From 6b5fb87d350610964d6444eddf8c57004ec7c890 Mon Sep 17 00:00:00 2001 From: Paul Romano Date: Wed, 10 Jan 2018 12:43:00 -0600 Subject: [PATCH] Move calc_zn to math module, remove calc_zn_scaled --- src/math.F90 | 1136 +++++++++++++++++++++++++ src/tallies/tally_filter_zernike.F90 | 1157 +------------------------- 2 files changed, 1138 insertions(+), 1155 deletions(-) diff --git a/src/math.F90 b/src/math.F90 index 2fa0a6ce1e..b96562734f 100644 --- a/src/math.F90 +++ b/src/math.F90 @@ -574,6 +574,1142 @@ contains end function calc_rn +!=============================================================================== +! CALC_ZN calculates the n-th order Zernike polynomial moment for a given angle +! (rho, theta) location in the unit disk. +!=============================================================================== + + pure function calc_zn(n, rho, phi) result(zn) + + integer, intent(in) :: n ! Order requested + real(8), intent(in) :: rho ! Radial location in the unit disk + real(8), intent(in) :: phi ! Theta (radians) location in the unit disk + real(8) :: zn(n + 1) ! The resultant Z_n(uvw) + + ! n == radial degree + ! m == azimuthal frequency + + select case(n) + case(0) + ! n = 0, m = 0 + zn(1) = ( ( 1.00 ) ) & + * ( 1.000000000000 ) + case(1) + ! n = 1, m = -1 + zn(1) = ( ( 1.00 ) * rho ) & + * ( 2.000000000000 ) * sin(1.00 * phi) + ! n = 1, m = 1 + zn(2) = ( ( 1.00 ) * rho ) & + * ( 2.000000000000 ) * cos(1.00 * phi) + case(2) + ! n = 2, m = -2 + zn(1) = ( ( 1.00 ) *rho * rho ) & + * ( 2.449489742783 ) * sin(2.00 * phi) + ! n = 2, m = 0 + zn(2) = ( ( -1.00 ) + & + ( 2.00 ) *rho * rho ) & + * ( 1.732050807569 ) + ! n = 2, m = 2 + zn(3) = ( ( 1.00 ) *rho * rho ) & + * ( 2.449489742783 ) * cos(2.00 * phi) + case(3) + ! n = 3, m = -3 + zn(1) = ( ( 1.00 ) *rho *rho * rho ) & + * ( 2.828427124746 ) * sin(3.00 * phi) + ! n = 3, m = -1 + zn(2) = ( ( -2.00 ) * rho + & + ( 3.00 ) *rho *rho * rho ) & + * ( 2.828427124746 ) * sin(3.00 * phi) + ! n = 3, m = 1 + zn(3) = ( ( -2.00 ) * rho + & + ( 3.00 ) *rho *rho * rho ) & + * ( 2.828427124746 ) * cos(3.00 * phi) + ! n = 3, m = 3 + zn(4) = ( ( 1.00 ) *rho *rho * rho ) & + * ( 2.828427124746 ) * cos(3.00 * phi) + case(4) + ! n = 4, m = -4 + zn(1) = ( ( 1.00 ) *rho *rho *rho * rho ) & + * ( 3.162277660168 ) * sin(4.00 * phi) + ! n = 4, m = -2 + zn(2) = ( ( -3.00 ) *rho * rho + & + ( 4.00 ) *rho *rho *rho * rho ) & + * ( 3.162277660168 ) * sin(4.00 * phi) + ! n = 4, m = 0 + zn(3) = ( ( 1.00 ) + & + ( -6.00 ) *rho * rho + & + ( 6.00 ) *rho *rho *rho * rho ) & + * ( 2.236067977500 ) + ! n = 4, m = 2 + zn(4) = ( ( -3.00 ) *rho * rho + & + ( 4.00 ) *rho *rho *rho * rho ) & + * ( 3.162277660168 ) * cos(4.00 * phi) + ! n = 4, m = 4 + zn(5) = ( ( 1.00 ) *rho *rho *rho * rho ) & + * ( 3.162277660168 ) * cos(4.00 * phi) + case(5) + ! n = 5, m = -5 + zn(1) = ( ( 1.00 ) *rho *rho *rho *rho * rho ) & + * ( 3.464101615138 ) * sin(5.00 * phi) + ! n = 5, m = -3 + zn(2) = ( ( -4.00 ) *rho *rho * rho + & + ( 5.00 ) *rho *rho *rho *rho * rho ) & + * ( 3.464101615138 ) * sin(5.00 * phi) + ! n = 5, m = -1 + zn(3) = ( ( 3.00 ) * rho + & + ( -12.00 ) *rho *rho * rho + & + ( 10.00 ) *rho *rho *rho *rho * rho ) & + * ( 3.464101615138 ) * sin(5.00 * phi) + ! n = 5, m = 1 + zn(4) = ( ( 3.00 ) * rho + & + ( -12.00 ) *rho *rho * rho + & + ( 10.00 ) *rho *rho *rho *rho * rho ) & + * ( 3.464101615138 ) * cos(5.00 * phi) + ! n = 5, m = 3 + zn(5) = ( ( -4.00 ) *rho *rho * rho + & + ( 5.00 ) *rho *rho *rho *rho * rho ) & + * ( 3.464101615138 ) * cos(5.00 * phi) + ! n = 5, m = 5 + zn(6) = ( ( 1.00 ) *rho *rho *rho *rho * rho ) & + * ( 3.464101615138 ) * cos(5.00 * phi) + case(6) + ! n = 6, m = -6 + zn(1) = ( ( 1.00 ) *rho *rho *rho *rho *rho * rho ) & + * ( 3.741657386774 ) * sin(6.00 * phi) + ! n = 6, m = -4 + zn(2) = ( ( -5.00 ) *rho *rho *rho * rho + & + ( 6.00 ) *rho *rho *rho *rho *rho * rho ) & + * ( 3.741657386774 ) * sin(6.00 * phi) + ! n = 6, m = -2 + zn(3) = ( ( 6.00 ) *rho * rho + & + ( -20.00 ) *rho *rho *rho * rho + & + ( 15.00 ) *rho *rho *rho *rho *rho * rho ) & + * ( 3.741657386774 ) * sin(6.00 * phi) + ! n = 6, m = 0 + zn(4) = ( ( -1.00 ) + & + ( 12.00 ) *rho * rho + & + ( -30.00 ) *rho *rho *rho * rho + & + ( 20.00 ) *rho *rho *rho *rho *rho * rho ) & + * ( 2.645751311065 ) + ! n = 6, m = 2 + zn(5) = ( ( 6.00 ) *rho * rho + & + ( -20.00 ) *rho *rho *rho * rho + & + ( 15.00 ) *rho *rho *rho *rho *rho * rho ) & + * ( 3.741657386774 ) * cos(6.00 * phi) + ! n = 6, m = 4 + zn(6) = ( ( -5.00 ) *rho *rho *rho * rho + & + ( 6.00 ) *rho *rho *rho *rho *rho * rho ) & + * ( 3.741657386774 ) * cos(6.00 * phi) + ! n = 6, m = 6 + zn(7) = ( ( 1.00 ) *rho *rho *rho *rho *rho * rho ) & + * ( 3.741657386774 ) * cos(6.00 * phi) + case(7) + ! n = 7, m = -7 + zn(1) = ( ( 1.00 ) *rho *rho *rho *rho *rho *rho * rho ) & + * ( 4.000000000000 ) * sin(7.00 * phi) + ! n = 7, m = -5 + zn(2) = ( ( -6.00 ) *rho *rho *rho *rho * rho + & + ( 7.00 ) *rho *rho *rho *rho *rho *rho * rho ) & + * ( 4.000000000000 ) * sin(7.00 * phi) + ! n = 7, m = -3 + zn(3) = ( ( 10.00 ) *rho *rho * rho + & + ( -30.00 ) *rho *rho *rho *rho * rho + & + ( 21.00 ) *rho *rho *rho *rho *rho *rho * rho ) & + * ( 4.000000000000 ) * sin(7.00 * phi) + ! n = 7, m = -1 + zn(4) = ( ( -4.00 ) * rho + & + ( 30.00 ) *rho *rho * rho + & + ( -60.00 ) *rho *rho *rho *rho * rho + & + ( 35.00 ) *rho *rho *rho *rho *rho *rho * rho ) & + * ( 4.000000000000 ) * sin(7.00 * phi) + ! n = 7, m = 1 + zn(5) = ( ( -4.00 ) * rho + & + ( 30.00 ) *rho *rho * rho + & + ( -60.00 ) *rho *rho *rho *rho * rho + & + ( 35.00 ) *rho *rho *rho *rho *rho *rho * rho ) & + * ( 4.000000000000 ) * cos(7.00 * phi) + ! n = 7, m = 3 + zn(6) = ( ( 10.00 ) *rho *rho * rho + & + ( -30.00 ) *rho *rho *rho *rho * rho + & + ( 21.00 ) *rho *rho *rho *rho *rho *rho * rho ) & + * ( 4.000000000000 ) * cos(7.00 * phi) + ! n = 7, m = 5 + zn(7) = ( ( -6.00 ) *rho *rho *rho *rho * rho + & + ( 7.00 ) *rho *rho *rho *rho *rho *rho * rho ) & + * ( 4.000000000000 ) * cos(7.00 * phi) + ! n = 7, m = 7 + zn(8) = ( ( 1.00 ) *rho *rho *rho *rho *rho *rho * rho ) & + * ( 4.000000000000 ) * cos(7.00 * phi) + case(8) + ! n = 8, m = -8 + zn(1) = ( ( 1.00 ) *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 4.242640687119 ) * sin(8.00 * phi) + ! n = 8, m = -6 + zn(2) = ( ( -7.00 ) *rho *rho *rho *rho *rho * rho + & + ( 8.00 ) *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 4.242640687119 ) * sin(8.00 * phi) + ! n = 8, m = -4 + zn(3) = ( ( 15.00 ) *rho *rho *rho * rho + & + ( -42.00 ) *rho *rho *rho *rho *rho * rho + & + ( 28.00 ) *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 4.242640687119 ) * sin(8.00 * phi) + ! n = 8, m = -2 + zn(4) = ( ( -10.00 ) *rho * rho + & + ( 60.00 ) *rho *rho *rho * rho + & + ( -105.00 ) *rho *rho *rho *rho *rho * rho + & + ( 56.00 ) *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 4.242640687119 ) * sin(8.00 * phi) + ! n = 8, m = 0 + zn(5) = ( ( 1.00 ) + & + ( -20.00 ) *rho * rho + & + ( 90.00 ) *rho *rho *rho * rho + & + ( -140.00 ) *rho *rho *rho *rho *rho * rho + & + ( 70.00 ) *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 3.000000000000 ) + ! n = 8, m = 2 + zn(6) = ( ( -10.00 ) *rho * rho + & + ( 60.00 ) *rho *rho *rho * rho + & + ( -105.00 ) *rho *rho *rho *rho *rho * rho + & + ( 56.00 ) *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 4.242640687119 ) * cos(8.00 * phi) + ! n = 8, m = 4 + zn(7) = ( ( 15.00 ) *rho *rho *rho * rho + & + ( -42.00 ) *rho *rho *rho *rho *rho * rho + & + ( 28.00 ) *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 4.242640687119 ) * cos(8.00 * phi) + ! n = 8, m = 6 + zn(8) = ( ( -7.00 ) *rho *rho *rho *rho *rho * rho + & + ( 8.00 ) *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 4.242640687119 ) * cos(8.00 * phi) + ! n = 8, m = 8 + zn(9) = ( ( 1.00 ) *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 4.242640687119 ) * cos(8.00 * phi) + case(9) + ! n = 9, m = -9 + zn(1) = ( ( 1.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 4.472135955000 ) * sin(9.00 * phi) + ! n = 9, m = -7 + zn(2) = ( ( -8.00 ) *rho *rho *rho *rho *rho *rho * rho + & + ( 9.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 4.472135955000 ) * sin(9.00 * phi) + ! n = 9, m = -5 + zn(3) = ( ( 21.00 ) *rho *rho *rho *rho * rho + & + ( -56.00 ) *rho *rho *rho *rho *rho *rho * rho + & + ( 36.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 4.472135955000 ) * sin(9.00 * phi) + ! n = 9, m = -3 + zn(4) = ( ( -20.00 ) *rho *rho * rho + & + ( 105.00 ) *rho *rho *rho *rho * rho + & + ( -168.00 ) *rho *rho *rho *rho *rho *rho * rho + & + ( 84.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 4.472135955000 ) * sin(9.00 * phi) + ! n = 9, m = -1 + zn(5) = ( ( 5.00 ) * rho + & + ( -60.00 ) *rho *rho * rho + & + ( 210.00 ) *rho *rho *rho *rho * rho + & + ( -280.00 ) *rho *rho *rho *rho *rho *rho * rho + & + ( 126.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 4.472135955000 ) * sin(9.00 * phi) + ! n = 9, m = 1 + zn(6) = ( ( 5.00 ) * rho + & + ( -60.00 ) *rho *rho * rho + & + ( 210.00 ) *rho *rho *rho *rho * rho + & + ( -280.00 ) *rho *rho *rho *rho *rho *rho * rho + & + ( 126.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 4.472135955000 ) * cos(9.00 * phi) + ! n = 9, m = 3 + zn(7) = ( ( -20.00 ) *rho *rho * rho + & + ( 105.00 ) *rho *rho *rho *rho * rho + & + ( -168.00 ) *rho *rho *rho *rho *rho *rho * rho + & + ( 84.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 4.472135955000 ) * cos(9.00 * phi) + ! n = 9, m = 5 + zn(8) = ( ( 21.00 ) *rho *rho *rho *rho * rho + & + ( -56.00 ) *rho *rho *rho *rho *rho *rho * rho + & + ( 36.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 4.472135955000 ) * cos(9.00 * phi) + ! n = 9, m = 7 + zn(9) = ( ( -8.00 ) *rho *rho *rho *rho *rho *rho * rho + & + ( 9.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 4.472135955000 ) * cos(9.00 * phi) + ! n = 9, m = 9 + zn(10) = ( ( 1.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 4.472135955000 ) * cos(9.00 * phi) + case(10) + ! n = 10, m = -10 + zn(1) = ( ( 1.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 4.690415759823 ) * sin(10.00 * phi) + ! n = 10, m = -8 + zn(2) = ( ( -9.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 10.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 4.690415759823 ) * sin(10.00 * phi) + ! n = 10, m = -6 + zn(3) = ( ( 28.00 ) *rho *rho *rho *rho *rho * rho + & + ( -72.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 45.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 4.690415759823 ) * sin(10.00 * phi) + ! n = 10, m = -4 + zn(4) = ( ( -35.00 ) *rho *rho *rho * rho + & + ( 168.00 ) *rho *rho *rho *rho *rho * rho + & + ( -252.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 120.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 4.690415759823 ) * sin(10.00 * phi) + ! n = 10, m = -2 + zn(5) = ( ( 15.00 ) *rho * rho + & + ( -140.00 ) *rho *rho *rho * rho + & + ( 420.00 ) *rho *rho *rho *rho *rho * rho + & + ( -504.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 210.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 4.690415759823 ) * sin(10.00 * phi) + ! n = 10, m = 0 + zn(6) = ( ( -1.00 ) + & + ( 30.00 ) *rho * rho + & + ( -210.00 ) *rho *rho *rho * rho + & + ( 560.00 ) *rho *rho *rho *rho *rho * rho + & + ( -630.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 252.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 3.316624790355 ) + ! n = 10, m = 2 + zn(7) = ( ( 15.00 ) *rho * rho + & + ( -140.00 ) *rho *rho *rho * rho + & + ( 420.00 ) *rho *rho *rho *rho *rho * rho + & + ( -504.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 210.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 4.690415759823 ) * cos(10.00 * phi) + ! n = 10, m = 4 + zn(8) = ( ( -35.00 ) *rho *rho *rho * rho + & + ( 168.00 ) *rho *rho *rho *rho *rho * rho + & + ( -252.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 120.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 4.690415759823 ) * cos(10.00 * phi) + ! n = 10, m = 6 + zn(9) = ( ( 28.00 ) *rho *rho *rho *rho *rho * rho + & + ( -72.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 45.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 4.690415759823 ) * cos(10.00 * phi) + ! n = 10, m = 8 + zn(10) = ( ( -9.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 10.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 4.690415759823 ) * cos(10.00 * phi) + ! n = 10, m = 10 + zn(11) = ( ( 1.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 4.690415759823 ) * cos(10.00 * phi) + case(11) + ! n = 11, m = -11 + zn(1) = ( ( 1.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 4.898979485566 ) * sin(11.00 * phi) + ! n = 11, m = -9 + zn(2) = ( ( -10.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 11.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 4.898979485566 ) * sin(11.00 * phi) + ! n = 11, m = -7 + zn(3) = ( ( 36.00 ) *rho *rho *rho *rho *rho *rho * rho + & + ( -90.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 55.