/
getLebedevSphere.m
5382 lines (5146 loc) · 221 KB
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getLebedevSphere.m
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% Copyright (c) 2010, Robert Parrish
% 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
% 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 OWNER OR CONTRIBUTORS 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.
%
function [leb_tmp] = getLebedevSphere(degree)
%
% getLebedevSphere
% @author Rob Parrish, The Sherrill Group, CCMST Georgia Tech
% @email robparrish@gmail.com
% @date 03/24/2010
%
% @description - function to compute normalized points and weights
% for Lebedev quadratures on the surface of the unit sphere at double precision.
% **********Relative error is generally expected to be ~2.0E-14 [1]********
% Lebedev quadratures are superbly accurate and efficient quadrature rules for
% approximating integrals of the form $v = \iint_{4\pi} f(\Omega) \ \ud
% \Omega$, where $\Omega is the solid angle on the surface of the unit
% sphere. Lebedev quadratures integrate all spherical harmonics up to $l =
% order$, where $degree \approx order(order+1)/3$. These grids may be easily
% combined with radial quadratures to provide robust cubature formulae. For
% example, see 'A. Becke, 1988c, J. Chem. Phys., 88(4), pp. 2547' (The first
% paper on tractable molecular Density Functional Theory methods, of which
% Lebedev grids and numerical cubature are an intrinsic part).
%
% @param degree - positive integer specifying number of points in the
% requested quadrature. Allowed values are (degree -> order):
% degree: { 6, 14, 26, 38, 50, 74, 86, 110, 146, 170, 194, 230, 266, 302,
% 350, 434, 590, 770, 974, 1202, 1454, 1730, 2030, 2354, 2702, 3074,
% 3470, 3890, 4334, 4802, 5294, 5810 };
% order: {3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,35,41,47,53,59,65,71,77,
% 83,89,95,101,107,113,119,125,131};
%
%
% @return leb_tmp - struct containing fields:
% x - x values of quadrature, constrained to unit sphere
% y - y values of quadrature, constrained to unit sphere
% z - z values of quadrature, constrained to unit sphere
% w - quadrature weights, normalized to $4\pi$.
%
% @example: $\int_S x^2+y^2-z^2 \ud \Omega = 4.188790204786399$
% f = @(x,y,z) x.^2+y.^2-z.^2;
% leb = getLebedevSphere(590);
% v = f(leb.x,leb.y,leb.z);
% int = sum(v.*leb.w);
%
% @citation - Translated from a Fortran code kindly provided by Christoph van
% Wuellen (Ruhr-Universitaet, Bochum, Germany), which in turn came from the
% original C routines coded by Dmitri Laikov (Moscow State University,
% Moscow, Russia). The MATLAB implementation of this code is designed for
% benchmarking of new DFT integration techniques to be implemented in the
% open source Psi4 ab initio quantum chemistry program.
%
% As per Professor Wuellen's request, any papers published using this code
% or its derivatives are requested to include the following citation:
%
% [1] V.I. Lebedev, and D.N. Laikov
% "A quadrature formula for the sphere of the 131st
% algebraic order of accuracy"
% Doklady Mathematics, Vol. 59, No. 3, 1999, pp. 477-481.
leb_tmp.x = zeros(degree,1);
leb_tmp.y = zeros(degree,1);
leb_tmp.z = zeros(degree,1);
leb_tmp.w = zeros(degree,1);
start = 1;
a = 0.0;
b = 0.0;
c = 0.0;
v = 0.0;
switch (degree)
case 6
v=0.1666666666666667E+0;
[leb_tmp start] = getLebedevReccurencePoints(1,start,a,b,v,leb_tmp);
case 14
v=0.6666666666666667E-1;
[leb_tmp start] = getLebedevReccurencePoints(1,start,a,b,v,leb_tmp);
v=0.7500000000000000E-1;
[leb_tmp start] = getLebedevReccurencePoints(3,start,a,b,v,leb_tmp);
case 26
v=0.4761904761904762E-1;
[leb_tmp start] = getLebedevReccurencePoints(1,start,a,b,v,leb_tmp);
v=0.3809523809523810E-1;
[leb_tmp start] = getLebedevReccurencePoints(2,start,a,b,v,leb_tmp);
v=0.3214285714285714E-1;
[leb_tmp start] = getLebedevReccurencePoints(3,start,a,b,v,leb_tmp);
case 38
v=0.9523809523809524E-2;
[leb_tmp start] = getLebedevReccurencePoints(1,start,a,b,v,leb_tmp);
v=0.3214285714285714E-1;
[leb_tmp start] = getLebedevReccurencePoints(3,start,a,b,v,leb_tmp);
a=0.4597008433809831E+0;
v=0.2857142857142857E-1;
[leb_tmp start] = getLebedevReccurencePoints(5,start,a,b,v,leb_tmp);
case 50
