:,:) + + !! Kinetic energy density (in libxc compatible format) + real(dp), allocatable :: tau_libxc(:,:) + + !! libxc related objects + type(xc_f03_func_t) :: xcfunc_x, xcfunc_c + + !! number of density grid points + integer(c_size_t) :: nn + + !! exchange and correlation energy on grid + real(dp), allocatable :: ex(:), ec(:) + + !! exchange and correlation potential on grid + real(dp), allocatable :: vx(:,:), vc(:,:) + + !! first partial derivative of the energy per unit volume in terms of sigma (exchange) + real(dp), allocatable :: vxsigma(:,:) + + !! first partial derivative of the energy per unit volume in terms of sigma (correlation) + real(dp), allocatable :: vcsigma(:,:) + + !! first partial derivative of the energy per unit volume in terms of tau (exchange) + real(dp), allocatable :: vxtau(:,:) + + !! first partial derivative of the energy per unit volume in terms of tau (correlation) + real(dp), allocatable :: vctau(:,:) + + !! laplacian for libxc (dummy) + real(dp), allocatable :: lapl(:,:) + + !! first partial derivative of the energy per unit volume in terms of laplacian (exchange) (dummy) + real(dp), allocatable :: vxlapl(:,:) + + !! first partial derivative of the energy per unit volume in terms of laplacian (correlation) (dummy) + real(dp), allocatable :: vclapl(:,:) + + nn = size(rho, dim=1) + ! divide by 4*pi to catch different normalization of spherical harmonics + allocate(rhor(2, nn)) + rhor(:,:) = transpose(rho) * rec4pi + + allocate(tau_libxc(2, nn)) + tau_libxc(:,:) = transpose(tau) * rec4pi + + allocate(ex(nn)) + ex(:) = 0.0_dp + allocate(ec(nn)) + ec(:) = 0.0_dp + allocate(vx(2, nn)) + vx(:,:) = 0.0_dp + allocate(vc(2, nn)) + vc(:,:) = 0.0_dp + + allocate(vxsigma(3, nn)) + vxsigma(:,:) = 0.0_dp + allocate(vcsigma(3, nn)) + vcsigma(:,:) = 0.0_dp + + allocate(vxtau(2, nn)) + vxtau(:,:) = 0.0_dp + allocate(vctau(2, nn)) + vctau(:,:) = 0.0_dp + + allocate(lapl(2, nn)) + lapl(:, :) = 0.0_dp + allocate(vxlapl(2, nn)) + vxlapl(:,:) = 0.0_dp + allocate(vclapl(2, nn)) + vclapl(:,:) = 0.0_dp + + call xc_f03_func_init(xcfunc_x, XC_MGGA_X_R4SCAN, XC_POLARIZED) + call xc_f03_func_init(xcfunc_c, XC_MGGA_C_R2SCAN, XC_POLARIZED) + + ! Exchange energy and potential + call xc_f03_mgga_exc_vxc(xcfunc_x, nn, rhor(1, 1), sigma(1, 1), lapl(1, 1), tau_libxc(1, 1),& + & ex(1), vx(1, 1), vxsigma(1, 1), vxlapl(1, 1), vxtau(1, 1)) + ! Correlation energy and potential + call xc_f03_mgga_exc_vxc(xcfunc_c, nn, rhor(1, 1), sigma(1, 1), lapl(1, 1), tau_libxc(1, 1),& + & ec(1), vc(1, 1), vcsigma(1, 1), vclapl(1, 1), vctau(1, 1)) + + call zeroOutCpotOfEmptyDensitySpinChannels(rho, vc) + + exc(:) = ex + ec + vxc(:,:) = transpose(vx + vc) + vtau(:, :) = transpose(vxtau + vctau) + + call libxcVxcToInternalVxc(abcissa, dz, dzdr, drho, vxsigma, vcsigma, vxc) + + ! finalize libxc objects + call xc_f03_func_end(xcfunc_x) + call xc_f03_func_end(xcfunc_c) + + end subroutine getExcVxc_MGGA_r4SCAN + + !> Calculates exc, vxc, and vtau for the MGGA-TASK xc-functional. + subroutine getExcVxc_MGGA_TASK(abcissa, dz, dzdr, rho, drho, sigma, tau, exc, vxc, vtau) + + !> numerical integration abcissas + real(dp), intent(in) :: abcissa(:) + + !> step width in linear coordinates + real(dp), intent(in) :: dz + + !