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 4.898979485566 ) * sin(11.00 * phi) + ! n = 11, m = -5 + zn(4) = ( ( -56.00 ) *rho *rho *rho *rho * rho + & + ( 252.00 ) *rho *rho *rho *rho *rho *rho * rho + & + ( -360.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 165.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 4.898979485566 ) * sin(11.00 * phi) + ! n = 11, m = -3 + zn(5) = ( ( 35.00 ) *rho *rho * rho + & + ( -280.00 ) *rho *rho *rho *rho * rho + & + ( 756.00 ) *rho *rho *rho *rho *rho *rho * rho + & + ( -840.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 330.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 4.898979485566 ) * sin(11.00 * phi) + ! n = 11, m = -1 + zn(6) = ( ( -6.00 ) * rho + & + ( 105.00 ) *rho *rho * rho + & + ( -560.00 ) *rho *rho *rho *rho * rho + & + ( 1260.00 ) *rho *rho *rho *rho *rho *rho * rho + & + ( -1260.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 462.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 4.898979485566 ) * sin(11.00 * phi) + ! n = 11, m = 1 + zn(7) = ( ( -6.00 ) * rho + & + ( 105.00 ) *rho *rho * rho + & + ( -560.00 ) *rho *rho *rho *rho * rho + & + ( 1260.00 ) *rho *rho *rho *rho *rho *rho * rho + & + ( -1260.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 462.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 4.898979485566 ) * cos(11.00 * phi) + ! n = 11, m = 3 + zn(8) = ( ( 35.00 ) *rho *rho * rho + & + ( -280.00 ) *rho *rho *rho *rho * rho + & + ( 756.00 ) *rho *rho *rho *rho *rho *rho * rho + & + ( -840.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 330.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 4.898979485566 ) * cos(11.00 * phi) + ! n = 11, m = 5 + zn(9) = ( ( -56.00 ) *rho *rho *rho *rho * rho + & + ( 252.00 ) *rho *rho *rho *rho *rho *rho * rho + & + ( -360.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 165.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 4.898979485566 ) * cos(11.00 * phi) + ! n = 11, m = 7 + zn(10) = ( ( 36.00 ) *rho *rho *rho *rho *rho *rho * rho + & + ( -90.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 55.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 4.898979485566 ) * cos(11.00 * phi) + ! n = 11, m = 9 + zn(11) = ( ( -10.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 11.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 4.898979485566 ) * cos(11.00 * phi) + ! n = 11, m = 11 + zn(12) = ( ( 1.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 4.898979485566 ) * cos(11.00 * phi) + case(12) + ! n = 12, m = -12 + zn(1) = ( ( 1.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 5.099019513593 ) * sin(12.00 * phi) + ! n = 12, m = -10 + zn(2) = ( ( -11.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 12.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 5.099019513593 ) * sin(12.00 * phi) + ! n = 12, m = -8 + zn(3) = ( ( 45.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -110.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 66.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 5.099019513593 ) * sin(12.00 * phi) + ! n = 12, m = -6 + zn(4) = ( ( -84.00 ) *rho *rho *rho *rho *rho * rho + & + ( 360.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -495.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 220.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 5.099019513593 ) * sin(12.00 * phi) + ! n = 12, m = -4 + zn(5) = ( ( 70.00 ) *rho *rho *rho * rho + & + ( -504.00 ) *rho *rho *rho *rho *rho * rho + & + ( 1260.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -1320.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 495.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 5.099019513593 ) * sin(12.00 * phi) + ! n = 12, m = -2 + zn(6) = ( ( -21.00 ) *rho * rho + & + ( 280.00 ) *rho *rho *rho * rho + & + ( -1260.00 ) *rho *rho *rho *rho *rho * rho + & + ( 2520.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -2310.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 792.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 5.099019513593 ) * sin(12.00 * phi) + ! n = 12, m = 0 + zn(7) = ( ( 1.00 ) + & + ( -42.00 ) *rho * rho + & + ( 420.00 ) *rho *rho *rho * rho + & + ( -1680.00 ) *rho *rho *rho *rho *rho * rho + & + ( 3150.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -2772.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 924.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 3.605551275464 ) + ! n = 12, m = 2 + zn(8) = ( ( -21.00 ) *rho * rho + & + ( 280.00 ) *rho *rho *rho * rho + & + ( -1260.00 ) *rho *rho *rho *rho *rho * rho + & + ( 2520.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -2310.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 792.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 5.099019513593 ) * cos(12.00 * phi) + ! n = 12, m = 4 + zn(9) = ( ( 70.00 ) *rho *rho *rho * rho + & + ( -504.00 ) *rho *rho *rho *rho *rho * rho + & + ( 1260.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -1320.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 495.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 5.099019513593 ) * cos(12.00 * phi) + ! n = 12, m = 6 + zn(10) = ( ( -84.00 ) *rho *rho *rho *rho *rho * rho + & + ( 360.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -495.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 220.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 5.099019513593 ) * cos(12.00 * phi) + ! n = 12, m = 8 + zn(11) = ( ( 45.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -110.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 66.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 5.099019513593 ) * cos(12.00 * phi) + ! n = 12, m = 10 + zn(12) = ( ( -11.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 12.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 5.099019513593 ) * cos(12.00 * phi) + ! n = 12, m = 12 + zn(13) = ( ( 1.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 5.099019513593 ) * cos(12.00 * phi) + case(13) + ! n = 13, m = -13 + zn(1) = ( ( 1.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 5.291502622129 ) * sin(13.00 * phi) + ! n = 13, m = -11 + zn(2) = ( ( -12.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 13.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 5.291502622129 ) * sin(13.00 * phi) + ! n = 13, m = -9 + zn(3) = ( ( 55.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -132.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 78.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 5.291502622129 ) * sin(13.00 * phi) + ! n = 13, m = -7 + zn(4) = ( ( -120.00 ) *rho *rho *rho *rho *rho *rho * rho + & + ( 495.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -660.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 286.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 5.291502622129 ) * sin(13.00 * phi) + ! n = 13, m = -5 + zn(5) = ( ( 126.00 ) *rho *rho *rho *rho * rho + & + ( -840.00 ) *rho *rho *rho *rho *rho *rho * rho + & + ( 1980.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -1980.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 715.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 5.291502622129 ) * sin(13.00 * phi) + ! n = 13, m = -3 + zn(6) = ( ( -56.00 ) *rho *rho * rho + & + ( 630.00 ) *rho *rho *rho *rho * rho + & + ( -2520.00 ) *rho *rho *rho *rho *rho *rho * rho + & + ( 4620.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -3960.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 1287.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 5.291502622129 ) * sin(13.00 * phi) + ! n = 13, m = -1 + zn(7) = ( ( 7.00 ) * rho + & + ( -168.00 ) *rho *rho * rho + & + ( 1260.00 ) *rho *rho *rho *rho * rho + & + ( -4200.00 ) *rho *rho *rho *rho *rho *rho * rho + & + ( 6930.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -5544.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 1716.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 5.291502622129 ) * sin(13.00 * phi) + ! n = 13, m = 1 + zn(8) = ( ( 7.00 ) * rho + & + ( -168.00 ) *rho *rho * rho + & + ( 1260.00 ) *rho *rho *rho *rho * rho + & + ( -4200.00 ) *rho *rho *rho *rho *rho *rho * rho + & + ( 6930.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -5544.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 1716.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 5.291502622129 ) * cos(13.00 * phi) + ! n = 13, m = 3 + zn(9) = ( ( -56.00 ) *rho *rho * rho + & + ( 630.00 ) *rho *rho *rho *rho * rho + & + ( -2520.00 ) *rho *rho *rho *rho *rho *rho * rho + & + ( 4620.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -3960.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 1287.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 5.291502622129 ) * cos(13.00 * phi) + ! n = 13, m = 5 + zn(10) = ( ( 126.00 ) *rho *rho *rho *rho * rho + & + ( -840.00 ) *rho *rho *rho *rho *rho *rho * rho + & + ( 1980.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -1980.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 715.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 5.291502622129 ) * cos(13.00 * phi) + ! n = 13, m = 7 + zn(11) = ( ( -120.00 ) *rho *rho *rho *rho *rho *rho * rho + & + ( 495.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -660.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 286.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 5.291502622129 ) * cos(13.00 * phi) + ! n = 13, m = 9 + zn(12) = ( ( 55.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -132.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 78.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 5.291502622129 ) * cos(13.00 * phi) + ! n = 13, m = 11 + zn(13) = ( ( -12.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 13.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 5.291502622129 ) * cos(13.00 * phi) + ! n = 13, m = 13 + zn(14) = ( ( 1.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 5.291502622129 ) * cos(13.00 * phi) + case(14) + ! n = 14, m = -14 + zn(1) = ( ( 1.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 5.477225575052 ) * sin(14.00 * phi) + ! n = 14, m = -12 + zn(2) = ( ( -13.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 14.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 5.477225575052 ) * sin(14.00 * phi) + ! n = 14, m = -10 + zn(3) = ( ( 66.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -156.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 91.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 5.477225575052 ) * sin(14.00 * phi) + ! n = 14, m = -8 + zn(4) = ( ( -165.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 660.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -858.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 364.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 5.477225575052 ) * sin(14.00 * phi) + ! n = 14, m = -6 + zn(5) = ( ( 210.00 ) *rho *rho *rho *rho *rho * rho + & + ( -1320.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 2970.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -2860.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 1001.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 5.477225575052 ) * sin(14.00 * phi) + ! n = 14, m = -4 + zn(6) = ( ( -126.00 ) *rho *rho *rho * rho + & + ( 1260.00 ) *rho *rho *rho *rho *rho * rho + & + ( -4620.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 7920.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -6435.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 2002.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 5.477225575052 ) * sin(14.00 * phi) + ! n = 14, m = -2 + zn(7) = ( ( 28.00 ) *rho * rho + & + ( -504.00 ) *rho *rho *rho * rho + & + ( 3150.00 ) *rho *rho *rho *rho *rho * rho + & + ( -9240.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 13860.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -10296.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 3003.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 5.477225575052 ) * sin(14.00 * phi) + ! n = 14, m = 0 + zn(8) = ( ( -1.00 ) + & + ( 56.00 ) *rho * rho + & + ( -756.00 ) *rho *rho *rho * rho + & + ( 4200.00 ) *rho *rho *rho *rho *rho * rho + & + ( -11550.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 16632.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -12012.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 3432.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 3.872983346207 ) + ! n = 14, m = 2 + zn(9) = ( ( 28.00 ) *rho * rho + & + ( -504.00 ) *rho *rho *rho * rho + & + ( 3150.00 ) *rho *rho *rho *rho *rho * rho + & + ( -9240.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 13860.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -10296.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 3003.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 5.477225575052 ) * cos(14.00 * phi) + ! n = 14, m = 4 + zn(10) = ( ( -126.00 ) *rho *rho *rho * rho + & + ( 1260.00 ) *rho *rho *rho *rho *rho * rho + & + ( -4620.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 7920.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -6435.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 2002.