// see below for algebraic expressions

L16:=[
[ 0.259581995716189839143258210779, 0.0, 0.303365127882585396055412204246 - 0.275569136850959071068686068818*I, 0.0, -0.148149115876933456832242984571 + 0.245118521260395464111026745507*I, 0.0, -0.284417497175417694338714369100 - 0.0337333262586313575436058586908*I, 0.0, -0.408883211882388408205598036284 + 0.184353991116932065265541885327*I, 0.0, 0.284417497175417694338714369100 + 0.0337333262586313575436058586908*I, 0.0, -0.148149115876933456832242984571 + 0.245118521260395464111026745507*I, 0.0, -0.303365127882585396055412204246 + 0.275569136850959071068686068818*I, 0.0, 0.259581995716189839143258210779 ]
] where I:=Sqrt(-1);

// squared length of the multipoles
[ 0.058824, 0.0, 0.0, 0.0, 0.0, 0.0, 0.066374, 0.15265, 0.029207, 0.071368, 0.049150, 0.0035333, 0.14209, 0.15218, 0.039472, 0.12027, 0.11488 ]

// cumulative squared lengths A_M:
          [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.066374, 0.21902, 0.24823,  0.31960,  0.36874,  0.37228,   0.51437, 0.66655, 0.70602,  0.82630, 0.94118 ]



//======================================================================
// exact values
//======================================================================

L16_algebraic:=[
[ 1/32*sqrt(23)*sqrt(3),
  0,
 -7/1472*sqrt(73)*sqrt(23)*sqrt(-1)*sqrt(2) + 17/1472*sqrt(23)*sqrt(5)*sqrt(3)*sqrt(2),
  0,
  3/4784*sqrt(73)*sqrt(23)*sqrt(13)*sqrt(-1)*sqrt(7) - 1/1196*sqrt(23)*sqrt(13)*sqrt(7)*sqrt(5)*sqrt(3),
  0,
 -1/210496*sqrt(73)*sqrt(23)*sqrt(13)*sqrt(11)*sqrt(-1)*sqrt(7)*sqrt(5)*sqrt(3)*sqrt(2) - 279/210496*sqrt(23)*sqrt(13)*sqrt(11)*sqrt(7)*sqrt(2),
  0,
  7/26312*sqrt(73)*sqrt(23)*sqrt(13)*sqrt(11)*sqrt(-1)*sqrt(2) - 137/105248*sqrt(23)*sqrt(13)*sqrt(11)*sqrt(5)*sqrt(3)*sqrt(2),
  0,
  1/210496*sqrt(73)*sqrt(23)*sqrt(13)*sqrt(11)*sqrt(-1)*sqrt(7)*sqrt(5)*sqrt(3)*sqrt(2) + 279/210496*sqrt(23)*sqrt(13)*sqrt(11)*sqrt(7)*sqrt(2),
  0,
  3/4784*sqrt(73)*sqrt(23)*sqrt(13)*sqrt(-1)*sqrt(7) - 1/1196*sqrt(23)*sqrt(13)*sqrt(7)*sqrt(5)*sqrt(3),
  0,
  7/1472*sqrt(73)*sqrt(23)*sqrt(-1)*sqrt(2) - 17/1472*sqrt(23)*sqrt(5)*sqrt(3)*sqrt(2),
  0,
  1/32*sqrt(23)*sqrt(3) ]
];

// squared length of the multipoles
[ 1/17, 0, 0, 0, 0, 0, 5424/81719, 1134/7429,    702/24035,   19952/279565,  261072/5311735,    48/13585, 772528/5436717,  72576/476905,     5488/139035,   114717/953810,  5249511/45696170 ]

// cumulative squared lengths A_M:
      [ 0, 0, 0, 0, 0, 5424/81719, 9 42/4301, 101424/408595, 339520/1062347,   6064/16445,   23264/62491, 147184/286143,  953648/1430715, 2087584/2956811, 2221097/2688010,      16/17 ]