> dz/dr + real(dp), intent(in) :: dzdr(:) + + !> density on grid + real(dp), intent(in) :: rho(:,:) + + !> 1st deriv. of density on grid + real(dp), intent(in) :: drho(:,:) + + !> contracted gradients of the density + real(dp), intent(in), allocatable :: sigma(:,:) + + !> Kinetic energy density + real(dp), intent(in) :: tau(:,:) + + !> exc energy density on grid + real(dp), intent(out) :: exc(:) + + !> xc potential on grid + real(dp), intent(out) :: vxc(:,:) + + !> orbital-dependent tau potential on grid + real(dp), intent(out) :: vtau(:, :) + + !! density in libxc compatible format, i.e. rho/(4pi) + real(dp), allocatable :: rhor(:,:) + + !! Kinetic energy density + real(dp), allocatable :: tau_libxc(:,:) + + !! libxc related objects + type(xc_f03_func_t) :: xcfunc_x, xcfunc_c + + !! number of density grid points + integer(c_size_t) :: nn + + !! exchange and correlation energy on grid + real(dp), allocatable :: ex(:), ec(:) + + !! exchange and correlation potential on grid + real(dp), allocatable :: vx(:,:), vc(:,:) + + !! first partial derivative of the energy per unit volume in terms of sigma (exchange) + real(dp), allocatable :: vxsigma(:,:) + + !! first partial derivative of the energy per unit volume in terms of tau (exchange) + real(dp), allocatable :: vxtau(:,:) + + !! laplacian for libxc (dummy) + real(dp), allocatable :: lapl(:,:) + + !! first partial derivative of the energy per unit volume in terms of laplacian (exchange) (dummy) + real(dp), allocatable :: vxlapl(:,:) + + nn = size(rho, dim=1) + ! divide by 4*pi to catch different normalization of spherical harmonics + allocate(rhor(2, nn)) + rhor(:,:) = transpose(rho) * rec4pi + + allocate(tau_libxc(2, nn)) + tau_libxc(:,:) = transpose(tau) * rec4pi + + allocate(ex(nn)) + ex(:) = 0.0_dp + allocate(ec(nn)) + ec(:) = 0.0_dp + allocate(vx(2, nn)) + vx(:,:) = 0.0_dp + allocate(vc(2, nn)) + vc(:,:) = 0.0_dp + + allocate(vxsigma(3, nn)) + vxsigma(:,:) = 0.0_dp + + allocate(vxtau(2, nn)) + vxtau(:,:) = 0.0_dp + + allocate(lapl(2, nn)) + lapl(:, :) = 0.0_dp + allocate(vxlapl(2, nn)) + vxlapl(:,:) = 0.0_dp + + call xc_f03_func_init(xcfunc_x, XC_MGGA_X_TASK, XC_POLARIZED) + call xc_f03_func_init(xcfunc_c, XC_LDA_C_PW, XC_POLARIZED) + + ! Exchange energy and potential + call xc_f03_mgga_exc_vxc(xcfunc_x, nn, rhor(1, 1), sigma(1, 1), lapl(1, 1), tau_libxc(1, 1),& + & ex(1), vx(1, 1), vxsigma(1, 1), vxlapl(1, 1), vxtau(1, 1)) + ! Correlation energy and potential + call xc_f03_lda_exc_vxc(xcfunc_c, nn, rhor(1, 1), ec(1), vc(1, 1)) + call zeroOutCpotOfEmptyDensitySpinChannels(rho, vc) + + exc(:) = ex + ec + vxc(:,:) = transpose(vx + vc) + vtau(:, :) = transpose(vxtau) + + call libxcVxcToInternalVxc(abcissa, dz, dzdr, drho, vxsigma, vxc) + + ! finalize libxc objects + call xc_f03_func_end(xcfunc_x) + call xc_f03_func_end(xcfunc_c) + + end subroutine getExcVxc_MGGA_TASK + + !> Calculates exc, vxc, and vtau for the MGGA-TASK+CC xc-functional. + subroutine getExcVxc_MGGA_TASK_CC(abcissa, dz, dzdr, rho, drho, sigma, tau, exc, vxc, vtau) + + ! TASK exchange with CC correlation + ! correlation: 10.1063/1.4865942 + ! total functional: 10.1103/PhysRevResearch.4.023061 + + !> numerical integration abcissas + real(dp), intent(in) :: abcissa(:) + + !