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 5.477225575052 ) * cos(14.00 * phi) + ! n = 14, m = 6 + zn(11) = ( ( 210.00 ) *rho *rho *rho *rho *rho * rho + & + ( -1320.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 2970.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -2860.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 1001.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 5.477225575052 ) * cos(14.00 * phi) + ! n = 14, m = 8 + zn(12) = ( ( -165.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 660.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -858.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 364.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 5.477225575052 ) * cos(14.00 * phi) + ! n = 14, m = 10 + zn(13) = ( ( 66.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -156.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 91.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 5.477225575052 ) * cos(14.00 * phi) + ! n = 14, m = 12 + zn(14) = ( ( -13.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 14.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 5.477225575052 ) * cos(14.00 * phi) + ! n = 14, m = 14 + zn(15) = ( ( 1.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 5.477225575052 ) * cos(14.00 * phi) + case(15) + ! n = 15, m = -15 + zn(1) = ( ( 1.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 5.656854249492 ) * sin(15.00 * phi) + ! n = 15, m = -13 + zn(2) = ( ( -14.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 15.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 5.656854249492 ) * sin(15.00 * phi) + ! n = 15, m = -11 + zn(3) = ( ( 78.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -182.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 105.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 5.656854249492 ) * sin(15.00 * phi) + ! n = 15, m = -9 + zn(4) = ( ( -220.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 858.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -1092.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 455.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 5.656854249492 ) * sin(15.00 * phi) + ! n = 15, m = -7 + zn(5) = ( ( 330.00 ) *rho *rho *rho *rho *rho *rho * rho + & + ( -1980.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 4290.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -4004.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 1365.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 5.656854249492 ) * sin(15.00 * phi) + ! n = 15, m = -5 + zn(6) = ( ( -252.00 ) *rho *rho *rho *rho * rho + & + ( 2310.00 ) *rho *rho *rho *rho *rho *rho * rho + & + ( -7920.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 12870.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -10010.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 3003.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 5.656854249492 ) * sin(15.00 * phi) + ! n = 15, m = -3 + zn(7) = ( ( 84.00 ) *rho *rho * rho + & + ( -1260.00 ) *rho *rho *rho *rho * rho + & + ( 6930.00 ) *rho *rho *rho *rho *rho *rho * rho + & + ( -18480.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 25740.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -18018.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 5005.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 5.656854249492 ) * sin(15.00 * phi) + ! n = 15, m = -1 + zn(8) = ( ( -8.00 ) * rho + & + ( 252.00 ) *rho *rho * rho + & + ( -2520.00 ) *rho *rho *rho *rho * rho + & + ( 11550.00 ) *rho *rho *rho *rho *rho *rho * rho + & + ( -27720.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 36036.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -24024.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 6435.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 5.656854249492 ) * sin(15.00 * phi) + ! n = 15, m = 1 + zn(9) = ( ( -8.00 ) * rho + & + ( 252.00 ) *rho *rho * rho + & + ( -2520.00 ) *rho *rho *rho *rho * rho + & + ( 11550.00 ) *rho *rho *rho *rho *rho *rho * rho + & + ( -27720.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 36036.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -24024.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 6435.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 5.656854249492 ) * cos(15.00 * phi) + ! n = 15, m = 3 + zn(10) = ( ( 84.00 ) *rho *rho * rho + & + ( -1260.00 ) *rho *rho *rho *rho * rho + & + ( 6930.00 ) *rho *rho *rho *rho *rho *rho * rho + & + ( -18480.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 25740.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -18018.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 5005.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 5.656854249492 ) * cos(15.00 * phi) + ! n = 15, m = 5 + zn(11) = ( ( -252.00 ) *rho *rho *rho *rho * rho + & + ( 2310.00 ) *rho *rho *rho *rho *rho *rho * rho + & + ( -7920.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 12870.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -10010.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 3003.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 5.656854249492 ) * cos(15.00 * phi) + ! n = 15, m = 7 + zn(12) = ( ( 330.00 ) *rho *rho *rho *rho *rho *rho * rho + & + ( -1980.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 4290.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -4004.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 1365.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 5.656854249492 ) * cos(15.00 * phi) + ! n = 15, m = 9 + zn(13) = ( ( -220.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 858.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -1092.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 455.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 5.656854249492 ) * cos(15.00 * phi) + ! n = 15, m = 11 + zn(14) = ( ( 78.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -182.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 105.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 5.656854249492 ) * cos(15.00 * phi) + ! n = 15, m = 13 + zn(15) = ( ( -14.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 15.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 5.656854249492 ) * cos(15.00 * phi) + ! n = 15, m = 15 + zn(16) = ( ( 1.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 5.656854249492 ) * cos(15.00 * phi) + case(16) + ! n = 16, m = -16 + zn(1) = ( ( 1.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 5.830951894845 ) * sin(16.00 * phi) + ! n = 16, m = -14 + zn(2) = ( ( -15.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 16.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 5.830951894845 ) * sin(16.00 * phi) + ! n = 16, m = -12 + zn(3) = ( ( 91.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -210.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 120.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 5.830951894845 ) * sin(16.00 * phi) + ! n = 16, m = -10 + zn(4) = ( ( -286.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 1092.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -1365.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 560.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 5.830951894845 ) * sin(16.00 * phi) + ! n = 16, m = -8 + zn(5) = ( ( 495.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -2860.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 6006.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -5460.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 1820.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 5.830951894845 ) * sin(16.00 * phi) + ! n = 16, m = -6 + zn(6) = ( ( -462.00 ) *rho *rho *rho *rho *rho * rho + & + ( 3960.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -12870.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 20020.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -15015.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 4368.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 5.830951894845 ) * sin(16.00 * phi) + ! n = 16, m = -4 + zn(7) = ( ( 210.00 ) *rho *rho *rho * rho + & + ( -2772.00 ) *rho *rho *rho *rho *rho * rho + & + ( 13860.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -34320.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 45045.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -30030.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 8008.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 5.830951894845 ) * sin(16.00 * phi) + ! n = 16, m = -2 + zn(8) = ( ( -36.00 ) *rho * rho + & + ( 840.00 ) *rho *rho *rho * rho + & + ( -6930.00 ) *rho *rho *rho *rho *rho * rho + & + ( 27720.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -60060.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 72072.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -45045.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 11440.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 5.830951894845 ) * sin(16.00 * phi) + ! n = 16, m = 0 + zn(9) = ( ( 1.00 ) + & + ( -72.00 ) *rho * rho + & + ( 1260.00 ) *rho *rho *rho * rho + & + ( -9240.00 ) *rho *rho *rho *rho *rho * rho + & + ( 34650.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -72072.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 84084.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -51480.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 12870.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 4.123105625618 ) + ! n = 16, m = 2 + zn(10) = ( ( -36.00 ) *rho * rho + & + ( 840.00 ) *rho *rho *rho * rho + & + ( -6930.00 ) *rho *rho *rho *rho *rho * rho + & + ( 27720.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -60060.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 72072.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -45045.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 11440.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 5.830951894845 ) * cos(16.00 * phi) + ! n = 16, m = 4 + zn(11) = ( ( 210.00 ) *rho *rho *rho * rho + & + ( -2772.00 ) *rho *rho *rho *rho *rho * rho + & + ( 13860.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -34320.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 45045.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -30030.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 8008.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 5.830951894845 ) * cos(16.00 * phi) + ! n = 16, m = 6 + zn(12) = ( ( -462.00 ) *rho *rho *rho *rho *rho * rho + & + ( 3960.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -12870.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 20020.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -15015.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 4368.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 5.830951894845 ) * cos(16.00 * phi) + ! n = 16, m = 8 + zn(13) = ( ( 495.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -2860.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 6006.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -5460.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 1820.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 5.830951894845 ) * cos(16.00 * phi) + ! n = 16, m = 10 + zn(14) = ( ( -286.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 1092.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -1365.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 560.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 5.830951894845 ) * cos(16.00 * phi) + ! n = 16, m = 12 + zn(15) = ( ( 91.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -210.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 120.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 5.830951894845 ) * cos(16.00 * phi) + ! n = 16, m = 14 + zn(16) = ( ( -15.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 16.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 5.830951894845 ) * cos(16.00 * phi) + ! n = 16, m = 16 + zn(17) = ( ( 1.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 5.830951894845 ) * cos(16.00 * phi) + case(17) + ! n = 17, m = -17 + zn(1) = ( ( 1.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 6.000000000000 ) * sin(17.00 * phi) + ! n = 17, m = -15 + zn(2) = ( ( -16.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 17.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 6.000000000000 ) * sin(17.00 * phi) + ! n = 17, m = -13 + zn(3) = ( ( 105.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -240.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 136.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 6.000000000000 ) * sin(17.00 * phi) + ! n = 17, m = -11 + zn(4) = ( ( -364.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 1365.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -1680.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 680.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 6.000000000000 ) * sin(17.00 * phi) + ! n = 17, m = -9 + zn(5) = ( ( 715.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -4004.