v=0.1269841269841270E-1;
[leb_tmp start] = getLebedevReccurencePoints(1,start,a,b,v,leb_tmp);
v=0.2257495590828924E-1;
[leb_tmp start] = getLebedevReccurencePoints(2,start,a,b,v,leb_tmp);
v=0.2109375000000000E-1;
[leb_tmp start] = getLebedevReccurencePoints(3,start,a,b,v,leb_tmp);
a=0.3015113445777636E+0;
v=0.2017333553791887E-1;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
case 74
v=0.5130671797338464E-3;
[leb_tmp start] = getLebedevReccurencePoints(1,start,a,b,v,leb_tmp);
v=0.1660406956574204E-1;
[leb_tmp start] = getLebedevReccurencePoints(2,start,a,b,v,leb_tmp);
v=-0.2958603896103896E-1;
[leb_tmp start] = getLebedevReccurencePoints(3,start,a,b,v,leb_tmp);
a=0.4803844614152614E+0;
v=0.2657620708215946E-1;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.3207726489807764E+0;
v=0.1652217099371571E-1;
[leb_tmp start] = getLebedevReccurencePoints(5,start,a,b,v,leb_tmp);
case 86
v=0.1154401154401154E-1;
[leb_tmp start] = getLebedevReccurencePoints(1,start,a,b,v,leb_tmp);
v=0.1194390908585628E-1;
[leb_tmp start] = getLebedevReccurencePoints(3,start,a,b,v,leb_tmp);
a=0.3696028464541502E+0;
v=0.1111055571060340E-1;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.6943540066026664E+0;
v=0.1187650129453714E-1;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.3742430390903412E+0;
v=0.1181230374690448E-1;
[leb_tmp start] = getLebedevReccurencePoints(5,start,a,b,v,leb_tmp);
case 110
v=0.3828270494937162E-2;
[leb_tmp start] = getLebedevReccurencePoints(1,start,a,b,v,leb_tmp);
v=0.9793737512487512E-2;
[leb_tmp start] = getLebedevReccurencePoints(3,start,a,b,v,leb_tmp);
a=0.1851156353447362E+0;
v=0.8211737283191111E-2;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.6904210483822922E+0;
v=0.9942814891178103E-2;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.3956894730559419E+0;
v=0.9595471336070963E-2;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.4783690288121502E+0;
v=0.9694996361663028E-2;
[leb_tmp start] = getLebedevReccurencePoints(5,start,a,b,v,leb_tmp);
case 146
v=0.5996313688621381E-3;
[leb_tmp start] = getLebedevReccurencePoints(1,start,a,b,v,leb_tmp);
v=0.7372999718620756E-2;
[leb_tmp start] = getLebedevReccurencePoints(2,start,a,b,v,leb_tmp);
v=0.7210515360144488E-2;
[leb_tmp start] = getLebedevReccurencePoints(3,start,a,b,v,leb_tmp);
a=0.6764410400114264E+0;
v=0.7116355493117555E-2;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.4174961227965453E+0;
v=0.6753829486314477E-2;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.1574676672039082E+0;
v=0.7574394159054034E-2;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.1403553811713183E+0;
b=0.4493328323269557E+0;
v=0.6991087353303262E-2;
[leb_tmp start] = getLebedevReccurencePoints(6,start,a,b,v,leb_tmp);
case 170
v=0.5544842902037365E-2;
[leb_tmp start] = getLebedevReccurencePoints(1,start,a,b,v,leb_tmp);
v=0.6071332770670752E-2;
[leb_tmp start] = getLebedevReccurencePoints(2,start,a,b,v,leb_tmp);
v=0.6383674773515093E-2;
[leb_tmp start] = getLebedevReccurencePoints(3,start,a,b,v,leb_tmp);
a=0.2551252621114134E+0;
v=0.5183387587747790E-2;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.6743601460362766E+0;
v=0.6317929009813725E-2;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.4318910696719410E+0;
v=0.6201670006589077E-2;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.2613931360335988E+0;
v=0.5477143385137348E-2;
[leb_tmp start] = getLebedevReccurencePoints(5,start,a,b,v,leb_tmp);
a=0.4990453161796037E+0;
b=0.1446630744325115E+0;
v=0.5968383987681156E-2;
[leb_tmp start] = getLebedevReccurencePoints(6,start,a,b,v,leb_tmp);
case 194
v=0.1782340447244611E-2;
[leb_tmp start] = getLebedevReccurencePoints(1,start,a,b,v,leb_tmp);
v=0.5716905949977102E-2;
[leb_tmp start] = getLebedevReccurencePoints(2,start,a,b,v,leb_tmp);
v=0.5573383178848738E-2;
[leb_tmp start] = getLebedevReccurencePoints(3,start,a,b,v,leb_tmp);
a=0.6712973442695226E+0;
v=0.5608704082587997E-2;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.2892465627575439E+0;
v=0.5158237711805383E-2;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.4446933178717437E+0;
v=0.5518771467273614E-2;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.1299335447650067E+0;
