L27:=[
[ 0.284257170599851632098483079973, 0.0, 0.0, 0.0, 0.0, 0.461223668871484442677432306984*I, 0.0, 0.0, 0.0, 0.0,  0.454390347867661156426616321977, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,  0.454390347867661156426616321977, 0.0, 0.0, 0.0, 0.0, 0.461223668871484442677432306984*I, 0.0, 0.0, 0.0, 0.0, 0.284257170599851632098483079973 ],
[ 0.297445837042689124985386271488, 0.0, 0.0, 0.0, 0.0, 0.0, -0.259723774154169042500997448235 + 0.459472512464611711183593481971*I, 0.0, 0.0, 0.0, 0.0,  0.364629326103298299345763547838, 0.0, 0.0, 0.0, 0.0,  0.364629326103298299345763547838, 0.0, 0.0, 0.0, 0.0, -0.259723774154169042500997448235 + 0.459472512464611711183593481971*I, 0.0, 0.0, 0.0, 0.0, 0.0, 0.297445837042689124985386271488 ],
[ 0.297445837042689124985386271488, 0.0, 0.0, 0.0, 0.0, 0.0,  0.259723774154169042500997448235 + 0.459472512464611711183593481971*I, 0.0, 0.0, 0.0, 0.0, -0.364629326103298299345763547838, 0.0, 0.0, 0.0, 0.0, -0.364629326103298299345763547838, 0.0, 0.0, 0.0, 0.0,  0.259723774154169042500997448235 + 0.459472512464611711183593481971*I, 0.0, 0.0, 0.0, 0.0, 0.0, 0.297445837042689124985386271488 ],
[ 0.284257170599851632098483079973, 0.0, 0.0, 0.0, 0.0, 0.461223668871484442677432306984*I, 0.0, 0.0, 0.0, 0.0, -0.454390347867661156426616321977, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -0.454390347867661156426616321977, 0.0, 0.0, 0.0, 0.0, 0.461223668871484442677432306984*I, 0.0, 0.0, 0.0, 0.0, 0.284257170599851632098483079973 ]
] where I:=Sqrt(-1);


// squared length of the multipoles
[ 0.035714, 0.0, 0.0, 0.0, 0.0, 0.0, 0.033358, 0.0099286, 0.011009,  0.0060377, 0.070907,   0.0053410, 0.026298, 0.043529, 0.052519, 0.031665, 0.078843, 0.037235, 0.040681, 0.0064337, 0.019920, 0.10138,  0.069290, 0.069968, 0.036979, 0.10284,  0.024482, 0.085643 ],
[ 0.035714, 0.0, 0.0, 0.0, 0.0, 0.0, 0.039866, 0.0071250, 0.0089645, 0.017899,  0.020867,   0.045804,  0.021297, 0.045957, 0.046366, 0.065302, 0.041949, 0.042826, 0.023105, 0.033342,  0.048967, 0.047235, 0.071045, 0.065727, 0.10136,  0.043194, 0.040495, 0.085588 ],
[ 0.035714, 0.0, 0.0, 0.0, 0.0, 0.0, 0.039866, 0.0071250, 0.0089645, 0.017899,  0.020867,   0.045804,  0.021297, 0.045957, 0.046366, 0.065302, 0.041949, 0.042826, 0.023105, 0.033342,  0.048967, 0.047235, 0.071045, 0.065727, 0.10136,  0.043194, 0.040495, 0.085588 ],
[ 0.035714, 0.0, 0.0, 0.0, 0.0, 0.0, 0.048615, 0.0099286, 0.0089501, 0.0060377, 0.00073728, 0.0053410, 0.10196,  0.043529, 0.063223, 0.031665, 0.033548, 0.026695, 0.053605, 0.050166,  0.024640, 0.028565, 0.067797, 0.13083,  0.036733, 0.077291, 0.024477, 0.089951 ]