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 8190.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -7280.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 2380.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 6.000000000000 ) * sin(17.00 * phi) + ! n = 17, m = -7 + zn(6) = ( ( -792.00 ) *rho *rho *rho *rho *rho *rho * rho + & + ( 6435.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -20020.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 30030.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -21840.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 6188.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 6.000000000000 ) * sin(17.00 * phi) + ! n = 17, m = -5 + zn(7) = ( ( 462.00 ) *rho *rho *rho *rho * rho + & + ( -5544.00 ) *rho *rho *rho *rho *rho *rho * rho + & + ( 25740.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -60060.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 75075.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -48048.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 12376.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 6.000000000000 ) * sin(17.00 * phi) + ! n = 17, m = -3 + zn(8) = ( ( -120.00 ) *rho *rho * rho + & + ( 2310.00 ) *rho *rho *rho *rho * rho + & + ( -16632.00 ) *rho *rho *rho *rho *rho *rho * rho + & + ( 60060.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -120120.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 135135.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -80080.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 19448.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 6.000000000000 ) * sin(17.00 * phi) + ! n = 17, m = -1 + zn(9) = ( ( 9.00 ) * rho + & + ( -360.00 ) *rho *rho * rho + & + ( 4620.00 ) *rho *rho *rho *rho * rho + & + ( -27720.00 ) *rho *rho *rho *rho *rho *rho * rho + & + ( 90090.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -168168.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 180180.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -102960.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 24310.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 6.000000000000 ) * sin(17.00 * phi) + ! n = 17, m = 1 + zn(10) = ( ( 9.00 ) * rho + & + ( -360.00 ) *rho *rho * rho + & + ( 4620.00 ) *rho *rho *rho *rho * rho + & + ( -27720.00 ) *rho *rho *rho *rho *rho *rho * rho + & + ( 90090.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -168168.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 180180.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -102960.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 24310.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 6.000000000000 ) * cos(17.00 * phi) + ! n = 17, m = 3 + zn(11) = ( ( -120.00 ) *rho *rho * rho + & + ( 2310.00 ) *rho *rho *rho *rho * rho + & + ( -16632.00 ) *rho *rho *rho *rho *rho *rho * rho + & + ( 60060.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -120120.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 135135.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -80080.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 19448.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 6.000000000000 ) * cos(17.00 * phi) + ! n = 17, m = 5 + zn(12) = ( ( 462.00 ) *rho *rho *rho *rho * rho + & + ( -5544.00 ) *rho *rho *rho *rho *rho *rho * rho + & + ( 25740.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -60060.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 75075.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -48048.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 12376.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 6.000000000000 ) * cos(17.00 * phi) + ! n = 17, m = 7 + zn(13) = ( ( -792.00 ) *rho *rho *rho *rho *rho *rho * rho + & + ( 6435.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -20020.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 30030.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -21840.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 6188.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 6.000000000000 ) * cos(17.00 * phi) + ! n = 17, m = 9 + zn(14) = ( ( 715.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -4004.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 8190.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -7280.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 2380.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 6.000000000000 ) * cos(17.00 * phi) + ! n = 17, m = 11 + zn(15) = ( ( -364.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 1365.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -1680.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 680.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 6.000000000000 ) * cos(17.00 * phi) + ! n = 17, m = 13 + zn(16) = ( ( 105.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -240.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 136.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 6.000000000000 ) * cos(17.00 * phi) + ! n = 17, m = 15 + zn(17) = ( ( -16.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 17.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 6.000000000000 ) * cos(17.00 * phi) + ! n = 17, m = 17 + zn(18) = ( ( 1.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 6.000000000000 ) * cos(17.00 * phi) + case(18) + ! n = 18, m = -18 + zn(1) = ( ( 1.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 6.164414002969 ) * sin(18.00 * phi) + ! n = 18, m = -16 + zn(2) = ( ( -17.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 18.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 6.164414002969 ) * sin(18.00 * phi) + ! n = 18, m = -14 + zn(3) = ( ( 120.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -272.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 153.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 6.164414002969 ) * sin(18.00 * phi) + ! n = 18, m = -12 + zn(4) = ( ( -455.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 1680.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -2040.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 816.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 6.164414002969 ) * sin(18.00 * phi) + ! n = 18, m = -10 + zn(5) = ( ( 1001.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -5460.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 10920.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -9520.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 3060.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 6.164414002969 ) * sin(18.00 * phi) + ! n = 18, m = -8 + zn(6) = ( ( -1287.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 10010.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -30030.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 43680.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -30940.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 8568.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 6.164414002969 ) * sin(18.00 * phi) + ! n = 18, m = -6 + zn(7) = ( ( 924.00 ) *rho *rho *rho *rho *rho * rho + & + ( -10296.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 45045.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -100100.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 120120.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -74256.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 18564.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 6.164414002969 ) * sin(18.00 * phi) + ! n = 18, m = -4 + zn(8) = ( ( -330.00 ) *rho *rho *rho * rho + & + ( 5544.00 ) *rho *rho *rho *rho *rho * rho + & + ( -36036.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 120120.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -225225.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 240240.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -136136.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 31824.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 6.164414002969 ) * sin(18.00 * phi) + ! n = 18, m = -2 + zn(9) = ( ( 45.00 ) *rho * rho + & + ( -1320.00 ) *rho *rho *rho * rho + & + ( 13860.00 ) *rho *rho *rho *rho *rho * rho + & + ( -72072.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 210210.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -360360.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 360360.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -194480.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 43758.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 6.164414002969 ) * sin(18.00 * phi) + ! n = 18, m = 0 + zn(10) = ( ( -1.00 ) + & + ( 90.00 ) *rho * rho + & + ( -1980.00 ) *rho *rho *rho * rho + & + ( 18480.00 ) *rho *rho *rho *rho *rho * rho + & + ( -90090.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 252252.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -420420.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 411840.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -218790.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 48620.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 4.358898943541 ) + ! n = 18, m = 2 + zn(11) = ( ( 45.00 ) *rho * rho + & + ( -1320.00 ) *rho *rho *rho * rho + & + ( 13860.00 ) *rho *rho *rho *rho *rho * rho + & + ( -72072.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 210210.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -360360.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 360360.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -194480.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 43758.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 6.164414002969 ) * cos(18.00 * phi) + ! n = 18, m = 4 + zn(12) = ( ( -330.00 ) *rho *rho *rho * rho + & + ( 5544.00 ) *rho *rho *rho *rho *rho * rho + & + ( -36036.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 120120.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -225225.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 240240.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -136136.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 31824.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 6.164414002969 ) * cos(18.00 * phi) + ! n = 18, m = 6 + zn(13) = ( ( 924.00 ) *rho *rho *rho *rho *rho * rho + & + ( -10296.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 45045.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -100100.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 120120.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -74256.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 18564.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 6.164414002969 ) * cos(18.00 * phi) + ! n = 18, m = 8 + zn(14) = ( ( -1287.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 10010.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -30030.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 43680.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -30940.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 8568.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 6.164414002969 ) * cos(18.00 * phi) + ! n = 18, m = 10 + zn(15) = ( ( 1001.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -5460.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 10920.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -9520.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 3060.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 6.164414002969 ) * cos(18.00 * phi) + ! n = 18, m = 12 + zn(16) = ( ( -455.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 1680.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -2040.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 816.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 6.164414002969 ) * cos(18.00 * phi) + ! n = 18, m = 14 + zn(17) = ( ( 120.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( -272.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 153.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 6.164414002969 ) * cos(18.00 * phi) + ! n = 18, m = 16 + zn(18) = ( ( -17.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & + ( 18.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 6.164414002969 ) * cos(18.00 * phi) + ! n = 18, m = 18 + zn(19) = ( ( 1.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & + * ( 6.164414002969 ) * cos(18.00 * phi) + case default + zn = ONE + end select + + end function calc_zn + !=============================================================================== ! EXPAND_HARMONIC expands a given series of real spherical harmonics !=============================================================================== diff --git a/src/tallies/tally_filter_zernike.F90 b/src/tallies/tally_filter_zernike.F90 index 6f00e131d8..08bc24e605 100644 --- a/src/tallies/tally_filter_zernike.F90 +++ b/src/tallies/tally_filter_zernike.F90 @@ -7,6 +7,7 @@ module tally_filter_zernike use constants use error use hdf5_interface + use math, only: calc_zn use particle_header, only: Particle use string, only: to_str use tally_filter_header @@ -76,7 +77,7 @@ contains i = 0 do n = 0, this % order ! Get moments for n-th order Zernike polynomial - tmp(1:n+1) = calc_zn_scaled(n, r, theta) + tmp(1:n+1) = calc_zn(n, r, theta) / SQRT_PI ! Indicate matching bins/weights do j = 1, n + 1 @@ -119,1160 +120,6 @@ contains end do end function text_label - -!