> step width in linear coordinates + real(dp), intent(in) :: dz + + !> dz/dr + real(dp), intent(in) :: dzdr(:) + + !> density on grid + real(dp), intent(in) :: rho(:,:) + + !> 1st deriv. of density on grid + real(dp), intent(in) :: drho(:,:) + + !> contracted gradients of the density + real(dp), intent(in), allocatable :: sigma(:,:) + + !> Kinetic energy density + real(dp), intent(in):: tau(:,:) + + !> exc energy density on grid + real(dp), intent(out) :: exc(:) + + !> xc potential on grid + real(dp), intent(out) :: vxc(:,:) + + !> orbital-dependent tau potential on grid + real(dp), intent(out) :: vtau(:, :) + + !! density in libxc compatible format, i.e. rho/(4pi) + real(dp), allocatable :: rhor(:,:) + + !! Kinetic energy density (in libxc compatible format) + real(dp), allocatable :: tau_libxc(:,:) + + !! libxc related objects + type(xc_f03_func_t) :: xcfunc_x, xcfunc_c + + !! number of density grid points + integer(c_size_t) :: nn + + !! exchange and correlation energy on grid + real(dp), allocatable :: ex(:), ec(:) + + !! exchange and correlation potential on grid + real(dp), allocatable :: vx(:,:), vc(:,:) + + !! first partial derivative of the energy per unit volume in terms of sigma (exchange) + real(dp), allocatable :: vxsigma(:,:) + + !! first partial derivative of the energy per unit volume in terms of sigma (correlation) + real(dp), allocatable :: vcsigma(:,:) + + !! first partial derivative of the energy per unit volume in terms of tau (exchange) + real(dp), allocatable :: vxtau(:,:) + + !! first partial derivative of the energy per unit volume in terms of tau (correlation) + real(dp), allocatable :: vctau(:,:) + + !! laplacian for libxc (dummy) + real(dp), allocatable :: lapl(:,:) + + !! first partial derivative of the energy per unit volume in terms of laplacian (exchange) (dummy) + real(dp), allocatable :: vxlapl(:,:) + + !! first partial derivative of the energy per unit volume in terms of laplacian (correlation) (dummy) + real(dp), allocatable :: vclapl(:,:) + + nn = size(rho, dim=1) + ! divide by 4*pi to catch different normalization of spherical harmonics + allocate(rhor(2, nn)) + rhor(:,:) = transpose(rho) * rec4pi + + allocate(tau_libxc(2, nn)) + tau_libxc(:,:) = transpose(tau) * rec4pi + + allocate(ex(nn)) + ex(:) = 0.0_dp + allocate(ec(nn)) + ec(:) = 0.0_dp + allocate(vx(2, nn)) + vx(:,:) = 0.0_dp + allocate(vc(2, nn)) + vc(:,:) = 0.0_dp + + allocate(vxsigma(3, nn)) + vxsigma(:,:) = 0.0_dp + allocate(vcsigma(3, nn)) + vcsigma(:,:) = 0.0_dp + + allocate(vxtau(2, nn)) + vxtau(:,:) = 0.0_dp + allocate(vctau(2, nn)) + vctau(:,:) = 0.0_dp + + allocate(lapl(2, nn)) + lapl(:, :) = 0.0_dp + allocate(vxlapl(2, nn)) + vxlapl(:,:) = 0.0_dp + allocate(vclapl(2, nn)) + vclapl(:,:) = 0.0_dp + + call xc_f03_func_init(xcfunc_x, XC_MGGA_X_TASK, XC_POLARIZED) + call xc_f03_func_init(xcfunc_c, XC_MGGA_C_CC, XC_POLARIZED) + + ! Exchange energy and potential + call xc_f03_mgga_exc_vxc(xcfunc_x, nn, rhor(1, 1), sigma(1, 1), lapl(1, 1), tau_libxc(1, 1),& + & ex(1), vx(1, 1), vxsigma(1, 1), vxlapl(1, 1), vxtau(1, 1)) + ! Correlation energy and potential + call xc_f03_mgga_exc_vxc(xcfunc_c, nn, rhor(1, 1), sigma(1, 1), lapl(1, 1), tau_libxc(1, 1),& + & ec(1), vc(1, 1), vcsigma(1, 1), vclapl(1, 1), vctau(1, 1)) + + call zeroOutCpotOfEmptyDensitySpinChannels(rho, vc) + + exc(:) = ex + ec + vxc(:,:) = transpose(vx + vc) + vtau(:, :) = transpose(vxtau + vctau) + + call libxcVxcToInternalVxc(abcissa, dz, dzdr, drho, vxsigma, vcsigma, vxc) + + ! finalize libxc objects + call xc_f03_func_end(xcfunc_x) + call xc_f03_func_end(xcfunc_c) + + end subroutine getExcVxc_MGGA_TASK_CC !