v=0.4106777028169394E-2;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.3457702197611283E+0;
v=0.5051846064614808E-2;
[leb_tmp start] = getLebedevReccurencePoints(5,start,a,b,v,leb_tmp);
a=0.1590417105383530E+0;
b=0.8360360154824589E+0;
v=0.5530248916233094E-2;
[leb_tmp start] = getLebedevReccurencePoints(6,start,a,b,v,leb_tmp);
case 230
v=-0.5522639919727325E-1;
[leb_tmp start] = getLebedevReccurencePoints(1,start,a,b,v,leb_tmp);
v=0.4450274607445226E-2;
[leb_tmp start] = getLebedevReccurencePoints(3,start,a,b,v,leb_tmp);
a=0.4492044687397611E+0;
v=0.4496841067921404E-2;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.2520419490210201E+0;
v=0.5049153450478750E-2;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.6981906658447242E+0;
v=0.3976408018051883E-2;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.6587405243460960E+0;
v=0.4401400650381014E-2;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.4038544050097660E-1;
v=0.1724544350544401E-1;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.5823842309715585E+0;
v=0.4231083095357343E-2;
[leb_tmp start] = getLebedevReccurencePoints(5,start,a,b,v,leb_tmp);
a=0.3545877390518688E+0;
v=0.5198069864064399E-2;
[leb_tmp start] = getLebedevReccurencePoints(5,start,a,b,v,leb_tmp);
a=0.2272181808998187E+0;
b=0.4864661535886647E+0;
v=0.4695720972568883E-2;
[leb_tmp start] = getLebedevReccurencePoints(6,start,a,b,v,leb_tmp);
case 266
v=-0.1313769127326952E-2;
[leb_tmp start] = getLebedevReccurencePoints(1,start,a,b,v,leb_tmp);
v=-0.2522728704859336E-2;
[leb_tmp start] = getLebedevReccurencePoints(2,start,a,b,v,leb_tmp);
v=0.4186853881700583E-2;
[leb_tmp start] = getLebedevReccurencePoints(3,start,a,b,v,leb_tmp);
a=0.7039373391585475E+0;
v=0.5315167977810885E-2;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.1012526248572414E+0;
v=0.4047142377086219E-2;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.4647448726420539E+0;
v=0.4112482394406990E-2;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.3277420654971629E+0;
v=0.3595584899758782E-2;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.6620338663699974E+0;
v=0.4256131351428158E-2;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.8506508083520399E+0;
v=0.4229582700647240E-2;
[leb_tmp start] = getLebedevReccurencePoints(5,start,a,b,v,leb_tmp);
a=0.3233484542692899E+0;
b=0.1153112011009701E+0;
v=0.4080914225780505E-2;
[leb_tmp start] = getLebedevReccurencePoints(6,start,a,b,v,leb_tmp);
a=0.2314790158712601E+0;
b=0.5244939240922365E+0;
v=0.4071467593830964E-2;
[leb_tmp start] = getLebedevReccurencePoints(6,start,a,b,v,leb_tmp);
case 302
v=0.8545911725128148E-3;
[leb_tmp start] = getLebedevReccurencePoints(1,start,a,b,v,leb_tmp);
v=0.3599119285025571E-2;
[leb_tmp start] = getLebedevReccurencePoints(3,start,a,b,v,leb_tmp);
a=0.3515640345570105E+0;
v=0.3449788424305883E-2;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.6566329410219612E+0;
v=0.3604822601419882E-2;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.4729054132581005E+0;
v=0.3576729661743367E-2;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.9618308522614784E-1;
v=0.2352101413689164E-2;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.2219645236294178E+0;
v=0.3108953122413675E-2;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.7011766416089545E+0;
v=0.3650045807677255E-2;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.2644152887060663E+0;
v=0.2982344963171804E-2;
[leb_tmp start] = getLebedevReccurencePoints(5,start,a,b,v,leb_tmp);
a=0.5718955891878961E+0;
v=0.3600820932216460E-2;
[leb_tmp start] = getLebedevReccurencePoints(5,start,a,b,v,leb_tmp);
a=0.2510034751770465E+0;
b=0.8000727494073952E+0;
v=0.3571540554273387E-2;
[leb_tmp start] = getLebedevReccurencePoints(6,start,a,b,v,leb_tmp);
a=0.1233548532583327E+0;
b=0.4127724083168531E+0;
v=0.3392312205006170E-2;
[leb_tmp start] = getLebedevReccurencePoints(6,start,a,b,v,leb_tmp);
case 350
v=0.3006796749453936E-2;
[leb_tmp start] = getLebedevReccurencePoints(1,start,a,b,v,leb_tmp);
v=0.3050627745650771E-2;
[leb_tmp start] = getLebedevReccurencePoints(3,start,a,b,v,leb_tmp);
a=0.7068965463912316E+0;
v=0.1621104600288991E-2;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.4794682625712025E+0;