=============================================================================== -! CALC_ZN calculates the n-th order Zernike polynomial moment for a given angle -! (rho, theta) location in the unit disk. -!=============================================================================== - - pure function calc_zn(n, rho, phi) result(zn) - - integer, intent(in) :: n ! Order requested - real(8), intent(in) :: rho ! Radial location in the unit disk - real(8), intent(in) :: phi ! Theta (radians) location in the unit disk - real(8) :: zn(n + 1) ! The resultant Z_n(uvw) - - ! n == radial degree - ! m == azimuthal frequency - - select case(n) - case(0) - ! n = 0, m = 0 - zn(1) = ( ( 1.00 ) ) & - * ( 1.000000000000 ) - case(1) - ! n = 1, m = -1 - zn(1) = ( ( 1.00 ) * rho ) & - * ( 2.000000000000 ) * sin(1.00 * phi) - ! n = 1, m = 1 - zn(2) = ( ( 1.00 ) * rho ) & - * ( 2.000000000000 ) * cos(1.00 * phi) - case(2) - ! n = 2, m = -2 - zn(1) = ( ( 1.00 ) *rho * rho ) & - * ( 2.449489742783 ) * sin(2.00 * phi) - ! n = 2, m = 0 - zn(2) = ( ( -1.00 ) + & - ( 2.00 ) *rho * rho ) & - * ( 1.732050807569 ) - ! n = 2, m = 2 - zn(3) = ( ( 1.00 ) *rho * rho ) & - * ( 2.449489742783 ) * cos(2.00 * phi) - case(3) - ! n = 3, m = -3 - zn(1) = ( ( 1.00 ) *rho *rho * rho ) & - * ( 2.828427124746 ) * sin(3.00 * phi) - ! n = 3, m = -1 - zn(2) = ( ( -2.00 ) * rho + & - ( 3.00 ) *rho *rho * rho ) & - * ( 2.828427124746 ) * sin(3.00 * phi) - ! n = 3, m = 1 - zn(3) = ( ( -2.00 ) * rho + & - ( 3.00 ) *rho *rho * rho ) & - * ( 2.828427124746 ) * cos(3.00 * phi) - ! n = 3, m = 3 - zn(4) = ( ( 1.00 ) *rho *rho * rho ) & - * ( 2.828427124746 ) * cos(3.00 * phi) - case(4) - ! n = 4, m = -4 - zn(1) = ( ( 1.00 ) *rho *rho *rho * rho ) & - * ( 3.162277660168 ) * sin(4.00 * phi) - ! n = 4, m = -2 - zn(2) = ( ( -3.00 ) *rho * rho + & - ( 4.00 ) *rho *rho *rho * rho ) & - * ( 3.162277660168 ) * sin(4.00 * phi) - ! n = 4, m = 0 - zn(3) = ( ( 1.00 ) + & - ( -6.00 ) *rho * rho + & - ( 6.00 ) *rho *rho *rho * rho ) & - * ( 2.236067977500 ) - ! n = 4, m = 2 - zn(4) = ( ( -3.00 ) *rho * rho + & - ( 4.00 ) *rho *rho *rho * rho ) & - * ( 3.162277660168 ) * cos(4.00 * phi) - ! n = 4, m = 4 - zn(5) = ( ( 1.00 ) *rho *rho *rho * rho ) & - * ( 3.162277660168 ) * cos(4.00 * phi) - case(5) - ! n = 5, m = -5 - zn(1) = ( ( 1.00 ) *rho *rho *rho *rho * rho ) & - * ( 3.464101615138 ) * sin(5.00 * phi) - ! n = 5, m = -3 - zn(2) = ( ( -4.00 ) *rho *rho * rho + & - ( 5.00 ) *rho *rho *rho *rho * rho ) & - * ( 3.464101615138 ) * sin(5.00 * phi) - ! n = 5, m = -1 - zn(3) = ( ( 3.00 ) * rho + & - ( -12.00 ) *rho *rho * rho + & - ( 10.00 ) *rho *rho *rho *rho * rho ) & - * ( 3.464101615138 ) * sin(5.00 * phi) - ! n = 5, m = 1 - zn(4) = ( ( 3.00 ) * rho + & - ( -12.00 ) *rho *rho * rho + & - ( 10.00 ) *rho *rho *rho *rho * rho ) & - * ( 3.464101615138 ) * cos(5.00 * phi) - ! n = 5, m = 3 - zn(5) = ( ( -4.00 ) *rho *rho * rho + & - ( 5.00 ) *rho *rho *rho *rho * rho ) & - * ( 3.464101615138 ) * cos(5.00 * phi) - ! n = 5, m = 5 - zn(6) = ( ( 1.00 ) *rho *rho *rho *rho * rho ) & - * ( 3.464101615138 ) * cos(5.00 * phi) - case(6) - ! n = 6, m = -6 - zn(1) = ( ( 1.00 ) *rho *rho *rho *rho *rho * rho ) & - * ( 3.741657386774 ) * sin(6.00 * phi) - ! n = 6, m = -4 - zn(2) = ( ( -5.00 ) *rho *rho *rho * rho + & - ( 6.00 ) *rho *rho *rho *rho *rho * rho ) & - * ( 3.741657386774 ) * sin(6.00 * phi) - ! n = 6, m = -2 - zn(3) = ( ( 6.00 ) *rho * rho + & - ( -20.00 ) *rho *rho *rho * rho + & - ( 15.00 ) *rho *rho *rho *rho *rho * rho ) & - * ( 3.741657386774 ) * sin(6.00 * phi) - ! n = 6, m = 0 - zn(4) = ( ( -1.00 ) + & - ( 12.00 ) *rho * rho + & - ( -30.00 ) *rho *rho *rho * rho + & - ( 20.00 ) *rho *rho *rho *rho *rho * rho ) & - * ( 2.645751311065 ) - ! n = 6, m = 2 - zn(5) = ( ( 6.00 ) *rho * rho + & - ( -20.00 ) *rho *rho *rho * rho + & - ( 15.00 ) *rho *rho *rho *rho *rho * rho ) & - * ( 3.741657386774 ) * cos(6.00 * phi) - ! n = 6, m = 4 - zn(6) = ( ( -5.00 ) *rho *rho *rho * rho + & - ( 6.00 ) *rho *rho *rho *rho *rho * rho ) & - * ( 3.741657386774 ) * cos(6.00 * phi) - ! n = 6, m = 6 - zn(7) = ( ( 1.00 ) *rho *rho *rho *rho *rho * rho ) & - * ( 3.741657386774 ) * cos(6.00 * phi) - case(7) - ! n = 7, m = -7 - zn(1) = ( ( 1.00 ) *rho *rho *rho *rho *rho *rho * rho ) & - * ( 4.000000000000 ) * sin(7.00 * phi) - ! n = 7, m = -5 - zn(2) = ( ( -6.00 ) *rho *rho *rho *rho * rho + & - ( 7.00 ) *rho *rho *rho *rho *rho *rho * rho ) & - * ( 4.000000000000 ) * sin(7.00 * phi) - ! n = 7, m = -3 - zn(3) = ( ( 10.00 ) *rho *rho * rho + & - ( -30.00 ) *rho *rho *rho *rho * rho + & - ( 21.00 ) *rho *rho *rho *rho *rho *rho * rho ) & - * ( 4.000000000000 ) * sin(7.00 * phi) - ! n = 7, m = -1 - zn(4) = ( ( -4.00 ) * rho + & - ( 30.00 ) *rho *rho * rho + & - ( -60.00 ) *rho *rho *rho *rho * rho + & - ( 35.00 ) *rho *rho *rho *rho *rho *rho * rho ) & - * ( 4.000000000000 ) * sin(7.00 * phi) - ! n = 7, m = 1 - zn(5) = ( ( -4.00 ) * rho + & - ( 30.00 ) *rho *rho * rho + & - ( -60.00 ) *rho *rho *rho *rho * rho + & - ( 35.00 ) *rho *rho *rho *rho *rho *rho * rho ) & - * ( 4.000000000000 ) * cos(7.00 * phi) - ! n = 7, m = 3 - zn(6) = ( ( 10.00 ) *rho *rho * rho + & - ( -30.00 ) *rho *rho *rho *rho * rho + & - ( 21.00 ) *rho *rho *rho *rho *rho *rho * rho ) & - * ( 4.000000000000 ) * cos(7.00 * phi) - ! n = 7, m = 5 - zn(7) = ( ( -6.00 ) *rho *rho *rho *rho * rho + & - ( 7.00 ) *rho *rho *rho *rho *rho *rho * rho ) & - * ( 4.000000000000 ) * cos(7.00 * phi) - ! n = 7, m = 7 - zn(8) = ( ( 1.00 ) *rho *rho *rho *rho *rho *rho * rho ) & - * ( 4.000000000000 ) * cos(7.00 * phi) - case(8) - ! n = 8, m = -8 - zn(1) = ( ( 1.00 ) *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 4.242640687119 ) * sin(8.00 * phi) - ! n = 8, m = -6 - zn(2) = ( ( -7.00 ) *rho *rho *rho *rho *rho * rho + & - ( 8.00 ) *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 4.242640687119 ) * sin(8.00 * phi) - ! n = 8, m = -4 - zn(3) = ( ( 15.00 ) *rho *rho *rho * rho + & - ( -42.00 ) *rho *rho *rho *rho *rho * rho + & - ( 28.00 ) *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 4.242640687119 ) * sin(8.00 * phi) - ! n = 8, m = -2 - zn(4) = ( ( -10.00 ) *rho * rho + & - ( 60.00 ) *rho *rho *rho * rho + & - ( -105.00 ) *rho *rho *rho *rho *rho * rho + & - ( 56.00 ) *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 4.242640687119 ) * sin(8.00 * phi) - ! n = 8, m = 0 - zn(5) = ( ( 1.00 ) + & - ( -20.00 ) *rho * rho + & - ( 90.00 ) *rho *rho *rho * rho + & - ( -140.00 ) *rho *rho *rho *rho *rho * rho + & - ( 70.00 ) *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 3.000000000000 ) - ! n = 8, m = 2 - zn(6) = ( ( -10.00 ) *rho * rho + & - ( 60.00 ) *rho *rho *rho * rho + & - ( -105.00 ) *rho *rho *rho *rho *rho * rho + & - ( 56.00 ) *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 4.242640687119 ) * cos(8.00 * phi) - ! n = 8, m = 4 - zn(7) = ( ( 15.00 ) *rho *rho *rho * rho + & - ( -42.00 ) *rho *rho *rho *rho *rho * rho + & - ( 28.00 ) *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 4.242640687119 ) * cos(8.00 * phi) - ! n = 8, m = 6 - zn(8) = ( ( -7.00 ) *rho *rho *rho *rho *rho * rho + & - ( 8.00 ) *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 4.242640687119 ) * cos(8.00 * phi) - ! n = 8, m = 8 - zn(9) = ( ( 1.00 ) *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 4.242640687119 ) * cos(8.00 * phi) - case(9) - ! n = 9, m = -9 - zn(1) = ( ( 1.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 4.472135955000 ) * sin(9.00 * phi) - ! n = 9, m = -7 - zn(2) = ( ( -8.00 ) *rho *rho *rho *rho *rho *rho * rho + & - ( 9.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 4.472135955000 ) * sin(9.00 * phi) - ! n = 9, m = -5 - zn(3) = ( ( 21.00 ) *rho *rho *rho *rho * rho + & - ( -56.00 ) *rho *rho *rho *rho *rho *rho * rho + & - ( 36.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 4.472135955000 ) * sin(9.00 * phi) - ! n = 9, m = -3 - zn(4) = ( ( -20.00 ) *rho *rho * rho + & - ( 105.00 ) *rho *rho *rho *rho * rho + & - ( -168.00 ) *rho *rho *rho *rho *rho *rho * rho + & - ( 84.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 4.472135955000 ) * sin(9.00 * phi) - ! n = 9, m = -1 - zn(5) = ( ( 5.00 ) * rho + & - ( -60.00 ) *rho *rho * rho + & - ( 210.00 ) *rho *rho *rho *rho * rho + & - ( -280.00 ) *rho *rho *rho *rho *rho *rho * rho + & - ( 126.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 4.472135955000 ) * sin(9.00 * phi) - ! n = 9, m = 1 - zn(6) = ( ( 5.00 ) * rho + & - ( -60.00 ) *rho *rho * rho + & - ( 210.00 ) *rho *rho *rho *rho * rho + & - ( -280.00 ) *rho *rho *rho *rho *rho *rho * rho + & - ( 126.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 4.472135955000 ) * cos(9.00 * phi) - ! n = 9, m = 3 - zn(7) = ( ( -20.00 ) *rho *rho * rho + & - ( 105.00 ) *rho *rho *rho *rho * rho + & - ( -168.00 ) *rho *rho *rho *rho *rho *rho * rho + & - ( 84.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 4.472135955000 ) * cos(9.00 * phi) - ! n = 9, m = 5 - zn(8) = ( ( 21.00 ) *rho *rho *rho *rho * rho + & - ( -56.00 ) *rho *rho *rho *rho *rho *rho * rho + & - ( 36.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 4.472135955000 ) * cos(9.00 * phi) - ! n = 9, m = 7 - zn(9) = ( ( -8.00 ) *rho *rho *rho *rho *rho *rho * rho + & - ( 9.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 4.472135955000 ) * cos(9.00 * phi) - ! n = 9, m = 9 - zn(10) = ( ( 1.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 4.472135955000 ) * cos(9.00 * phi) - case(10) - ! n = 10, m = -10 - zn(1) = ( ( 1.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 4.690415759823 ) * sin(10.00 * phi) - ! n = 10, m = -8 - zn(2) = ( ( -9.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 10.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 4.690415759823 ) * sin(10.00 * phi) - ! n = 10, m = -6 - zn(3) = ( ( 28.00 ) *rho *rho *rho *rho *rho * rho + & - ( -72.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 45.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 4.690415759823 ) * sin(10.00 * phi) - ! n = 10, m = -4 - zn(4) = ( ( -35.00 ) *rho *rho *rho * rho + & - ( 168.00 ) *rho *rho *rho *rho *rho * rho + & - ( -252.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 120.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 4.690415759823 ) * sin(10.00 * phi) - ! n = 10, m = -2 - zn(5) = ( ( 15.00 ) *rho * rho + & - ( -140.00 ) *rho *rho *rho * rho + & - ( 420.00 ) *rho *rho *rho *rho *rho * rho + & - ( -504.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 210.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 4.690415759823 ) * sin(10.00 * phi) - ! n = 10, m = 0 - zn(6) = ( ( -1.00 ) + & - ( 30.00 ) *rho * rho + & - ( -210.00 ) *rho *rho *rho * rho + & - ( 560.00 ) *rho *rho *rho *rho *rho * rho + & - ( -630.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 252.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 3.316624790355 ) - ! n = 10, m = 2 - zn(7) = ( ( 15.00 ) *rho * rho + & - ( -140.00 ) *rho *rho *rho * rho + & - ( 420.00 ) *rho *rho *rho *rho *rho * rho + & - ( -504.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 210.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 4.690415759823 ) * cos(10.00 * phi) - ! n = 10, m = 4 - zn(8) = ( ( -35.00 ) *rho *rho *rho * rho + & - ( 168.00 ) *rho *rho *rho *rho *rho * rho + & - ( -252.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 120.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 4.690415759823 ) * cos(10.00 * phi) - ! n = 10, m = 6 - zn(9) = ( ( 28.00 ) *rho *rho *rho *rho *rho * rho + & - ( -72.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 45.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 4.690415759823 ) * cos(10.00 * phi) - ! n = 10, m = 8 - zn(10) = ( ( -9.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 10.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 4.690415759823 ) * cos(10.00 * phi) - ! n = 10, m = 10 - zn(11) = ( ( 1.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 4.690415759823 ) * cos(10.00 * phi) - case(11) - ! n = 11, m = -11 - zn(1) = ( ( 1.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 4.898979485566 ) * sin(11.00 * phi) - ! n = 11, m = -9 - zn(2) = ( ( -10.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 11.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 4.898979485566 ) * sin(11.00 * phi) - ! n = 11, m = -7 - zn(3) = ( ( 36.00 ) *rho *rho *rho *rho *rho *rho * rho + & - ( -90.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 55.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 4.898979485566 ) * sin(11.00 * phi) - ! n = 11, m = -5 - zn(4) = ( ( -56.00 ) *rho *rho *rho *rho * rho + & - ( 252.00 ) *rho *rho *rho *rho *rho *rho * rho + & - ( -360.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 165.