> Calculates exc and vxc for the LCY-PBE96 xc-functional. subroutine getExcVxc_LCY_PBE96(abcissa, dz, dzdr, rho, drho, sigma, omega, exc, vxc) diff --git a/slateratom/prog/main.f90 b/slateratom/prog/main.f90 index a4143149..4301fb0b 100644 --- a/slateratom/prog/main.f90 +++ b/slateratom/prog/main.f90 @@ -12,9 +12,10 @@ program HFAtom use output, only : write_eigvec, write_eigval, write_moments, write_energies,& & write_energies_tagged, write_potentials_file_standard, write_densities_file_standard,& & write_waves_file_standard, write_wave_coeffs_file, cusp_values, writeAveragePotential + use sap, only : sap_start_pot use totalenergy, only : getTotalEnergy, getTotalEnergyZora - use dft, only : check_accuracy, dft_start_pot, density_grid - use utilities, only : check_electron_number, check_convergence + use dft, only : check_accuracy, density_grid + use utilities, only : check_electron_number, check_convergence_energy, check_convergence_orbgrad use zora_routines, only : scaled_zora use cmdargs, only : parse_command_arguments use common_poisson, only : TBeckeGridParams @@ -73,6 +74,14 @@ program HFAtom if (nuc > 36) num_mesh_points = 1250 if (nuc > 54) num_mesh_points = 1500 + !> meta-GGA functionals exhibit extraordinary + !> sensititvity with respect to grid, which + !> especially affects convergence with tight + !> settings; see 10.1063/5.0121187 + if (xcFunctional%isMGGA(xcnr)) then + num_mesh_points = num_mesh_points + 2000 + end if + call echo_input(nuc, max_l, occ_shells, maxiter, scftol, poly_order, num_alpha, alpha, conf_r0,& & conf_power, occ, num_occ, num_power, num_alphas, xcnr, tZora, num_mesh_points, xalpha_const) @@ -109,12 +118,15 @@ program HFAtom call hfex_lr(kk_lr, max_l, num_alpha, alpha, poly_order, problemsize, omega, grid_params) end if - ! convergence flag - tConverged = .false. + ! convergence flags + tOrbGradConverged = .false. + tEnergyConverged = .false. - ! DFT start potential + ! Generate guess for DFT; + !> Thomas-Fermi guess potential is currently disabled if (.not. (xcnr == xcFunctional%HF_Exchange)) then - call dft_start_pot(abcissa, num_mesh_points, nuc, vxc) + !> SAP potential + call sap_start_pot(abcissa, num_mesh_points, nuc, vxc) end if ! build initial fock matrix, core hamiltonian only @@ -126,17 +138,18 @@ program HFAtom ! kinetic energy, nuclear-electron, and confinement matrix elements which are constant during SCF call build_hamiltonian(pMixer, 0, tt, uu, nuc, vconf, jj, kk, kk_lr, pp, max_l, num_alpha,& - & poly_order, problemsize, xcnr, num_mesh_points, weight, abcissa, vxc, alpha, pot_old,& + & poly_order, problemsize, xcnr, num_mesh_points, weight, abcissa, vxc, vtau, alpha, pot_old,& & pot_new, tZora, ff, camAlpha, camBeta) ! self-consistency cycles write(*,*) 'Energies in Hartree' write(*,*) - write(*,*) ' Iter | Total energy | HF-X energy | XC energy | Change in