v=0.3005701484901752E-2;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.1927533154878019E+0;
v=0.2990992529653774E-2;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.6930357961327123E+0;
v=0.2982170644107595E-2;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.3608302115520091E+0;
v=0.2721564237310992E-2;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.6498486161496169E+0;
v=0.3033513795811141E-2;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.1932945013230339E+0;
v=0.3007949555218533E-2;
[leb_tmp start] = getLebedevReccurencePoints(5,start,a,b,v,leb_tmp);
a=0.3800494919899303E+0;
v=0.2881964603055307E-2;
[leb_tmp start] = getLebedevReccurencePoints(5,start,a,b,v,leb_tmp);
a=0.2899558825499574E+0;
b=0.7934537856582316E+0;
v=0.2958357626535696E-2;
[leb_tmp start] = getLebedevReccurencePoints(6,start,a,b,v,leb_tmp);
a=0.9684121455103957E-1;
b=0.8280801506686862E+0;
v=0.3036020026407088E-2;
[leb_tmp start] = getLebedevReccurencePoints(6,start,a,b,v,leb_tmp);
a=0.1833434647041659E+0;
b=0.9074658265305127E+0;
v=0.2832187403926303E-2;
[leb_tmp start] = getLebedevReccurencePoints(6,start,a,b,v,leb_tmp);
case 434
v=0.5265897968224436E-3;
[leb_tmp start] = getLebedevReccurencePoints(1,start,a,b,v,leb_tmp);
v=0.2548219972002607E-2;
[leb_tmp start] = getLebedevReccurencePoints(2,start,a,b,v,leb_tmp);
v=0.2512317418927307E-2;
[leb_tmp start] = getLebedevReccurencePoints(3,start,a,b,v,leb_tmp);
a=0.6909346307509111E+0;
v=0.2530403801186355E-2;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.1774836054609158E+0;
v=0.2014279020918528E-2;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.4914342637784746E+0;
v=0.2501725168402936E-2;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.6456664707424256E+0;
v=0.2513267174597564E-2;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.2861289010307638E+0;
v=0.2302694782227416E-2;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.7568084367178018E-1;
v=0.1462495621594614E-2;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.3927259763368002E+0;
v=0.2445373437312980E-2;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.8818132877794288E+0;
v=0.2417442375638981E-2;
[leb_tmp start] = getLebedevReccurencePoints(5,start,a,b,v,leb_tmp);
a=0.9776428111182649E+0;
v=0.1910951282179532E-2;
[leb_tmp start] = getLebedevReccurencePoints(5,start,a,b,v,leb_tmp);
a=0.2054823696403044E+0;
b=0.8689460322872412E+0;
v=0.2416930044324775E-2;
[leb_tmp start] = getLebedevReccurencePoints(6,start,a,b,v,leb_tmp);
a=0.5905157048925271E+0;
b=0.7999278543857286E+0;
v=0.2512236854563495E-2;
[leb_tmp start] = getLebedevReccurencePoints(6,start,a,b,v,leb_tmp);
a=0.5550152361076807E+0;
b=0.7717462626915901E+0;
v=0.2496644054553086E-2;
[leb_tmp start] = getLebedevReccurencePoints(6,start,a,b,v,leb_tmp);
a=0.9371809858553722E+0;
b=0.3344363145343455E+0;
v=0.2236607760437849E-2;
[leb_tmp start] = getLebedevReccurencePoints(6,start,a,b,v,leb_tmp);
case 590
v=0.3095121295306187E-3;
[leb_tmp start] = getLebedevReccurencePoints(1,start,a,b,v,leb_tmp);
v=0.1852379698597489E-2;
[leb_tmp start] = getLebedevReccurencePoints(3,start,a,b,v,leb_tmp);
a=0.7040954938227469E+0;
v=0.1871790639277744E-2;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.6807744066455243E+0;
v=0.1858812585438317E-2;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.6372546939258752E+0;
v=0.1852028828296213E-2;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.5044419707800358E+0;
v=0.1846715956151242E-2;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.4215761784010967E+0;
v=0.1818471778162769E-2;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.3317920736472123E+0;
v=0.1749564657281154E-2;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.2384736701421887E+0;
v=0.1617210647254411E-2;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.1459036449157763E+0;
v=0.1384737234851692E-2;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.6095034115507196E-1;
v=0.9764331165051050E-3;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.6116843442009876E+0;
v=0.1857161196774078E-2;
[leb_tmp start] = getLebedevReccurencePoints(5,start,a,b,v,leb_tmp);
a=0.3964755348199858E+0;
v=0.1705153996395864E-2;