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 4.898979485566 ) * sin(11.00 * phi) - ! n = 11, m = -3 - zn(5) = ( ( 35.00 ) *rho *rho * rho + & - ( -280.00 ) *rho *rho *rho *rho * rho + & - ( 756.00 ) *rho *rho *rho *rho *rho *rho * rho + & - ( -840.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 330.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 4.898979485566 ) * sin(11.00 * phi) - ! n = 11, m = -1 - zn(6) = ( ( -6.00 ) * rho + & - ( 105.00 ) *rho *rho * rho + & - ( -560.00 ) *rho *rho *rho *rho * rho + & - ( 1260.00 ) *rho *rho *rho *rho *rho *rho * rho + & - ( -1260.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 462.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 4.898979485566 ) * sin(11.00 * phi) - ! n = 11, m = 1 - zn(7) = ( ( -6.00 ) * rho + & - ( 105.00 ) *rho *rho * rho + & - ( -560.00 ) *rho *rho *rho *rho * rho + & - ( 1260.00 ) *rho *rho *rho *rho *rho *rho * rho + & - ( -1260.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 462.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 4.898979485566 ) * cos(11.00 * phi) - ! n = 11, m = 3 - zn(8) = ( ( 35.00 ) *rho *rho * rho + & - ( -280.00 ) *rho *rho *rho *rho * rho + & - ( 756.00 ) *rho *rho *rho *rho *rho *rho * rho + & - ( -840.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 330.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 4.898979485566 ) * cos(11.00 * phi) - ! n = 11, m = 5 - zn(9) = ( ( -56.00 ) *rho *rho *rho *rho * rho + & - ( 252.00 ) *rho *rho *rho *rho *rho *rho * rho + & - ( -360.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 165.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 4.898979485566 ) * cos(11.00 * phi) - ! n = 11, m = 7 - zn(10) = ( ( 36.00 ) *rho *rho *rho *rho *rho *rho * rho + & - ( -90.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 55.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 4.898979485566 ) * cos(11.00 * phi) - ! n = 11, m = 9 - zn(11) = ( ( -10.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 11.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 4.898979485566 ) * cos(11.00 * phi) - ! n = 11, m = 11 - zn(12) = ( ( 1.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 4.898979485566 ) * cos(11.00 * phi) - case(12) - ! n = 12, m = -12 - zn(1) = ( ( 1.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 5.099019513593 ) * sin(12.00 * phi) - ! n = 12, m = -10 - zn(2) = ( ( -11.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 12.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 5.099019513593 ) * sin(12.00 * phi) - ! n = 12, m = -8 - zn(3) = ( ( 45.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -110.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 66.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 5.099019513593 ) * sin(12.00 * phi) - ! n = 12, m = -6 - zn(4) = ( ( -84.00 ) *rho *rho *rho *rho *rho * rho + & - ( 360.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -495.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 220.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 5.099019513593 ) * sin(12.00 * phi) - ! n = 12, m = -4 - zn(5) = ( ( 70.00 ) *rho *rho *rho * rho + & - ( -504.00 ) *rho *rho *rho *rho *rho * rho + & - ( 1260.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -1320.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 495.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 5.099019513593 ) * sin(12.00 * phi) - ! n = 12, m = -2 - zn(6) = ( ( -21.00 ) *rho * rho + & - ( 280.00 ) *rho *rho *rho * rho + & - ( -1260.00 ) *rho *rho *rho *rho *rho * rho + & - ( 2520.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -2310.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 792.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 5.099019513593 ) * sin(12.00 * phi) - ! n = 12, m = 0 - zn(7) = ( ( 1.00 ) + & - ( -42.00 ) *rho * rho + & - ( 420.00 ) *rho *rho *rho * rho + & - ( -1680.00 ) *rho *rho *rho *rho *rho * rho + & - ( 3150.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -2772.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 924.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 3.605551275464 ) - ! n = 12, m = 2 - zn(8) = ( ( -21.00 ) *rho * rho + & - ( 280.00 ) *rho *rho *rho * rho + & - ( -1260.00 ) *rho *rho *rho *rho *rho * rho + & - ( 2520.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -2310.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 792.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 5.099019513593 ) * cos(12.00 * phi) - ! n = 12, m = 4 - zn(9) = ( ( 70.00 ) *rho *rho *rho * rho + & - ( -504.00 ) *rho *rho *rho *rho *rho * rho + & - ( 1260.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -1320.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 495.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 5.099019513593 ) * cos(12.00 * phi) - ! n = 12, m = 6 - zn(10) = ( ( -84.00 ) *rho *rho *rho *rho *rho * rho + & - ( 360.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -495.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 220.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 5.099019513593 ) * cos(12.00 * phi) - ! n = 12, m = 8 - zn(11) = ( ( 45.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -110.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 66.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 5.099019513593 ) * cos(12.00 * phi) - ! n = 12, m = 10 - zn(12) = ( ( -11.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 12.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 5.099019513593 ) * cos(12.00 * phi) - ! n = 12, m = 12 - zn(13) = ( ( 1.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 5.099019513593 ) * cos(12.00 * phi) - case(13) - ! n = 13, m = -13 - zn(1) = ( ( 1.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 5.291502622129 ) * sin(13.00 * phi) - ! n = 13, m = -11 - zn(2) = ( ( -12.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 13.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 5.291502622129 ) * sin(13.00 * phi) - ! n = 13, m = -9 - zn(3) = ( ( 55.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -132.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 78.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 5.291502622129 ) * sin(13.00 * phi) - ! n = 13, m = -7 - zn(4) = ( ( -120.00 ) *rho *rho *rho *rho *rho *rho * rho + & - ( 495.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -660.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 286.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 5.291502622129 ) * sin(13.00 * phi) - ! n = 13, m = -5 - zn(5) = ( ( 126.00 ) *rho *rho *rho *rho * rho + & - ( -840.00 ) *rho *rho *rho *rho *rho *rho * rho + & - ( 1980.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -1980.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 715.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 5.291502622129 ) * sin(13.00 * phi) - ! n = 13, m = -3 - zn(6) = ( ( -56.00 ) *rho *rho * rho + & - ( 630.00 ) *rho *rho *rho *rho * rho + & - ( -2520.00 ) *rho *rho *rho *rho *rho *rho * rho + & - ( 4620.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -3960.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 1287.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 5.291502622129 ) * sin(13.00 * phi) - ! n = 13, m = -1 - zn(7) = ( ( 7.00 ) * rho + & - ( -168.00 ) *rho *rho * rho + & - ( 1260.00 ) *rho *rho *rho *rho * rho + & - ( -4200.00 ) *rho *rho *rho *rho *rho *rho * rho + & - ( 6930.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -5544.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 1716.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 5.291502622129 ) * sin(13.00 * phi) - ! n = 13, m = 1 - zn(8) = ( ( 7.00 ) * rho + & - ( -168.00 ) *rho *rho * rho + & - ( 1260.00 ) *rho *rho *rho *rho * rho + & - ( -4200.00 ) *rho *rho *rho *rho *rho *rho * rho + & - ( 6930.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -5544.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 1716.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 5.291502622129 ) * cos(13.00 * phi) - ! n = 13, m = 3 - zn(9) = ( ( -56.00 ) *rho *rho * rho + & - ( 630.00 ) *rho *rho *rho *rho * rho + & - ( -2520.00 ) *rho *rho *rho *rho *rho *rho * rho + & - ( 4620.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -3960.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 1287.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 5.291502622129 ) * cos(13.00 * phi) - ! n = 13, m = 5 - zn(10) = ( ( 126.00 ) *rho *rho *rho *rho * rho + & - ( -840.00 ) *rho *rho *rho *rho *rho *rho * rho + & - ( 1980.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -1980.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 715.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 5.291502622129 ) * cos(13.00 * phi) - ! n = 13, m = 7 - zn(11) = ( ( -120.00 ) *rho *rho *rho *rho *rho *rho * rho + & - ( 495.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -660.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 286.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 5.291502622129 ) * cos(13.00 * phi) - ! n = 13, m = 9 - zn(12) = ( ( 55.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -132.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 78.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 5.291502622129 ) * cos(13.00 * phi) - ! n = 13, m = 11 - zn(13) = ( ( -12.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 13.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 5.291502622129 ) * cos(13.00 * phi) - ! n = 13, m = 13 - zn(14) = ( ( 1.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 5.291502622129 ) * cos(13.00 * phi) - case(14) - ! n = 14, m = -14 - zn(1) = ( ( 1.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 5.477225575052 ) * sin(14.00 * phi) - ! n = 14, m = -12 - zn(2) = ( ( -13.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 14.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 5.477225575052 ) * sin(14.00 * phi) - ! n = 14, m = -10 - zn(3) = ( ( 66.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -156.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 91.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 5.477225575052 ) * sin(14.00 * phi) - ! n = 14, m = -8 - zn(4) = ( ( -165.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 660.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -858.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 364.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 5.477225575052 ) * sin(14.00 * phi) - ! n = 14, m = -6 - zn(5) = ( ( 210.00 ) *rho *rho *rho *rho *rho * rho + & - ( -1320.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 2970.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -2860.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 1001.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 5.477225575052 ) * sin(14.00 * phi) - ! n = 14, m = -4 - zn(6) = ( ( -126.00 ) *rho *rho *rho * rho + & - ( 1260.00 ) *rho *rho *rho *rho *rho * rho + & - ( -4620.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 7920.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -6435.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 2002.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 5.477225575052 ) * sin(14.00 * phi) - ! n = 14, m = -2 - zn(7) = ( ( 28.00 ) *rho * rho + & - ( -504.00 ) *rho *rho *rho * rho + & - ( 3150.00 ) *rho *rho *rho *rho *rho * rho + & - ( -9240.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 13860.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -10296.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 3003.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 5.477225575052 ) * sin(14.00 * phi) - ! n = 14, m = 0 - zn(8) = ( ( -1.00 ) + & - ( 56.00 ) *rho * rho + & - ( -756.00 ) *rho *rho *rho * rho + & - ( 4200.00 ) *rho *rho *rho *rho *rho * rho + & - ( -11550.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 16632.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -12012.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 3432.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 3.872983346207 ) - ! n = 14, m = 2 - zn(9) = ( ( 28.00 ) *rho * rho + & - ( -504.00 ) *rho *rho *rho * rho + & - ( 3150.00 ) *rho *rho *rho *rho *rho * rho + & - ( -9240.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 13860.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -10296.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 3003.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 5.477225575052 ) * cos(14.00 * phi) - ! n = 14, m = 4 - zn(10) = ( ( -126.00 ) *rho *rho *rho * rho + & - ( 1260.00 ) *rho *rho *rho *rho *rho * rho + & - ( -4620.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 7920.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -6435.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 2002.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 5.477225575052 ) * cos(14.00 * phi) - ! n = 14, m = 6 - zn(11) = ( ( 210.00 ) *rho *rho *rho *rho *rho * rho + & - ( -1320.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 2970.