#Defining polynomial for the field of definition of the Gram-matrix:
mpadppm5 := delta^4-14/3*delta^3+583/72*delta^2-1339/216*delta+183509/103680;
#Among its real roots the ones in the following postions
#(roots in increasing order)
#yield the relevant real Gram-matrices:
rootadppm5:=[1];
#(Warning: Use at least 10 digits)
#Minimal polynomial of trace of Gram-matrix:
Tradppm5 := lambda^2-26/3*lambda+149/9;
#Numerical approximations of Eigenvalues of relevant Gram-matrices:
EVGadppm51 := [1.38196601122691, 1.38196601122691, 3.06011329560749];
#Formal Gram-matrix:
Gadppm5 := Matrix(12,12,[
[400/43*delta^3-4240/129*delta^2+14992/387*delta-17293/1161, -200/43*delta^3+2120/129*delta^2-14605/774*delta+8066/1161, -200/43*delta^3+2120/129*delta^2-14605/774*delta+8066/1161, 400/43*delta^3-4240/129*delta^2+14992/387*delta-35747/2322, -2000/43*delta^3+21200/129*delta^2-73799/387*delta+337733/4644, 400/43*delta^3-4240/129*delta^2+14992/387*delta-35747/2322, -800/43*delta^3+8480/129*delta^2-30371/387*delta+36908/1161, 1600/43*delta^3-16960/129*delta^2+58420/387*delta-261595/4644, -1400/43*delta^3+14840/129*delta^2-101461/774*delta+222365/4644, -1400/43*delta^3+14840/129*delta^2-101461/774*delta+222365/4644, 1600/43*delta^3-16960/129*delta^2+58420/387*delta-261595/4644, 1600/43*delta^3-16960/129*delta^2+58420/387*delta-259273/4644],
[-200/43*delta^3+2120/129*delta^2-14605/774*delta+8066/1161, -800/43*delta^3+8480/129*delta^2-29597/387*delta+34586/1161, -800/43*delta^3+8480/129*delta^2-29597/387*delta+68011/2322, -200/43*delta^3+2120/129*delta^2-14605/774*delta+8066/1161, 2800/43*delta^3-29680/129*delta^2+103396/387*delta-118729/1161, 1600/43*delta^3-16960/129*delta^2+58420/387*delta-261595/4644, 400/43*delta^3-4240/129*delta^2+15379/387*delta-77299/4644, -800/43*delta^3+8480/129*delta^2-29597/387*delta+68011/2322, 1600/43*delta^3-16960/129*delta^2+58420/387*delta-261595/4644, 1600/43*delta^3-16960/129*delta^2+58420/387*delta-259273/4644, -2600/43*delta^3+27560/129*delta^2-190639/774*delta+429881/4644, -2600/43*delta^3+27560/129*delta^2-190639/774*delta+429881/4644],
[-200/43*delta^3+2120/129*delta^2-14605/774*delta+8066/1161, -800/43*delta^3+8480/129*delta^2-29597/387*delta+68011/2322, -800/43*delta^3+8480/129*delta^2-29597/387*delta+34586/1161, 1600/43*delta^3-16960/129*delta^2+58420/387*delta-261595/4644, 2800/43*delta^3-29680/129*delta^2+103396/387*delta-118729/1161, -200/43*delta^3+2120/129*delta^2-14605/774*delta+8066/1161, 400/43*delta^3-4240/129*delta^2+15379/387*delta-77299/4644, -2600/43*delta^3+27560/129*delta^2-190639/774*delta+429881/4644, 1600/43*delta^3-16960/129*delta^2+58420/387*delta-259273/4644, 1600/43*delta^3-16960/129*delta^2+58420/387*delta-261595/4644, -800/43*delta^3+8480/129*delta^2-29597/387*delta+68011/2322, -2600/43*delta^3+27560/129*delta^2-190639/774*delta+429881/4644],