pot' - write(*,*) '--------------------------------------------------------------------------' + write(*,*) ' Iter | Total energy | HF-X energy | XC energy | Orbital gradient norm | Delta (Total energy) ' + write(*,*) '-----------------------------------------------------------------------------------------------------------' lpScf: do iScf = 1, maxiter pot_old(:,:,:,:) = pot_new + total_ene_old = total_ene ! diagonalize call diagonalize(max_l, num_alpha, poly_order, ff, ss, cof, eigval) @@ -146,11 +159,11 @@ program HFAtom ! get electron density, derivatives, exc related potentials and energy densities call density_grid(pp, max_l, num_alpha, poly_order, alpha, num_mesh_points, abcissa, dzdr,& - & dz, xcnr, omega, camAlpha, camBeta, rho, drho, ddrho, vxc, exc, xalpha_const) + & dz, xcnr, omega, camAlpha, camBeta, rho, drho, ddrho, tau, vxc, vtau, exc, xalpha_const) ! build Fock matrix and get total energy during SCF call build_hamiltonian(pMixer, iScf, tt, uu, nuc, vconf, jj, kk, kk_lr, pp, max_l, num_alpha,& - & poly_order, problemsize, xcnr, num_mesh_points, weight, abcissa, vxc, alpha, pot_old,& + & poly_order, problemsize, xcnr, num_mesh_points, weight, abcissa, vxc, vtau, alpha, pot_old,& & pot_new, tZora, ff, camAlpha, camBeta) if (tZora) then @@ -164,13 +177,14 @@ program HFAtom & nuclear_energy, coulomb_energy, exchange_energy, x_en_2, conf_energy, total_ene) end if - call check_convergence(pot_old, pot_new, max_l, problemsize, scftol, iScf, change_max,& - & tConverged) + call check_convergence_orbgrad(max_l, num_alpha, poly_order, ff, cof, occ, scftol, iScf, orb_grad_norm, tOrbGradConverged) + call check_convergence_energy(total_ene_old, total_ene, scftol, iScf, total_ene_diff, tEnergyConverged) - write(*, '(I4,2X,3(1X,F16.9),3X,E16.9)') iScf, total_ene, exchange_energy, x_en_2, change_max + ! Print SCF loop information + write(*, '(I4,2X,3(1X,F16.9),7X,E16.9,8X,E16.9)') iScf, total_ene, exchange_energy, x_en_2, orb_grad_norm, total_ene_diff ! if self-consistency is reached, exit loop - if (tConverged) exit lpScf + if (tOrbGradConverged .and. tEnergyConverged) exit lpScf ! check conservation of number of electrons during SCF call check_electron_number(cof, ss, occ, max_l, num_alpha, poly_order, problemsize) @@ -180,7 +194,7 @@ program HFAtom end do lpScf ! handle non-converged calculations - if (.not. tConverged) then + if (.not. (tEnergyConverged .and. tOrbGradConverged)) then call error('SCF is NOT converged, maximal SCF iterations exceeded.') end if @@ -212,7 +226,7 @@ program HFAtom & conf_energy, total_ene) end if - write(*, '(A,E20.12)') 'Potential Matrix Elements converged to ', change_max + write(*, '(A,E20.12)') 'Occupied-virtual orbital gradient converged to ', orb_grad_norm write(*, '(A)') ' ' if (tZora) then @@ -226,7 +240,7 @@ program HFAtom call write_potentials_file_standard(num_mesh_points, abcissa, weight, vxc, rho, nuc, pp, max_l,& & num_alpha, poly_order, alpha, problemsize) - call write_densities_file_standard(num_mesh_points, abcissa, weight, rho, drho, ddrho) + call write_densities_file_standard(num_mesh_points, abcissa, weight, rho, drho, ddrho, tau) ! write wave functions and eventually invert to have positive starting gradient call write_waves_file_standard(num_mesh_points, abcissa, weight, alpha, num_alpha, poly_order,&