// see below for algebraic expressions

L17:=[
[ 0.0, 0.435874159108882218062287930846, 0.0, 0.0, -0.158009774587787744550689083318 + 0.300431770262860477462910652992*I, 0.0, 0.0, 0.438536379196715874196225888208 - 0.0497315201215424581151788471498*I, 0.0, 0.0, 0.438536379196715874196225888208 - 0.0497315201215424581151788471498*I, 0.0, 0.0, -0.158009774587787744550689083318 + 0.300431770262860477462910652992*I, 0.0, 0.0, 0.435874159108882218062287930846, 0.0 ]
] where I:=Sqrt(-1);

// squared length of the multipoles
[ 0.055555, 0.0, 0.0, 0.0, 0.0, 0.024845, 0.065538, 0.022785, 0.090348, 0.059162, 0.063227, 0.082377, 0.072752, 0.048934, 0.078913, 0.15056, 0.073666, 0.11134 ]

// cumulative squared lengths A_M:
          [ 0.0, 0.0, 0.0, 0.0, 0.024845, 0.090384, 0.11317,  0.20352,  0.26268,  0.32590,  0.40828,  0.48103,  0.52997,  0.60888,  0.75945, 0.83311,  0.94444 ]



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

L17_algebraic:=[
[  0,
   1/918*Sqrt(17)*Sqrt(9418),
   0,
   0,
   1/4450005*Sqrt(-1)*Sqrt(5)*Sqrt(7)*Sqrt(17)*Sqrt(9418)*Sqrt(3195*Sqrt(20995)-575935/4)-1/988890*Sqrt(5)*Sqrt(7)*Sqrt(17)*Sqrt(9418)*Sqrt(20995)+71/890001*Sqrt(5)*Sqrt(7)*Sqrt(17)*Sqrt(9418),
   0,
   0,
   1/989878890*Sqrt(9418)*Sqrt(17)*Sqrt(13)*Sqrt(11)*Sqrt(2)*Sqrt(-1)*Sqrt(3195*Sqrt(20995)-575935/4)*Sqrt(20995)-142/890891001*Sqrt(9418)*Sqrt(17)*Sqrt(13)*Sqrt(11)*Sqrt(2)*Sqrt(-1)*Sqrt(3195*Sqrt(20995)-575935/4)+71/65991926*Sqrt(2)*Sqrt(11)*Sqrt(13)*Sqrt(17)*Sqrt(9418)*Sqrt(20995)-108197/1187854668*Sqrt(2)*Sqrt(11)*Sqrt(13)*Sqrt(17)*Sqrt(9418),
   0,
   0,
   1/989878890*Sqrt(9418)*Sqrt(17)*Sqrt(13)*Sqrt(11)*Sqrt(2)*Sqrt(-1)*Sqrt(3195*Sqrt(20995)-575935/4)*Sqrt(20995)-142/890891001*Sqrt(9418)*Sqrt(17)*Sqrt(13)*Sqrt(11)*Sqrt(2)*Sqrt(-1)*Sqrt(3195*Sqrt(20995)-575935/4)+71/65991926*Sqrt(2)*Sqrt(11)*Sqrt(13)*Sqrt(17)*Sqrt(9418)*Sqrt(20995)-108197/1187854668*Sqrt(2)*Sqrt(11)*Sqrt(13)*Sqrt(17)*Sqrt(9418),
   0,
   0,
   1/4450005*Sqrt(-1)*Sqrt(5)*Sqrt(7)*Sqrt(17)*Sqrt(9418)*Sqrt(3195*Sqrt(20995)-575935/4)-1/988890*Sqrt(5)*Sqrt(7)*Sqrt(17)*Sqrt(9418)*Sqrt(20995)+71/890001*Sqrt(5)*Sqrt(7)*Sqrt(17)*Sqrt(9418),
   0,
   0,
   1/918*Sqrt(17)*Sqrt(9418),
   0]
];