[400/43*delta^3-4240/129*delta^2+14992/387*delta-35747/2322, -200/43*delta^3+2120/129*delta^2-14605/774*delta+8066/1161, 1600/43*delta^3-16960/129*delta^2+58420/387*delta-261595/4644, 400/43*delta^3-4240/129*delta^2+14992/387*delta-17293/1161, -2000/43*delta^3+21200/129*delta^2-73799/387*delta+337733/4644, -1400/43*delta^3+14840/129*delta^2-101461/774*delta+222365/4644, -800/43*delta^3+8480/129*delta^2-30371/387*delta+36908/1161, -200/43*delta^3+2120/129*delta^2-14605/774*delta+8066/1161, 400/43*delta^3-4240/129*delta^2+14992/387*delta-35747/2322, -1400/43*delta^3+14840/129*delta^2-101461/774*delta+222365/4644, 1600/43*delta^3-16960/129*delta^2+58420/387*delta-259273/4644, 1600/43*delta^3-16960/129*delta^2+58420/387*delta-261595/4644],
[-2000/43*delta^3+21200/129*delta^2-73799/387*delta+337733/4644, 2800/43*delta^3-29680/129*delta^2+103396/387*delta-118729/1161, 2800/43*delta^3-29680/129*delta^2+103396/387*delta-118729/1161, -2000/43*delta^3+21200/129*delta^2-73799/387*delta+337733/4644, -4400/43*delta^3+46640/129*delta^2-162590/387*delta+374641/2322, -2000/43*delta^3+21200/129*delta^2-73799/387*delta+337733/4644, 400/43*delta^3-4240/129*delta^2+14605/387*delta-63367/4644, 2800/43*delta^3-29680/129*delta^2+103396/387*delta-118729/1161, -2000/43*delta^3+21200/129*delta^2-73799/387*delta+337733/4644, -2000/43*delta^3+21200/129*delta^2-73799/387*delta+337733/4644, 2800/43*delta^3-29680/129*delta^2+103396/387*delta-118729/1161, 2800/43*delta^3-29680/129*delta^2+103396/387*delta-118729/1161],
[400/43*delta^3-4240/129*delta^2+14992/387*delta-35747/2322, 1600/43*delta^3-16960/129*delta^2+58420/387*delta-261595/4644, -200/43*delta^3+2120/129*delta^2-14605/774*delta+8066/1161, -1400/43*delta^3+14840/129*delta^2-101461/774*delta+222365/4644, -2000/43*delta^3+21200/129*delta^2-73799/387*delta+337733/4644, 400/43*delta^3-4240/129*delta^2+14992/387*delta-17293/1161, -800/43*delta^3+8480/129*delta^2-30371/387*delta+36908/1161, 1600/43*delta^3-16960/129*delta^2+58420/387*delta-259273/4644, -1400/43*delta^3+14840/129*delta^2-101461/774*delta+222365/4644, 400/43*delta^3-4240/129*delta^2+14992/387*delta-35747/2322, -200/43*delta^3+2120/129*delta^2-14605/774*delta+8066/1161, 1600/43*delta^3-16960/129*delta^2+58420/387*delta-261595/4644],
[-800/43*delta^3+8480/129*delta^2-30371/387*delta+36908/1161, 400/43*delta^3-4240/129*delta^2+15379/387*delta-77299/4644, 400/43*delta^3-4240/129*delta^2+15379/387*delta-77299/4644, -800/43*delta^3+8480/129*delta^2-30371/387*delta+36908/1161, 400/43*delta^3-4240/129*delta^2+14605/387*delta-63367/4644, -800/43*delta^3+8480/129*delta^2-30371/387*delta+36908/1161, 1600/43*delta^3-16960/129*delta^2+60355/387*delta-144149/2322, 400/43*delta^3-4240/129*delta^2+15379/387*delta-77299/4644, -800/43*delta^3+8480/129*delta^2-30371/387*delta+36908/1161, -800/43*delta^3+8480/129*delta^2-30371/387*delta+36908/1161, 400/43*delta^3-4240/129*delta^2+15379/387*delta-77299/4644, 400/43*delta^3-4240/129*delta^2+15379/387*delta-77299/4644],
[1600/43*delta^3-16960/129*delta^2+58420/387*delta-261595/4644, -800/43*delta^3+8480/129*delta^2-29597/387*delta+68011/2322, -2600/43*delta^3+27560/129*delta^2-190639/774*delta+429881/4644, -200/43*delta^3+2120/129*delta^2-14605/774*delta+8066/1161, 2800/43*delta^3-29680/129*delta^2+103396/387*delta-118729/1161, 1600/43*delta^3-16960/129*delta^2+58420/387*delta-259273/4644, 400/43*delta^3-4240/129*delta^2+15379/387*delta-77299/4644, -800/43*delta^3+8480/129*delta^2-29597/387*delta+34586/1161, -200/43*delta^3+2120/129*delta^2-14605/774*delta+8066/1161, 1600/43*delta^3-16960/129*delta^2+58420/387*delta-261595/4644, -2600/43*delta^3+27560/129*delta^2-190639/774*delta+429881/4644, -800/43*delta^3+8480/129*delta^2-29597/387*delta+68011/2322],