[leb_tmp start] = getLebedevReccurencePoints(5,start,a,b,v,leb_tmp);
a=0.1724782009907724E+0;
v=0.1300321685886048E-2;
[leb_tmp start] = getLebedevReccurencePoints(5,start,a,b,v,leb_tmp);
a=0.5610263808622060E+0;
b=0.3518280927733519E+0;
v=0.1842866472905286E-2;
[leb_tmp start] = getLebedevReccurencePoints(6,start,a,b,v,leb_tmp);
a=0.4742392842551980E+0;
b=0.2634716655937950E+0;
v=0.1802658934377451E-2;
[leb_tmp start] = getLebedevReccurencePoints(6,start,a,b,v,leb_tmp);
a=0.5984126497885380E+0;
b=0.1816640840360209E+0;
v=0.1849830560443660E-2;
[leb_tmp start] = getLebedevReccurencePoints(6,start,a,b,v,leb_tmp);
a=0.3791035407695563E+0;
b=0.1720795225656878E+0;
v=0.1713904507106709E-2;
[leb_tmp start] = getLebedevReccurencePoints(6,start,a,b,v,leb_tmp);
a=0.2778673190586244E+0;
b=0.8213021581932511E-1;
v=0.1555213603396808E-2;
[leb_tmp start] = getLebedevReccurencePoints(6,start,a,b,v,leb_tmp);
a=0.5033564271075117E+0;
b=0.8999205842074875E-1;
v=0.1802239128008525E-2;
[leb_tmp start] = getLebedevReccurencePoints(6,start,a,b,v,leb_tmp);
case 770
v=0.2192942088181184E-3;
[leb_tmp start] = getLebedevReccurencePoints(1,start,a,b,v,leb_tmp);
v=0.1436433617319080E-2;
[leb_tmp start] = getLebedevReccurencePoints(2,start,a,b,v,leb_tmp);
v=0.1421940344335877E-2;
[leb_tmp start] = getLebedevReccurencePoints(3,start,a,b,v,leb_tmp);
a=0.5087204410502360E-1;
v=0.6798123511050502E-3;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.1228198790178831E+0;
v=0.9913184235294912E-3;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.2026890814408786E+0;
v=0.1180207833238949E-2;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.2847745156464294E+0;
v=0.1296599602080921E-2;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.3656719078978026E+0;
v=0.1365871427428316E-2;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.4428264886713469E+0;
v=0.1402988604775325E-2;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.5140619627249735E+0;
v=0.1418645563595609E-2;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.6306401219166803E+0;
v=0.1421376741851662E-2;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.6716883332022612E+0;
v=0.1423996475490962E-2;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.6979792685336881E+0;
v=0.1431554042178567E-2;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.1446865674195309E+0;
v=0.9254401499865368E-3;
[leb_tmp start] = getLebedevReccurencePoints(5,start,a,b,v,leb_tmp);
a=0.3390263475411216E+0;
v=0.1250239995053509E-2;
[leb_tmp start] = getLebedevReccurencePoints(5,start,a,b,v,leb_tmp);
a=0.5335804651263506E+0;
v=0.1394365843329230E-2;
[leb_tmp start] = getLebedevReccurencePoints(5,start,a,b,v,leb_tmp);
a=0.6944024393349413E-1;
b=0.2355187894242326E+0;
v=0.1127089094671749E-2;
[leb_tmp start] = getLebedevReccurencePoints(6,start,a,b,v,leb_tmp);
a=0.2269004109529460E+0;
b=0.4102182474045730E+0;
v=0.1345753760910670E-2;
[leb_tmp start] = getLebedevReccurencePoints(6,start,a,b,v,leb_tmp);
a=0.8025574607775339E-1;
b=0.6214302417481605E+0;
v=0.1424957283316783E-2;
[leb_tmp start] = getLebedevReccurencePoints(6,start,a,b,v,leb_tmp);
a=0.1467999527896572E+0;
b=0.3245284345717394E+0;
v=0.1261523341237750E-2;
[leb_tmp start] = getLebedevReccurencePoints(6,start,a,b,v,leb_tmp);
a=0.1571507769824727E+0;
b=0.5224482189696630E+0;
v=0.1392547106052696E-2;
[leb_tmp start] = getLebedevReccurencePoints(6,start,a,b,v,leb_tmp);
a=0.2365702993157246E+0;
b=0.6017546634089558E+0;
v=0.1418761677877656E-2;
[leb_tmp start] = getLebedevReccurencePoints(6,start,a,b,v,leb_tmp);
a=0.7714815866765732E-1;
b=0.4346575516141163E+0;
v=0.1338366684479554E-2;
[leb_tmp start] = getLebedevReccurencePoints(6,start,a,b,v,leb_tmp);
a=0.3062936666210730E+0;
b=0.4908826589037616E+0;
v=0.1393700862676131E-2;
[leb_tmp start] = getLebedevReccurencePoints(6,start,a,b,v,leb_tmp);
a=0.3822477379524787E+0;
b=0.5648768149099500E+0;
v=0.1415914757466932E-2;
[leb_tmp start] = getLebedevReccurencePoints(6,start,a,b,v,leb_tmp);
case 974
v=0.1438294190527431E-3;
[leb_tmp start] = getLebedevReccurencePoints(1,start,a,b,v,leb_tmp);
v=0.1125772288287004E-2;
[leb_tmp start] = getLebedevReccurencePoints(3,start,a,b,v,leb_tmp);
a=0.4292963545341347E-1;