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -2860.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 1001.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 5.477225575052 ) * cos(14.00 * phi) - ! n = 14, m = 8 - zn(12) = ( ( -165.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 660.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -858.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 364.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 5.477225575052 ) * cos(14.00 * phi) - ! n = 14, m = 10 - zn(13) = ( ( 66.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -156.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 91.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 5.477225575052 ) * cos(14.00 * phi) - ! n = 14, m = 12 - zn(14) = ( ( -13.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 14.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 5.477225575052 ) * cos(14.00 * phi) - ! n = 14, m = 14 - zn(15) = ( ( 1.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 5.477225575052 ) * cos(14.00 * phi) - case(15) - ! n = 15, m = -15 - zn(1) = ( ( 1.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 5.656854249492 ) * sin(15.00 * phi) - ! n = 15, m = -13 - zn(2) = ( ( -14.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 15.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 5.656854249492 ) * sin(15.00 * phi) - ! n = 15, m = -11 - zn(3) = ( ( 78.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -182.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 105.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 5.656854249492 ) * sin(15.00 * phi) - ! n = 15, m = -9 - zn(4) = ( ( -220.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 858.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -1092.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 455.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 5.656854249492 ) * sin(15.00 * phi) - ! n = 15, m = -7 - zn(5) = ( ( 330.00 ) *rho *rho *rho *rho *rho *rho * rho + & - ( -1980.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 4290.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -4004.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 1365.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 5.656854249492 ) * sin(15.00 * phi) - ! n = 15, m = -5 - zn(6) = ( ( -252.00 ) *rho *rho *rho *rho * rho + & - ( 2310.00 ) *rho *rho *rho *rho *rho *rho * rho + & - ( -7920.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 12870.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -10010.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 3003.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 5.656854249492 ) * sin(15.00 * phi) - ! n = 15, m = -3 - zn(7) = ( ( 84.00 ) *rho *rho * rho + & - ( -1260.00 ) *rho *rho *rho *rho * rho + & - ( 6930.00 ) *rho *rho *rho *rho *rho *rho * rho + & - ( -18480.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 25740.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -18018.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 5005.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 5.656854249492 ) * sin(15.00 * phi) - ! n = 15, m = -1 - zn(8) = ( ( -8.00 ) * rho + & - ( 252.00 ) *rho *rho * rho + & - ( -2520.00 ) *rho *rho *rho *rho * rho + & - ( 11550.00 ) *rho *rho *rho *rho *rho *rho * rho + & - ( -27720.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 36036.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -24024.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 6435.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 5.656854249492 ) * sin(15.00 * phi) - ! n = 15, m = 1 - zn(9) = ( ( -8.00 ) * rho + & - ( 252.00 ) *rho *rho * rho + & - ( -2520.00 ) *rho *rho *rho *rho * rho + & - ( 11550.00 ) *rho *rho *rho *rho *rho *rho * rho + & - ( -27720.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 36036.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -24024.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 6435.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 5.656854249492 ) * cos(15.00 * phi) - ! n = 15, m = 3 - zn(10) = ( ( 84.00 ) *rho *rho * rho + & - ( -1260.00 ) *rho *rho *rho *rho * rho + & - ( 6930.00 ) *rho *rho *rho *rho *rho *rho * rho + & - ( -18480.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 25740.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -18018.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 5005.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 5.656854249492 ) * cos(15.00 * phi) - ! n = 15, m = 5 - zn(11) = ( ( -252.00 ) *rho *rho *rho *rho * rho + & - ( 2310.00 ) *rho *rho *rho *rho *rho *rho * rho + & - ( -7920.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 12870.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -10010.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 3003.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 5.656854249492 ) * cos(15.00 * phi) - ! n = 15, m = 7 - zn(12) = ( ( 330.00 ) *rho *rho *rho *rho *rho *rho * rho + & - ( -1980.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 4290.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -4004.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 1365.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 5.656854249492 ) * cos(15.00 * phi) - ! n = 15, m = 9 - zn(13) = ( ( -220.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 858.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -1092.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 455.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 5.656854249492 ) * cos(15.00 * phi) - ! n = 15, m = 11 - zn(14) = ( ( 78.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -182.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 105.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 5.656854249492 ) * cos(15.00 * phi) - ! n = 15, m = 13 - zn(15) = ( ( -14.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 15.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 5.656854249492 ) * cos(15.00 * phi) - ! n = 15, m = 15 - zn(16) = ( ( 1.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 5.656854249492 ) * cos(15.00 * phi) - case(16) - ! n = 16, m = -16 - zn(1) = ( ( 1.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 5.830951894845 ) * sin(16.00 * phi) - ! n = 16, m = -14 - zn(2) = ( ( -15.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 16.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 5.830951894845 ) * sin(16.00 * phi) - ! n = 16, m = -12 - zn(3) = ( ( 91.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -210.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 120.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 5.830951894845 ) * sin(16.00 * phi) - ! n = 16, m = -10 - zn(4) = ( ( -286.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 1092.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -1365.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 560.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 5.830951894845 ) * sin(16.00 * phi) - ! n = 16, m = -8 - zn(5) = ( ( 495.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -2860.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 6006.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -5460.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 1820.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 5.830951894845 ) * sin(16.00 * phi) - ! n = 16, m = -6 - zn(6) = ( ( -462.00 ) *rho *rho *rho *rho *rho * rho + & - ( 3960.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -12870.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 20020.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -15015.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 4368.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 5.830951894845 ) * sin(16.00 * phi) - ! n = 16, m = -4 - zn(7) = ( ( 210.00 ) *rho *rho *rho * rho + & - ( -2772.00 ) *rho *rho *rho *rho *rho * rho + & - ( 13860.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -34320.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 45045.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -30030.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 8008.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 5.830951894845 ) * sin(16.00 * phi) - ! n = 16, m = -2 - zn(8) = ( ( -36.00 ) *rho * rho + & - ( 840.00 ) *rho *rho *rho * rho + & - ( -6930.00 ) *rho *rho *rho *rho *rho * rho + & - ( 27720.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -60060.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 72072.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -45045.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 11440.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 5.830951894845 ) * sin(16.00 * phi) - ! n = 16, m = 0 - zn(9) = ( ( 1.00 ) + & - ( -72.00 ) *rho * rho + & - ( 1260.00 ) *rho *rho *rho * rho + & - ( -9240.00 ) *rho *rho *rho *rho *rho * rho + & - ( 34650.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -72072.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 84084.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -51480.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 12870.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 4.123105625618 ) - ! n = 16, m = 2 - zn(10) = ( ( -36.00 ) *rho * rho + & - ( 840.00 ) *rho *rho *rho * rho + & - ( -6930.00 ) *rho *rho *rho *rho *rho * rho + & - ( 27720.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -60060.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 72072.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -45045.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 11440.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 5.830951894845 ) * cos(16.00 * phi) - ! n = 16, m = 4 - zn(11) = ( ( 210.00 ) *rho *rho *rho * rho + & - ( -2772.00 ) *rho *rho *rho *rho *rho * rho + & - ( 13860.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -34320.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 45045.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -30030.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 8008.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 5.830951894845 ) * cos(16.00 * phi) - ! n = 16, m = 6 - zn(12) = ( ( -462.00 ) *rho *rho *rho *rho *rho * rho + & - ( 3960.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -12870.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 20020.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -15015.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 4368.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 5.830951894845 ) * cos(16.00 * phi) - ! n = 16, m = 8 - zn(13) = ( ( 495.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -2860.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 6006.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -5460.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 1820.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 5.830951894845 ) * cos(16.00 * phi) - ! n = 16, m = 10 - zn(14) = ( ( -286.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 1092.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -1365.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 560.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 5.830951894845 ) * cos(16.00 * phi) - ! n = 16, m = 12 - zn(15) = ( ( 91.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -210.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 120.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 5.830951894845 ) * cos(16.00 * phi) - ! n = 16, m = 14 - zn(16) = ( ( -15.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 16.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 5.830951894845 ) * cos(16.00 * phi) - ! n = 16, m = 16 - zn(17) = ( ( 1.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 5.830951894845 ) * cos(16.00 * phi) - case(17) - ! n = 17, m = -17 - zn(1) = ( ( 1.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 6.000000000000 ) * sin(17.00 * phi) - ! n = 17, m = -15 - zn(2) = ( ( -16.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 17.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 6.000000000000 ) * sin(17.00 * phi) - ! n = 17, m = -13 - zn(3) = ( ( 105.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -240.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 136.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 6.000000000000 ) * sin(17.00 * phi) - ! n = 17, m = -11 - zn(4) = ( ( -364.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 1365.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -1680.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 680.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 6.000000000000 ) * sin(17.00 * phi) - ! n = 17, m = -9 - zn(5) = ( ( 715.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -4004.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 8190.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -7280.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 2380.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 6.000000000000 ) * sin(17.00 * phi) - ! n = 17, m = -7 - zn(6) = ( ( -792.00 ) *rho *rho *rho *rho *rho *rho * rho + & - ( 6435.