// see below for algebraic expressions

L18:=[
[ 0.328165061656946796167482946482, 0.0, 0.0, 0.0, 0.0, 0.626344707256070223825437174786*I, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.626344707256070223825437174786*I, 0.0, 0.0, 0.0, 0.0, 0.328165061656946796167482946482 ]
] where I:=Sqrt(-1);

// squared length of the multipoles
[ 0.052631, 0.0, 0.0, 0.0, 0.0, 0.0, 0.081787, 0.0,      0.13191, 0.0,     0.11043, 0.0,     0.12947, 0.0,     0.13413, 0.0,     0.23489, 0.0,     0.12475 ]

// cumulative squared lengths A_M:
          [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.081787, 0.081787, 0.21370, 0.21370, 0.32413, 0.32413, 0.45360, 0.45360, 0.58772, 0.58772, 0.82262, 0.82262, 0.94736 ]



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

L18_algebraic:=[
[ 1/65*Sqrt(5)*Sqrt(7)*Sqrt(13), 0, 0, 0, 0, 1/130*Sqrt(-1)*Sqrt(2)*Sqrt(3)*Sqrt(5)*Sqrt(13)*Sqrt(17), 0, 0, 0, 0, 0, 0, 0, 1/130*Sqrt(-1)*Sqrt(2)*Sqrt(3)*Sqrt(5)*Sqrt(13)*Sqrt(17), 0, 0, 0, 0, 1/65*Sqrt(5)*Sqrt(7)*Sqrt(13) ]
];

// squared length of the multipoles
[ 1/19, 0, 0, 0, 0, 0, 22338/273125, 0, 108086/819375, 0, 34986/316825, 0, 50864/392863, 0, 26299/196075, 0, 3035508/12923125, 0, 43950683/352295625 ]

// cumulative squared lengths A_M:
      [ 0, 0, 0, 0, 0, 22338/273125, 22338/273125, 7004/32775, 7004/32775, 308074/950475, 308074/950475, 703426/1550775, 703426/1550775, 10025699/17058525, 10025699/17058525, 15252793/18541875, 15252793/18541875, 18/19 ]