v=0.4948029341949241E-3;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.1051426854086404E+0;
v=0.7357990109125470E-3;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.1750024867623087E+0;
v=0.8889132771304384E-3;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.2477653379650257E+0;
v=0.9888347838921435E-3;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.3206567123955957E+0;
v=0.1053299681709471E-2;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.3916520749849983E+0;
v=0.1092778807014578E-2;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.4590825874187624E+0;
v=0.1114389394063227E-2;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.5214563888415861E+0;
v=0.1123724788051555E-2;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.6253170244654199E+0;
v=0.1125239325243814E-2;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.6637926744523170E+0;
v=0.1126153271815905E-2;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.6910410398498301E+0;
v=0.1130286931123841E-2;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.7052907007457760E+0;
v=0.1134986534363955E-2;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.1236686762657990E+0;
v=0.6823367927109931E-3;
[leb_tmp start] = getLebedevReccurencePoints(5,start,a,b,v,leb_tmp);
a=0.2940777114468387E+0;
v=0.9454158160447096E-3;
[leb_tmp start] = getLebedevReccurencePoints(5,start,a,b,v,leb_tmp);
a=0.4697753849207649E+0;
v=0.1074429975385679E-2;
[leb_tmp start] = getLebedevReccurencePoints(5,start,a,b,v,leb_tmp);
a=0.6334563241139567E+0;
v=0.1129300086569132E-2;
[leb_tmp start] = getLebedevReccurencePoints(5,start,a,b,v,leb_tmp);
a=0.5974048614181342E-1;
b=0.2029128752777523E+0;
v=0.8436884500901954E-3;
[leb_tmp start] = getLebedevReccurencePoints(6,start,a,b,v,leb_tmp);
a=0.1375760408473636E+0;
b=0.4602621942484054E+0;
v=0.1075255720448885E-2;
[leb_tmp start] = getLebedevReccurencePoints(6,start,a,b,v,leb_tmp);
a=0.3391016526336286E+0;
b=0.5030673999662036E+0;
v=0.1108577236864462E-2;
[leb_tmp start] = getLebedevReccurencePoints(6,start,a,b,v,leb_tmp);
a=0.1271675191439820E+0;
b=0.2817606422442134E+0;
v=0.9566475323783357E-3;
[leb_tmp start] = getLebedevReccurencePoints(6,start,a,b,v,leb_tmp);
a=0.2693120740413512E+0;
b=0.4331561291720157E+0;
v=0.1080663250717391E-2;
[leb_tmp start] = getLebedevReccurencePoints(6,start,a,b,v,leb_tmp);
a=0.1419786452601918E+0;
b=0.6256167358580814E+0;
v=0.1126797131196295E-2;
[leb_tmp start] = getLebedevReccurencePoints(6,start,a,b,v,leb_tmp);
a=0.6709284600738255E-1;
b=0.3798395216859157E+0;
v=0.1022568715358061E-2;
[leb_tmp start] = getLebedevReccurencePoints(6,start,a,b,v,leb_tmp);
a=0.7057738183256172E-1;
b=0.5517505421423520E+0;
v=0.1108960267713108E-2;
[leb_tmp start] = getLebedevReccurencePoints(6,start,a,b,v,leb_tmp);
a=0.2783888477882155E+0;
b=0.6029619156159187E+0;
v=0.1122790653435766E-2;
[leb_tmp start] = getLebedevReccurencePoints(6,start,a,b,v,leb_tmp);
a=0.1979578938917407E+0;
b=0.3589606329589096E+0;
v=0.1032401847117460E-2;
[leb_tmp start] = getLebedevReccurencePoints(6,start,a,b,v,leb_tmp);
a=0.2087307061103274E+0;
b=0.5348666438135476E+0;
v=0.1107249382283854E-2;
[leb_tmp start] = getLebedevReccurencePoints(6,start,a,b,v,leb_tmp);
a=0.4055122137872836E+0;
b=0.5674997546074373E+0;
v=0.1121780048519972E-2;
[leb_tmp start] = getLebedevReccurencePoints(6,start,a,b,v,leb_tmp);
case 1202
v=0.1105189233267572E-3;
[leb_tmp start] = getLebedevReccurencePoints(1,start,a,b,v,leb_tmp);
v=0.9205232738090741E-3;
[leb_tmp start] = getLebedevReccurencePoints(2,start,a,b,v,leb_tmp);
v=0.9133159786443561E-3;
[leb_tmp start] = getLebedevReccurencePoints(3,start,a,b,v,leb_tmp);
a=0.3712636449657089E-1;
v=0.3690421898017899E-3;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.9140060412262223E-1;
v=0.5603990928680660E-3;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.1531077852469906E+0;
v=0.6865297629282609E-3;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.2180928891660612E+0;
v=0.7720338551145630E-3;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.2839874532200175E+0;
v=0.8301545958894795E-3;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.3491177600963764E+0;
v=0.8686692550179628E-3;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.4121431461444309E+0;
