// 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 ]