// see below for algebraic expressions

L20:=[
[ 0.315805847528720299554473065492, 0.0, 0.0, 0.0, 0.0, 0.578273291792038412139525179710, 0.0, 0.0, 0.0, 0.0, -0.362950869035098651784880308382, 0.0, 0.0, 0.0, 0.0, -0.578273291792038412139525179710, 0.0, 0.0, 0.0, 0.0, 0.315805847528720299554473065492 ],
[ 0.315805847528720299554473065492, 0.0, 0.0, 0.0, 0.0, 0.578273291792038412139525179710, 0.0, 0.0, 0.0, 0.0,  0.362950869035098651784880308382, 0.0, 0.0, 0.0, 0.0, -0.578273291792038412139525179710, 0.0, 0.0, 0.0, 0.0, 0.315805847528720299554473065492 ]
];

// squared lengths of the multipoles
[ 0.047619, 0.0, 0.0, 0.0, 0.0, 0.0, 0.051933, 0.0,      0.11787,  0.0,      0.092184, 0.0,     0.10079, 0.0,     0.14004, 0.0,     0.12242, 0.0,     0.21332, 0.0,     0.11382 ],
[ 0.047619, 0.0, 0.0, 0.0, 0.0, 0.0, 0.093330, 0.0,      0.0,      0.0,      0.18543,  0.0,     0.15162, 0.0,     0.0,     0.0,     0.22476, 0.0,     0.17880, 0.0,     0.11844 ]

// cumulative squared lengths A_M:
          [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.051933, 0.051933, 0.16980,  0.16980,  0.26199,  0.26199, 0.36277, 0.36277, 0.50282, 0.50282, 0.62524, 0.62524, 0.83855, 0.83855, 0.95238 ],
          [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.093330, 0.093330, 0.093330, 0.093330, 0.27876,  0.27876, 0.43038, 0.43038, 0.43038, 0.43038, 0.65514, 0.65514, 0.83394, 0.83394, 0.95238 ]



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

L20_algebraic:=[
[ 1/75*sqrt(17)*sqrt(11)*sqrt(3), 0, 0, 0, 0, 1/25*sqrt(19)*sqrt(11), 0, 0, 0, 0, -1/75*sqrt(19)*sqrt(13)*sqrt(3), 0, 0, 0, 0, -1/25*sqrt(19)*sqrt(11), 0, 0, 0, 0, 1/75*sqrt(17)*sqrt(11)*sqrt(3) ],
[ 1/75*sqrt(17)*sqrt(11)*sqrt(3), 0, 0, 0, 0, 1/25*sqrt(19)*sqrt(11), 0, 0, 0, 0,  1/75*sqrt(19)*sqrt(13)*sqrt(3), 0, 0, 0, 0, -1/25*sqrt(19)*sqrt(11), 0, 0, 0, 0, 1/75*sqrt(17)*sqrt(11)*sqrt(3) ]
];

// squared length of the multipoles
[ 1/21, 0, 0, 0, 0, 0, 499712939/9622265625, 0,                    276394976/2344921875, 0, 4556722937/49430953125, 0, 11722183/116308125, 0, 14041456/100265625, 0, 2304912531416/18827377734375, 0, 61352309392/287609765625, 0, 461439517/4053928125 ],
[ 1/21, 0, 0, 0, 0, 0,      2299/24633,      0,                    0, 0, 586625/3163581, 0, 3135/20677, 0, 0, 0, 349448/1554777, 0, 131648/736281, 0, 15895/134199 ]

// cumulative squared lengths A_M:
      [ 0, 0, 0, 0, 0, 499712939/9622265625, 499712939/9622265625, 379061419/2232365625, 379061419/2232365625, 5332445912/20353921875, 5332445912/20353921875, 2461275979/6784640625, 2461275979/6784640625, 2046848701/4070784375, 2046848701/4070784375, 511808164067/818581640625, 511808164067/818581640625, 23796110881/28377496875, 23796110881/28377496875, 20/21 ],
      [ 0, 0, 0, 0, 0,      2299/24633,           2299/24633,      2299/24633, 2299/24633, 363128/1302651, 363128/1302651, 560633/1302651, 560633/1302651, 560633/1302651, 560633/1302651, 1372883/2095569, 1372883/2095569, 783395/939393, 783395/939393, 20/21 ]