v=0.8927076285846890E-3;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.4718993627149127E+0;
v=0.9060820238568219E-3;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.5273145452842337E+0;
v=0.9119777254940867E-3;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.6209475332444019E+0;
v=0.9128720138604181E-3;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.6569722711857291E+0;
v=0.9130714935691735E-3;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.6841788309070143E+0;
v=0.9152873784554116E-3;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.7012604330123631E+0;
v=0.9187436274321654E-3;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.1072382215478166E+0;
v=0.5176977312965694E-3;
[leb_tmp start] = getLebedevReccurencePoints(5,start,a,b,v,leb_tmp);
a=0.2582068959496968E+0;
v=0.7331143682101417E-3;
[leb_tmp start] = getLebedevReccurencePoints(5,start,a,b,v,leb_tmp);
a=0.4172752955306717E+0;
v=0.8463232836379928E-3;
[leb_tmp start] = getLebedevReccurencePoints(5,start,a,b,v,leb_tmp);
a=0.5700366911792503E+0;
v=0.9031122694253992E-3;
[leb_tmp start] = getLebedevReccurencePoints(5,start,a,b,v,leb_tmp);
a=0.9827986018263947E+0;
b=0.1771774022615325E+0;
v=0.6485778453163257E-3;
[leb_tmp start] = getLebedevReccurencePoints(6,start,a,b,v,leb_tmp);
a=0.9624249230326228E+0;
b=0.2475716463426288E+0;
v=0.7435030910982369E-3;
[leb_tmp start] = getLebedevReccurencePoints(6,start,a,b,v,leb_tmp);
a=0.9402007994128811E+0;
b=0.3354616289066489E+0;
v=0.7998527891839054E-3;
[leb_tmp start] = getLebedevReccurencePoints(6,start,a,b,v,leb_tmp);
a=0.9320822040143202E+0;
b=0.3173615246611977E+0;
v=0.8101731497468018E-3;
[leb_tmp start] = getLebedevReccurencePoints(6,start,a,b,v,leb_tmp);
a=0.9043674199393299E+0;
b=0.4090268427085357E+0;
v=0.8483389574594331E-3;
[leb_tmp start] = getLebedevReccurencePoints(6,start,a,b,v,leb_tmp);
a=0.8912407560074747E+0;
b=0.3854291150669224E+0;
v=0.8556299257311812E-3;
[leb_tmp start] = getLebedevReccurencePoints(6,start,a,b,v,leb_tmp);
a=0.8676435628462708E+0;
b=0.4932221184851285E+0;
v=0.8803208679738260E-3;
[leb_tmp start] = getLebedevReccurencePoints(6,start,a,b,v,leb_tmp);
a=0.8581979986041619E+0;
b=0.4785320675922435E+0;
v=0.8811048182425720E-3;
[leb_tmp start] = getLebedevReccurencePoints(6,start,a,b,v,leb_tmp);
a=0.8396753624049856E+0;
b=0.4507422593157064E+0;
v=0.8850282341265444E-3;
[leb_tmp start] = getLebedevReccurencePoints(6,start,a,b,v,leb_tmp);
a=0.8165288564022188E+0;
b=0.5632123020762100E+0;
v=0.9021342299040653E-3;
[leb_tmp start] = getLebedevReccurencePoints(6,start,a,b,v,leb_tmp);
a=0.8015469370783529E+0;
b=0.5434303569693900E+0;
v=0.9010091677105086E-3;
[leb_tmp start] = getLebedevReccurencePoints(6,start,a,b,v,leb_tmp);
a=0.7773563069070351E+0;
b=0.5123518486419871E+0;
v=0.9022692938426915E-3;
[leb_tmp start] = getLebedevReccurencePoints(6,start,a,b,v,leb_tmp);
a=0.7661621213900394E+0;
b=0.6394279634749102E+0;
v=0.9158016174693465E-3;
[leb_tmp start] = getLebedevReccurencePoints(6,start,a,b,v,leb_tmp);
a=0.7553584143533510E+0;
b=0.6269805509024392E+0;
v=0.9131578003189435E-3;
[leb_tmp start] = getLebedevReccurencePoints(6,start,a,b,v,leb_tmp);
a=0.7344305757559503E+0;
b=0.6031161693096310E+0;
v=0.9107813579482705E-3;
[leb_tmp start] = getLebedevReccurencePoints(6,start,a,b,v,leb_tmp);
a=0.7043837184021765E+0;
b=0.5693702498468441E+0;
v=0.9105760258970126E-3;
[leb_tmp start] = getLebedevReccurencePoints(6,start,a,b,v,leb_tmp);
case 1454
v=0.7777160743261247E-4;
[leb_tmp start] = getLebedevReccurencePoints(1,start,a,b,v,leb_tmp);
v=0.7557646413004701E-3;
[leb_tmp start] = getLebedevReccurencePoints(3,start,a,b,v,leb_tmp);
a=0.3229290663413854E-1;
v=0.2841633806090617E-3;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.8036733271462222E-1;
v=0.4374419127053555E-3;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.1354289960531653E+0;
v=0.5417174740872172E-3;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.1938963861114426E+0;
v=0.6148000891358593E-3;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.2537343715011275E+0;
v=0.6664394485800705E-3;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.3135251434752570E+0;
