// see below for algebraic expressions

L11:=[
[ 0.343592135468138379151784154665, 0.0, 0.0, 0.618016540591305245725949786734*I, 0.0, 0.0, 0.0, 0.0, 0.618016540591305245725949786734*I, 0.0, 0.0, 0.343592135468138379151784154665 ],
[ 0.0, 0.518187725171600835864137530129, 0.0, 0.0, -0.356817841719003855851691968292 + 0.322742171574266682371949505203*I, 0.0, 0.0, -0.356817841719003855851691968292 + 0.322742171574266682371949505203*I, 0.0, 0.0, 0.518187725171600835864137530129, 0.0 ]
] where I:=Sqrt(-1);


// squared length of the multipoles
[ 0.083333, 0.0, 0.0, 0.0, 0.042193, 0.073931, 0.20389,  0.052530, 0.071441, 0.20056, 0.099142, 0.17298 ]
[ 0.083333, 0.0, 0.0, 0.0, 0.052238, 0.096662, 0.096403, 0.13202,  0.12667,  0.10404, 0.14136,  0.16727 ]

// cumulative squared lengths A_M:
          [ 0.0, 0.0, 0.0, 0.042193, 0.11612,  0.32001,  0.37254,  0.44398,  0.64454, 0.74368,  0.91666 ]
          [ 0.0, 0.0, 0.0, 0.052238, 0.14890,  0.24530,  0.37733,  0.50399,  0.60803, 0.74940,  0.91666 ]

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

L11_algebraic:=[
[ 1/12*sqrt(17), 0, 0, 1/12*sqrt(55)*sqrt(-1), 0, 0, 0, 0, 1/12*sqrt(55)*sqrt(-1), 0, 0, 1/12*sqrt(17) ],
[ 0, sqrt(87)/18, 0, 0, (5*sqrt(-1)*sqrt(290638)-175*sqrt(290))/8352, 0, 0, (5*sqrt(-1)*sqrt(290638)-175*sqrt(290))/8352, 0, 0, sqrt(87)/18, 0 ]
];

// squared length of the multipoles
[ 1/12, 0, 0, 0, 5687/134784, 21175/286416, 1331/6528, 21175/403104, 847/11856, 247445/1233792, 83003/837216, 4055069/23442048 ]
[ 1/12, 0, 0, 0, 5737/109824, 21875/226304, 249211/2585088, 5109125/38697984, 864997/6829056, 171155/1645056, 420799/2976768, 1307053/7814016 ]

// cumulative squared lengths A_M:
      [ 0, 0, 0, 5687/134784, 88693/763776, 61105/190944, 675785/1813968, 3872/8721, 15109391/23442048, 17433475/23442048, 11/12 ]
      [ 0, 0, 0, 5737/109824, 1111991/7468032, 1498855/6110208, 10951405/29023488, 1500271/2976768, 38009581/62512128, 5855795/7814016, 11/12 ]