// see below for algebraic expressions

L13:=[
[ 0.258198889747161125678617693319, 0.0, 0.0, 0.658280588604383300581282034792*I, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.658280588604383300581282034792*I, 0.0, 0.0, 0.258198889747161125678617693319 ]
] where I:=Sqrt(-1);


// squared length of the multipoles
[ 0.071428, 0.0, 0.0, 0.0, 0.044028, 0.0,      0.14943, 0.099661, 0.038250, 0.067921, 0.15393, 0.16468, 0.042927, 0.16774 ]

// cumulative squared lengths A_M:
          [ 0.0, 0.0, 0.0, 0.044028, 0.044028, 0.19346, 0.29312,  0.33137,  0.39929,  0.55322, 0.71790, 0.76083,  0.92857 ]


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

L13_algebraic:=[
[ 1/15*sqrt(5)*sqrt(3), 0, 0, 1/30*sqrt(390)*sqrt(-1), 0, 0, 0, 0, 0, 0, 1/30*sqrt(390)*sqrt(-1), 0, 0, 1/15*sqrt(5)*sqrt(3) ]
];

// squared length of the multipoles
[ 1/14, 0, 0, 0, 247/5610, 0, 5574803/37306500, 676/6783, 7631/199500, 1859/27370, 34307/222870, 13689/83125, 6697/156009, 50636/301875 ]


// cumulative squared lengths A_M:
      [ 0, 0, 0, 247/5610, 247/5610, 656123/3391500, 994123/3391500, 169/510, 16393/41055, 863083/1560090, 19999967/27858750, 459353/603750, 13/14 ]