/*
Generated by Allan Steel in Magma, 2010.

Field defining polynomial: x^4 - 3*x^2 + 4.

Traces:    [ 0, 0 ]
Density:   [ 0.071562500, 0.99843750 ]
Numer max: [ 4, 322 ]
Numer av:  [ 0.038320312, 15.353672 ]
Denom max: [ 2, 180 ], [ [ <2, 1> ], [ <2, 2>, <3, 2>, <5, 1> ] ]
Denom LCM: [ 2, 180 ], [ [ <2, 1> ], [ <2, 2>, <3, 2>, <5, 1> ] ]

Character:
( 80, -80, 0, -1, 80*zeta(28)_4, -80*zeta(28)_4, 0, 0, 0, 0, 0, 1, zeta(28)_7^4 
    + zeta(28)_7^2 + zeta(28)_7, -zeta(28)_7^4 - zeta(28)_7^2 - zeta(28)_7
    - 1, 0, 0, 0, 0, zeta(28)_4, -zeta(28)_4, zeta(28)_7^4 + zeta(28)_7^2
    + zeta(28)_7 + 1, -zeta(28)_7^4 - zeta(28)_7^2 - zeta(28)_7, 0,
    0, 0, 0, zeta(28)_4*zeta(28)_7^4 + zeta(28)_4*zeta(28)_7^2
    + zeta(28)_4*zeta(28)_7, -zeta(28)_4*zeta(28)_7^4 -
    zeta(28)_4*zeta(28)_7^2 - zeta(28)_4*zeta(28)_7,
    -zeta(28)_4*zeta(28)_7^4 - zeta(28)_4*zeta(28)_7^2 -
    zeta(28)_4*zeta(28)_7 - zeta(28)_4, zeta(28)_4*zeta(28)_7^4 +
    zeta(28)_4*zeta(28)_7^2 + zeta(28)_4*zeta(28)_7 + zeta(28)_4 )
*/

