// see below for algebraic expressions

L10:=[
[  0.0, -0.559016994374947424102293417183, 0.0, 0.0, 0.0, 0.612372435695794524549321018676, 0.0, 0.0, 0.0, 0.559016994374947424102293417183, 0.0 ],
[  0.408248290463863016366214012320, 0.0, 0.0, 0.0, 0.707106781186547524400844362107, 0.0, 0.0, 0.0, 0.0, 0.577350269189625764509148780446, 0.0 ],
[ -0.408248290463863016366214012530, 0.0, 0.0, 0.0, 0.707106781186547524400844362105, 0.0, 0.0, 0.0, 0.0, 0.577350269189625764509148780457, 0.0 ],
[  0.0, 0.559016994374947424102293417184, 0.0, 0.0, 0.0, -0.612372435695794524549321018675, 0.0, 0.0, 0.0, 0.559016994374947424102293417184, 0.0 ],
[  0.0, 0.522912516583797217486357516115, 0.0, 0.395284707521047416499861693058, 0.0, -0.374999999999999999999999999998, 0.0, 0.395284707521047416499861693058, 0.0, 0.522912516583797217486357516115, 0.0 ],
[  0.377964473009227227214516536230, 0.0, 0.0, 0.597614304667196819984408589847, 0.0, 0.0, 0.0, 0.597614304667196819984408589847, 0.0, 0.0, -0.377964473009227227214516536230 ],
[  0.447213595499957939281834733742, 0.0, 0.0, 0.0, 0.0, -0.774596669241483377035853079957, 0.0, 0.0, 0.0, 0.0, -0.447213595499957939281834733742 ],
[  0.447213595499957939281834733742, 0.0, 0.0, 0.0, 0.0,  0.774596669241483377035853079957, 0.0, 0.0, 0.0, 0.0,  0.447213595499957939281834733742 ]
];


// squared length of the multipoles

[ 0.090909, 0.0, 0.0, 0.0, 0.0078671, 0.21635,  0.18048,  0.031816, 0.094256, 0.22059,  0.15774 ]
[ 0.090909, 0.0, 0.0, 0.0, 0.010489,  0.21635,  0.16343,  0.059389, 0.077429, 0.22426,  0.15774 ]
[ 0.090909, 0.0, 0.0, 0.0, 0.010489,  0.21635,  0.16343,  0.059389, 0.077429, 0.22426,  0.15774 ]
[ 0.090909, 0.0, 0.0, 0.0, 0.12587,   0.0,      0.24064,  0.0,      0.32389,  0.0,      0.21869 ]
[ 0.090909, 0.0, 0.0, 0.0, 0.12587,   0.0,      0.24064,  0.0,      0.32389,  0.0,      0.21869 ]
[ 0.090909, 0.0, 0.0, 0.0, 0.12587,   0.0,      0.24064,  0.0,      0.32389,  0.0,      0.21869 ]
[ 0.090909, 0.0, 0.0, 0.0, 0.12587,   0.0,      0.24064,  0.0,      0.32389,  0.0,      0.21869 ]
[ 0.090909, 0.0, 0.0, 0.0, 0.12587,   0.055385, 0.028877, 0.32579,  0.071255, 0.098824, 0.20308 ]

// cumulative squared lengths A_M:
          [ 0.0, 0.0, 0.0, 0.0078671, 0.22421,  0.40469,  0.43651,  0.53077,  0.75136,  0.90909 ]
          [ 0.0, 0.0, 0.0, 0.010489,  0.22684,  0.39027,  0.44966,  0.52709,  0.75136,  0.90909 ]
          [ 0.0, 0.0, 0.0, 0.010489,  0.22684,  0.39027,  0.44966,  0.52709,  0.75136,  0.90909 ]
          [ 0.0, 0.0, 0.0, 0.12587,   0.12587,  0.36652,  0.36652,  0.69040,  0.69040,  0.90909 ]
          [ 0.0, 0.0, 0.0, 0.12587,   0.12587,  0.36652,  0.36652,  0.69040,  0.69040,  0.90909 ]
          [ 0.0, 0.0, 0.0, 0.12587,   0.12587,  0.36652,  0.36652,  0.69040,  0.69040,  0.90909 ]
          [ 0.0, 0.0, 0.0, 0.12587,   0.12587,  0.36652,  0.36652,  0.69040,  0.69040,  0.90909 ]
          [ 0.0, 0.0, 0.0, 0.12587,   0.18126,  0.21014,  0.53593,  0.60719,  0.70601,  0.90909 ]