[-1400/43*delta^3+14840/129*delta^2-101461/774*delta+222365/4644, 1600/43*delta^3-16960/129*delta^2+58420/387*delta-261595/4644, 1600/43*delta^3-16960/129*delta^2+58420/387*delta-259273/4644, 400/43*delta^3-4240/129*delta^2+14992/387*delta-35747/2322, -2000/43*delta^3+21200/129*delta^2-73799/387*delta+337733/4644, -1400/43*delta^3+14840/129*delta^2-101461/774*delta+222365/4644, -800/43*delta^3+8480/129*delta^2-30371/387*delta+36908/1161, -200/43*delta^3+2120/129*delta^2-14605/774*delta+8066/1161, 400/43*delta^3-4240/129*delta^2+14992/387*delta-17293/1161, 400/43*delta^3-4240/129*delta^2+14992/387*delta-35747/2322, 1600/43*delta^3-16960/129*delta^2+58420/387*delta-261595/4644, -200/43*delta^3+2120/129*delta^2-14605/774*delta+8066/1161],
[-1400/43*delta^3+14840/129*delta^2-101461/774*delta+222365/4644, 1600/43*delta^3-16960/129*delta^2+58420/387*delta-259273/4644, 1600/43*delta^3-16960/129*delta^2+58420/387*delta-261595/4644, -1400/43*delta^3+14840/129*delta^2-101461/774*delta+222365/4644, -2000/43*delta^3+21200/129*delta^2-73799/387*delta+337733/4644, 400/43*delta^3-4240/129*delta^2+14992/387*delta-35747/2322, -800/43*delta^3+8480/129*delta^2-30371/387*delta+36908/1161, 1600/43*delta^3-16960/129*delta^2+58420/387*delta-261595/4644, 400/43*delta^3-4240/129*delta^2+14992/387*delta-35747/2322, 400/43*delta^3-4240/129*delta^2+14992/387*delta-17293/1161, -200/43*delta^3+2120/129*delta^2-14605/774*delta+8066/1161, -200/43*delta^3+2120/129*delta^2-14605/774*delta+8066/1161],
[1600/43*delta^3-16960/129*delta^2+58420/387*delta-261595/4644, -2600/43*delta^3+27560/129*delta^2-190639/774*delta+429881/4644, -800/43*delta^3+8480/129*delta^2-29597/387*delta+68011/2322, 1600/43*delta^3-16960/129*delta^2+58420/387*delta-259273/4644, 2800/43*delta^3-29680/129*delta^2+103396/387*delta-118729/1161, -200/43*delta^3+2120/129*delta^2-14605/774*delta+8066/1161, 400/43*delta^3-4240/129*delta^2+15379/387*delta-77299/4644, -2600/43*delta^3+27560/129*delta^2-190639/774*delta+429881/4644, 1600/43*delta^3-16960/129*delta^2+58420/387*delta-261595/4644, -200/43*delta^3+2120/129*delta^2-14605/774*delta+8066/1161, -800/43*delta^3+8480/129*delta^2-29597/387*delta+34586/1161, -800/43*delta^3+8480/129*delta^2-29597/387*delta+68011/2322],
[1600/43*delta^3-16960/129*delta^2+58420/387*delta-259273/4644, -2600/43*delta^3+27560/129*delta^2-190639/774*delta+429881/4644, -2600/43*delta^3+27560/129*delta^2-190639/774*delta+429881/4644, 1600/43*delta^3-16960/129*delta^2+58420/387*delta-261595/4644, 2800/43*delta^3-29680/129*delta^2+103396/387*delta-118729/1161, 1600/43*delta^3-16960/129*delta^2+58420/387*delta-261595/4644, 400/43*delta^3-4240/129*delta^2+15379/387*delta-77299/4644, -800/43*delta^3+8480/129*delta^2-29597/387*delta+68011/2322, -200/43*delta^3+2120/129*delta^2-14605/774*delta+8066/1161, -200/43*delta^3+2120/129*delta^2-14605/774*delta+8066/1161, -800/43*delta^3+8480/129*delta^2-29597/387*delta+68011/2322, -800/43*delta^3+8480/129*delta^2-29597/387*delta+34586/1161]
]):