// cumulative squared lengths A_M:
          [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.033358, 0.043286,  0.054295,  0.060332,  0.13124,    0.13658,    0.16288, 0.20641,  0.25893,  0.29059,  0.36943,  0.40667,  0.44735,  0.45378,   0.47371,  0.57509,  0.64438,  0.71435,  0.75133,  0.85416,  0.87865,  0.96429 ],
          [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.039866, 0.046991,  0.055955,  0.073854,  0.094721,   0.14053,    0.16182, 0.20778,  0.25415,  0.31945,  0.36140,  0.40422,  0.42733,  0.46067,   0.50964,  0.55687,  0.62791,  0.69364,  0.79501,  0.83820,  0.87870,  0.96429 ],
          [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.039866, 0.046991,  0.055955,  0.073854,  0.094721,   0.14053,    0.16182, 0.20778,  0.25415,  0.31945,  0.36140,  0.40422,  0.42733,  0.46067,   0.50964,  0.55687,  0.62791,  0.69364,  0.79501,  0.83820,  0.87870,  0.96429 ],
          [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.048615, 0.058543,  0.067493,  0.073531,  0.074268,   0.079609,   0.18157, 0.22510,  0.28832,  0.31999,  0.35353,  0.38023,  0.43383,  0.48400,   0.50864,  0.53721,  0.60500,  0.73583,  0.77257,  0.84986,  0.87434,  0.96429 ]


L27_algebraic:=[
[ 1/1870*sqrt(11)*sqrt(17)*sqrt(1511), 0, 0, 0, 0,  3/110*sqrt(-1)*sqrt(2)*sqrt(11)*sqrt(13), 0, 0, 0, 0,  3/170*sqrt(3)*sqrt(13)*sqrt(17), 0, 0, 0, 0, 0, 0,  3/170*sqrt(3)*sqrt(13)*sqrt(17), 0, 0, 0, 0,  3/110*sqrt(-1)*sqrt(2)*sqrt(11)*sqrt(13), 0, 0, 0, 0, 1/1870*sqrt(11)*sqrt(17)*sqrt(1511) ],
[ 1/308*sqrt(7)*sqrt(11)*sqrt(109), 0, 0, 0, 0, 0,  9/248710*sqrt(-1)*sqrt(5)*sqrt(7)*sqrt(13)*sqrt(17)*sqrt(19)*sqrt(1097) - 13/17765*sqrt(2)*sqrt(3)*sqrt(5)*sqrt(13)*sqrt(17)*sqrt(19), 0, 0, 0, 0,  3/220*sqrt(5)*sqrt(11)*sqrt(13), 0, 0, 0, 0,  3/220*sqrt(5)*sqrt(11)*sqrt(13), 0, 0, 0, 0,  9/248710*sqrt(-1)*sqrt(5)*sqrt(7)*sqrt(13)*sqrt(17)*sqrt(19)*sqrt(1097) - 13/17765*sqrt(2)*sqrt(3)*sqrt(5)*sqrt(13)*sqrt(17)*sqrt(19), 0, 0, 0, 0, 0, 1/308*sqrt(7)*sqrt(11)*sqrt(109) ],
[ 1/308*sqrt(7)*sqrt(11)*sqrt(109), 0, 0, 0, 0, 0,  9/248710*sqrt(-1)*sqrt(5)*sqrt(7)*sqrt(13)*sqrt(17)*sqrt(19)*sqrt(1097) + 13/17765*sqrt(2)*sqrt(3)*sqrt(5)*sqrt(13)*sqrt(17)*sqrt(19), 0, 0, 0, 0, -3/220*sqrt(5)*sqrt(11)*sqrt(13), 0, 0, 0, 0, -3/220*sqrt(5)*sqrt(11)*sqrt(13), 0, 0, 0, 0,  9/248710*sqrt(-1)*sqrt(5)*sqrt(7)*sqrt(13)*sqrt(17)*sqrt(19)*sqrt(1097) + 13/17765*sqrt(2)*sqrt(3)*sqrt(5)*sqrt(13)*sqrt(17)*sqrt(19), 0, 0, 0, 0, 0, 1/308*sqrt(7)*sqrt(11)*sqrt(109) ],
[ 1/1870*sqrt(11)*sqrt(17)*sqrt(1511), 0, 0, 0, 0,  3/110*sqrt(-1)*sqrt(2)*sqrt(11)*sqrt(13), 0, 0, 0, 0, -3/170*sqrt(3)*sqrt(13)*sqrt(17), 0, 0, 0, 0, 0, 0, -3/170*sqrt(3)*sqrt(13)*sqrt(17), 0, 0, 0, 0,  3/110*sqrt(-1)*sqrt(2)*sqrt(11)*sqrt(13), 0, 0, 0, 0, 1/1870*sqrt(11)*sqrt(17)*sqrt(1511) ]
];