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


L10_algebraic:=[
[            0,  -1/4*Sqrt(5), 0,             0,           0,   1/4*Sqrt(6), 0,             0, 0,   1/4*Sqrt(5),            0 ],
[  1/6*Sqrt(6),             0, 0,             0, 1/2*Sqrt(2),             0, 0,             0, 0,   1/3*Sqrt(3),            0 ],
[ -1/6*Sqrt(6),             0, 0,             0, 1/2*Sqrt(2),             0, 0,             0, 0,   1/3*Sqrt(3),            0 ],
[            0,   1/4*Sqrt(5), 0,             0,           0,  -1/4*Sqrt(6), 0,             0, 0,   1/4*Sqrt(5),            0 ],
[            0, 1/16*Sqrt(70), 0,  1/8*Sqrt(10),           0,          -3/8, 0,  1/8*Sqrt(10), 0, 1/16*Sqrt(70),            0 ],
[  1/7*Sqrt(7),             0, 0, 1/14*Sqrt(70),           0,             0, 0, 1/14*Sqrt(70), 0,             0, -1/7*Sqrt(7) ],
[  1/5*Sqrt(5),             0, 0,             0,           0, -1/5*Sqrt(15), 0,             0, 0,             0, -1/5*Sqrt(5) ],
[  1/5*Sqrt(5),             0, 0,             0,           0,  1/5*Sqrt(15), 0,             0, 0,             0,  1/5*Sqrt(5) ]
];

// squared length of the multipoles
[ 1/11, 0, 0, 0, 9/1144, 45/208, 135/748,  225/7072, 745/7904, 15/68,  8967/56848 ]
[ 1/11, 0, 0, 0,  3/286, 45/208, 489/2992, 105/1768, 153/1976, 61/272, 8967/56848 ]
[ 1/11, 0, 0, 0,  3/286, 45/208, 489/2992, 105/1768, 153/1976, 61/272, 8967/56848 ]
[ 1/11, 0, 0, 0, 18/143,      0,  45/187,         0,  80/247,       0,  777/3553 ]
[ 1/11, 0, 0, 0, 18/143,      0,  45/187,         0,  80/247,       0,  777/3553 ]
[ 1/11, 0, 0, 0, 18/143,      0,  45/187,         0,  80/247,       0,  777/3553 ]
[ 1/11, 0, 0, 0, 18/143,      0,  45/187,         0,  80/247,       0,  777/3553 ]
[ 1/11, 0, 0, 0, 18/143, 18/325,  27/935,   72/221,   88/1235, 42/425, 18039/88825 ]

// cumulative squared lengths A_M:
      [ 0, 0, 0, 9/1144, 513/2288, 1431/3536, 3087/7072, 2743/5168, 3883/5168,  10/11 ]
      [ 0, 0, 0,  3/286, 519/2288,  345/884,   795/1768,  681/1292, 3883/5168,  10/11 ]
      [ 0, 0, 0,  3/286, 519/2288,  345/884,   795/1768,  681/1292, 3883/5168,  10/11 ]
      [ 0, 0, 0, 18/143,  18/143,    81/221,    81/221,   223/323,   223/323,   10/11 ]
      [ 0, 0, 0, 18/143,  18/143,    81/221,    81/221,   223/323,   223/323,   10/11 ]
      [ 0, 0, 0, 18/143,  18/143,    81/221,    81/221,   223/323,   223/323,   10/11 ]
      [ 0, 0, 0, 18/143,  18/143,    81/221,    81/221,   223/323,   223/323,   10/11 ]
      [ 0, 0, 0, 18/143, 648/3575, 1161/5525, 2961/5525, 4903/8075,  5701/8075, 10/11 ]