v=0.7025039356923220E-3;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.3721558339375338E+0;
v=0.7268511789249627E-3;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.4286809575195696E+0;
v=0.7422637534208629E-3;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.4822510128282994E+0;
v=0.7509545035841214E-3;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.5320679333566263E+0;
v=0.7548535057718401E-3;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.6172998195394274E+0;
v=0.7554088969774001E-3;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.6510679849127481E+0;
v=0.7553147174442808E-3;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.6777315251687360E+0;
v=0.7564767653292297E-3;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.6963109410648741E+0;
v=0.7587991808518730E-3;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.7058935009831749E+0;
v=0.7608261832033027E-3;
[leb_tmp start] = getLebedevReccurencePoints(4,start,a,b,v,leb_tmp);
a=0.9955546194091857E+0;
v=0.4021680447874916E-3;
[leb_tmp start] = getLebedevReccurencePoints(5,start,a,b,v,leb_tmp);
a=0.9734115901794209E+0;
v=0.5804871793945964E-3;
[leb_tmp start] = getLebedevReccurencePoints(5,start,a,b,v,leb_tmp);
a=0.9275693732388626E+0;
v=0.6792151955945159E-3;
[leb_tmp start] = getLebedevReccurencePoints(5,start,a,b,v,leb_tmp);
a=0.8568022422795103E+0;
v=0.7336741211286294E-3;
[leb_tmp start] = getLebedevReccurencePoints(5,start,a,b,v,leb_tmp);
a=0.7623495553719372E+0;
v=0.7581866300989608E-3;
[leb_tmp start] = getLebedevReccurencePoints(5,start,a,b,v,leb_tmp);
a=0.5707522908892223E+0;
b=0.4387028039889501E+0;
v=0.7538257859800743E-3;
[leb_tmp start] = getLebedevReccurencePoints(6,start,a,b,v,leb_tmp);
a=0.5196463388403083E+0;
b=0.3858908414762617E+0;
v=0.7483517247053123E-3;
[leb_tmp start] = getLebedevReccurencePoints(6,start,a,b,v,leb_tmp);
a=0.4646337531215351E+0;
b=0.3301937372343854E+0;
v=0.7371763661112059E-3;
[leb_tmp start] = getLebedevReccurencePoints(6,start,a,b,v,leb_tmp);
a=0.4063901697557691E+0;
b=0.2725423573563777E+0;
v=0.7183448895756934E-3;
[leb_tmp start] = getLebedevReccurencePoints(6,start,a,b,v,leb_tmp);
a=0.3456329466643087E+0;
b=0.2139510237495250E+0;
v=0.6895815529822191E-3;
[leb_tmp start] = getLebedevReccurencePoints(6,start,a,b,v,leb_tmp);
a=0.2831395121050332E+0;
b=0.1555922309786647E+0;
v=0.6480105801792886E-3;
[leb_tmp start] = getLebedevReccurencePoints(6,start,a,b,v,leb_tmp);
a=0.2197682022925330E+0;
b=0.9892878979686097E-1;
v=0.5897558896594636E-3;
[leb_tmp start] = getLebedevReccurencePoints(6,start,a,b,v,leb_tmp);
a=0.1564696098650355E+0;
b=0.4598642910675510E-1;
v=0.5095708849247346E-3;
[leb_tmp start] = getLebedevReccurencePoints(6,start,a,b,v,leb_tmp);
a=0.6027356673721295E+0;
b=0.3376625140173426E+0;
v=0.7536906428909755E-3;
[leb_tmp start] = getLebedevReccurencePoints(6,start,a,b,v,leb_tmp);
a=0.5496032320255096E+0;
b=0.2822301309727988E+0;
v=0.7472505965575118E-3;
[leb_tmp start] = getLebedevReccurencePoints(6,start,a,b,v,leb_tmp);
a=0.4921707755234567E+0;
b=0.2248632342592540E+0;
v=0.7343017132279698E-3;
[leb_tmp start] = getLebedevReccurencePoints(6,start,a,b,v,leb_tmp);
a=0.4309422998598483E+0;
b=0.1666224723456479E+0;
v=0.7130871582177445E-3;
[leb_tmp start] = getLebedevReccurencePoints(6,start,a,b,v,leb_tmp);
a=0.3664108182313672E+0;
b=0.1086964901822169E+0;
v=0.6817022032112776E-3;
[leb_tmp start] = getLebedevReccurencePoints(6,start,a,b,v,leb_tmp);
a=0.2990189057758436E+0;
b=0.5251989784120085E-1;
v=0.6380941145604121E-3;
[leb_tmp start] = getLebedevReccurencePoints(6,start,a,b,v,leb_tmp);
a=0.6268724013144998E+0;
b=0.2297523657550023E+0;
v=0.7550381377920310E-3;
[leb_tmp start] = getLebedevReccurencePoints(6,start,a,b,v,leb_tmp);
a=0.5707324144834607E+0;
b=0.1723080607093800E+0;
v=0.7478646640144802E-3;
[leb_tmp start] = getLebedevReccurencePoints(6,start,a,b,v,leb_tmp);
a=0.5096360901960365E+0;
b=0.1140238465390513E+0;
v=0.7335918720601220E-3;
[leb_tmp start] = getLebedevReccurencePoints(6,start,a,b,v,leb_tmp);
a=0.4438729938312456E+0;
b=0.5611522095882537E-1;
v=0.7110120527658118E-3;
[leb_tmp start] = getLebedevReccurencePoints(6,start,a,b,v,leb_tmp);
a=0.6419978471082389E+0;
b=0.1164174423140873E+0;
v=0.7571363978689501E-3;