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -20020.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 30030.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -21840.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 6188.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 6.000000000000 ) * sin(17.00 * phi) - ! n = 17, m = -5 - zn(7) = ( ( 462.00 ) *rho *rho *rho *rho * rho + & - ( -5544.00 ) *rho *rho *rho *rho *rho *rho * rho + & - ( 25740.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -60060.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 75075.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -48048.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 12376.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 6.000000000000 ) * sin(17.00 * phi) - ! n = 17, m = -3 - zn(8) = ( ( -120.00 ) *rho *rho * rho + & - ( 2310.00 ) *rho *rho *rho *rho * rho + & - ( -16632.00 ) *rho *rho *rho *rho *rho *rho * rho + & - ( 60060.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -120120.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 135135.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -80080.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 19448.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 6.000000000000 ) * sin(17.00 * phi) - ! n = 17, m = -1 - zn(9) = ( ( 9.00 ) * rho + & - ( -360.00 ) *rho *rho * rho + & - ( 4620.00 ) *rho *rho *rho *rho * rho + & - ( -27720.00 ) *rho *rho *rho *rho *rho *rho * rho + & - ( 90090.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -168168.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 180180.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -102960.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 24310.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 6.000000000000 ) * sin(17.00 * phi) - ! n = 17, m = 1 - zn(10) = ( ( 9.00 ) * rho + & - ( -360.00 ) *rho *rho * rho + & - ( 4620.00 ) *rho *rho *rho *rho * rho + & - ( -27720.00 ) *rho *rho *rho *rho *rho *rho * rho + & - ( 90090.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -168168.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 180180.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -102960.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 24310.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 6.000000000000 ) * cos(17.00 * phi) - ! n = 17, m = 3 - zn(11) = ( ( -120.00 ) *rho *rho * rho + & - ( 2310.00 ) *rho *rho *rho *rho * rho + & - ( -16632.00 ) *rho *rho *rho *rho *rho *rho * rho + & - ( 60060.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -120120.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 135135.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -80080.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 19448.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 6.000000000000 ) * cos(17.00 * phi) - ! n = 17, m = 5 - zn(12) = ( ( 462.00 ) *rho *rho *rho *rho * rho + & - ( -5544.00 ) *rho *rho *rho *rho *rho *rho * rho + & - ( 25740.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -60060.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 75075.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -48048.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 12376.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 6.000000000000 ) * cos(17.00 * phi) - ! n = 17, m = 7 - zn(13) = ( ( -792.00 ) *rho *rho *rho *rho *rho *rho * rho + & - ( 6435.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -20020.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 30030.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -21840.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 6188.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 6.000000000000 ) * cos(17.00 * phi) - ! n = 17, m = 9 - zn(14) = ( ( 715.00 ) *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -4004.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 8190.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -7280.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 2380.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 6.000000000000 ) * cos(17.00 * phi) - ! n = 17, m = 11 - zn(15) = ( ( -364.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 1365.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -1680.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 680.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 6.000000000000 ) * cos(17.00 * phi) - ! n = 17, m = 13 - zn(16) = ( ( 105.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -240.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 136.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 6.000000000000 ) * cos(17.00 * phi) - ! n = 17, m = 15 - zn(17) = ( ( -16.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 17.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 6.000000000000 ) * cos(17.00 * phi) - ! n = 17, m = 17 - zn(18) = ( ( 1.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 6.000000000000 ) * cos(17.00 * phi) - case(18) - ! n = 18, m = -18 - zn(1) = ( ( 1.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 6.164414002969 ) * sin(18.00 * phi) - ! n = 18, m = -16 - zn(2) = ( ( -17.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 18.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 6.164414002969 ) * sin(18.00 * phi) - ! n = 18, m = -14 - zn(3) = ( ( 120.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -272.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 153.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 6.164414002969 ) * sin(18.00 * phi) - ! n = 18, m = -12 - zn(4) = ( ( -455.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 1680.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -2040.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 816.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 6.164414002969 ) * sin(18.00 * phi) - ! n = 18, m = -10 - zn(5) = ( ( 1001.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -5460.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 10920.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -9520.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 3060.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 6.164414002969 ) * sin(18.00 * phi) - ! n = 18, m = -8 - zn(6) = ( ( -1287.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 10010.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -30030.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 43680.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -30940.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 8568.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 6.164414002969 ) * sin(18.00 * phi) - ! n = 18, m = -6 - zn(7) = ( ( 924.00 ) *rho *rho *rho *rho *rho * rho + & - ( -10296.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 45045.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -100100.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 120120.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -74256.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 18564.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 6.164414002969 ) * sin(18.00 * phi) - ! n = 18, m = -4 - zn(8) = ( ( -330.00 ) *rho *rho *rho * rho + & - ( 5544.00 ) *rho *rho *rho *rho *rho * rho + & - ( -36036.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 120120.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -225225.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 240240.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -136136.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 31824.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 6.164414002969 ) * sin(18.00 * phi) - ! n = 18, m = -2 - zn(9) = ( ( 45.00 ) *rho * rho + & - ( -1320.00 ) *rho *rho *rho * rho + & - ( 13860.00 ) *rho *rho *rho *rho *rho * rho + & - ( -72072.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 210210.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -360360.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 360360.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -194480.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 43758.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 6.164414002969 ) * sin(18.00 * phi) - ! n = 18, m = 0 - zn(10) = ( ( -1.00 ) + & - ( 90.00 ) *rho * rho + & - ( -1980.00 ) *rho *rho *rho * rho + & - ( 18480.00 ) *rho *rho *rho *rho *rho * rho + & - ( -90090.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 252252.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -420420.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 411840.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -218790.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 48620.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 4.358898943541 ) - ! n = 18, m = 2 - zn(11) = ( ( 45.00 ) *rho * rho + & - ( -1320.00 ) *rho *rho *rho * rho + & - ( 13860.00 ) *rho *rho *rho *rho *rho * rho + & - ( -72072.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 210210.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -360360.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 360360.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -194480.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 43758.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 6.164414002969 ) * cos(18.00 * phi) - ! n = 18, m = 4 - zn(12) = ( ( -330.00 ) *rho *rho *rho * rho + & - ( 5544.00 ) *rho *rho *rho *rho *rho * rho + & - ( -36036.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 120120.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -225225.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 240240.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -136136.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 31824.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 6.164414002969 ) * cos(18.00 * phi) - ! n = 18, m = 6 - zn(13) = ( ( 924.00 ) *rho *rho *rho *rho *rho * rho + & - ( -10296.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 45045.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -100100.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 120120.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -74256.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 18564.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 6.164414002969 ) * cos(18.00 * phi) - ! n = 18, m = 8 - zn(14) = ( ( -1287.00 ) *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 10010.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -30030.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 43680.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -30940.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 8568.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 6.164414002969 ) * cos(18.00 * phi) - ! n = 18, m = 10 - zn(15) = ( ( 1001.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -5460.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 10920.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -9520.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 3060.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 6.164414002969 ) * cos(18.00 * phi) - ! n = 18, m = 12 - zn(16) = ( ( -455.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 1680.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -2040.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 816.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 6.164414002969 ) * cos(18.00 * phi) - ! n = 18, m = 14 - zn(17) = ( ( 120.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( -272.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 153.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 6.164414002969 ) * cos(18.00 * phi) - ! n = 18, m = 16 - zn(18) = ( ( -17.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho + & - ( 18.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 6.164414002969 ) * cos(18.00 * phi) - ! n = 18, m = 18 - zn(19) = ( ( 1.00 ) *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho *rho * rho ) & - * ( 6.164414002969 ) * cos(18.00 * phi) - case default - zn = ONE - end select - - end function calc_zn - -!=============================================================================== -! CALC_ZN_SCALED calculates the n-th order Zernike polynomial moment for a given -! angle (rho, theta) location in the unit disk, scaled correctly for orthogonal -! integration. -!=============================================================================== - - pure function calc_zn_scaled(n, rho, phi) result(zn) - - integer, intent(in) :: n ! Order requested - real(8), intent(in) :: rho ! Radial location in the unit disk - real(8), intent(in) :: phi ! Theta (radians) location in the unit disk - real(8) :: zn(n + 1) ! The resultant Z_n(uvw) - - zn = calc_zn(n, rho, phi) / SQRT_PI - - end function calc_zn_scaled - !=============================================================================== ! C API FUNCTIONS !===============================================================================