//G:=c9Group("4al34p");
G := PermutationGroup(ATLASGroup("4aL34"));
M :=
GModule(G, [
    Matrix(SparseMatrix(K, 80, 80, [
    <1, 1, 1/2*(-w^3 + w + 2)>, <1, 2, 1>, <1, 3, -1>, <1, 4, 1/2*(w^3 - w + 
    2)>, 
    <2, 1, 1>, <2, 2, 1/2*(w^3 - w)>, <2, 4, -1>, 
    <3, 1, 1/2*(-w^3 + w + 2)>, <3, 2, 1/2*(-w^3 + w)>, <3, 3, -2>, <3, 4, 
    1/2*(w^3 - w + 4)>, 
    <4, 1, 1>, <4, 2, -1>, <4, 3, -1>, <4, 4, 1>, 
    <5, 5, -1>, <5, 6, 1/2*(-w^3 + w)>, <5, 8, 1/2*(-w^3 + w)>, 
    <6, 5, -1>, <6, 6, 1/2*(-w^3 + w + 2)>, <6, 7, 1/2*(w^3 - w)>, <6, 8, 
    1/2*(-w^3 + w + 2)>, 
    <7, 5, 1/2*(w^3 - w)>, <7, 8, 1/2*(w^3 - w)>, 
    <8, 5, 1>, <8, 6, 1/2*(w^3 - w)>, <8, 7, 1/2*(-w^3 + w)>, <8, 8, 1/2*(w^3 - 
    w)>, 
    <9, 14, 1>, <9, 15, 1/2*(-w^3 + w)>, 
    <10, 10, 1>, 
    <11, 10, -1>, <11, 13, 1>, <11, 17, 1/2*(w^3 - w)>, <11, 21, 1>, 
    <12, 10, 1>, <12, 12, 1>, <12, 13, -1>, <12, 14, 1/2*(-w^3 + w + 2)>, <12, 
    15, 1/2*(-w^3 + w)>, <12, 16, -1>, <12, 17, 1/2*(-w^3 + w)>, <12, 18, 
    1/2*(-w^3 + w)>, <12, 21, -1>, 
    <13, 11, 1/2*(-w^3 + w + 2)>, <13, 13, 1/2*(-w^3 + w)>, <13, 17, 1>, <13, 
    19, 1/2*(w^3 - w)>, 
    <14, 10, -1>, <14, 11, 1/2*(-w^3 + w)>, <14, 13, 1/2*(-w^3 + w)>, <14, 14, 
    1/2*(w^3 - w)>, <14, 15, 1>, <14, 16, 1>, <14, 17, 1>, <14, 18, 1>, <14, 19,
    1/2*(w^3 - w)>, <14, 21, 1/2*(-w^3 + w)>, 
    <15, 9, 1/2*(w^3 - w)>, <15, 10, 1/2*(w^3 - w)>, <15, 11, -1>, <15, 13, -1>,
    <15, 14, 1>, <15, 15, 1/2*(-w^3 + w)>, <15, 16, 1/2*(-w^3 + w)>, <15, 17, 
    1/2*(-w^3 + w)>, <15, 18, 1/2*(-w^3 + w)>, <15, 19, 1>, <15, 21, -1>, 
    <16, 10, 1/2*(w^3 - w)>, <16, 11, 1/2*(-w^3 + w - 2)>, <16, 13, 1/2*(-w^3 + 
    w - 2)>, <16, 14, 2>, <16, 15, 1/2*(-w^3 + w + 2)>, <16, 16, 1/2*(-w^3 + 
    w)>, <16, 17, 1/2*(-w^3 + w + 2)>, <16, 18, 1/2*(-w^3 + w + 2)>, <16, 19, 
    1/2*(w^3 - w + 2)>, <16, 21, 1/2*(-w^3 + w - 2)>, 
    <17, 10, 1/2*(-w^3 + w)>, <17, 11, 1>, <17, 13, 1>, <17, 19, 1/2*(w^3 - w - 
    2)>, <17, 21, -1>, 
    <18, 9, 1/2*(-w^3 + w)>, <18, 10, 1/2*(-w^3 + w)>, <18, 11, 1/2*(w^3 - w + 
    2)>, <18, 13, 1/2*(w^3 - w + 2)>, <18, 14, -1>, <18, 15, 1/2*(w^3 - w - 2)>,
    <18, 16, 1/2*(w^3 - w)>, <18, 17, 1/2*(w^3 - w - 2)>, <18, 18, 1/2*(w^3 - w 
    - 2)>, <18, 19, -1>, <18, 21, 1/2*(w^3 - w + 2)>, 
    <19, 10, 1/2*(-w^3 + w)>, <19, 11, 1>, <19, 13, 1>, <19, 17, 1/2*(w^3 - w)>,
    <19, 19, -1>, <19, 21, 1>, 
    <20, 12, 1/2*(-w^3 + w)>, <20, 19, 1/2*(w^3 - w)>, <20, 22, 1/2*(-w^3 + w)>,
    <20, 24, 1/2*(-w^3 + w)>, 
    <21, 17, -1>, <21, 19, 1>, <21, 21, 1/2*(w^3 - w)>, 
    <22, 10, 1/2*(-w^3 + w - 2)>, <22, 11, 1>, <22, 12, -1>, <22, 13, 1>, <22, 
    14, -2>, <22, 15, 1/2*(w^3 - w)>, <22, 16, 1/2*(w^3 - w + 2)>, <22, 17, 
    1/2*(w^3 - w)>, <22, 18, 1/2*(w^3 - w)>, <22, 20, 1/2*(w^3 - w)>, <22, 21, 
    1>, <22, 23, 1/2*(-w^3 + w)>, <22, 24, -1>, 
    <23, 10, 1/2*(w^3 - w)>, <23, 23, -1>, 
    <24, 13, 1>, <24, 14, 1/2*(w^3 - w + 2)>, <24, 16, 1/2*(-w^3 + w)>, <24, 17,
    1/2*(w^3 - w)>, <24, 19, -1>, <24, 21, 1>, <24, 23, 1/2*(w^3 - w)>, <24, 24,
    1>, 
    <25, 30, 1>, <25, 31, 1/2*(-w^3 + w)>, 
    <26, 26, 1>, 
    <27, 26, -1>, <27, 29, 1>, <27, 33, 1/2*(w^3 - w)>, <27, 37, 1>, 
    <28, 26, 1>, <28, 28, 1>, <28, 29, -1>, <28, 30, 1/2*(-w^3 + w + 2)>, <28, 
    31, 1/2*(-w^3 + w)>, <28, 32, -1>, <28, 33, 1/2*(-w^3 + w)>, <28, 34, 
    1/2*(-w^3 + w)>, <28, 37, -1>, 
    <29, 27, 1/2*(-w^3 + w + 2)>, <29, 29, 1/2*(-w^3 + w)>, <29, 33, 1>, <29, 
    35, 1/2*(w^3 - w)>, 
    <30, 26, -1>, <30, 27, 1/2*(-w^3 + w)>, <30, 29, 1/2*(-w^3 + w)>, <30, 30, 
    1/2*(w^3 - w)>, <30, 31, 1>, <30, 32, 1>, <30, 33, 1>, <30, 34, 1>, <30, 35,
    1/2*(w^3 - w)>, <30, 37, 1/2*(-w^3 + w)>, 
    <31, 25, 1/2*(w^3 - w)>, <31, 26, 1/2*(w^3 - w)>, <31, 27, -1>, <31, 29, 
    -1>, <31, 30, 1>, <31, 31, 1/2*(-w^3 + w)>, <31, 32, 1/2*(-w^3 + w)>, <31, 
    33, 1/2*(-w^3 + w)>, <31, 34, 1/2*(-w^3 + w)>, <31, 35, 1>, <31, 37, -1>, 
    <32, 26, 1/2*(w^3 - w)>, <32, 27, 1/2*(-w^3 + w - 2)>, <32, 29, 1/2*(-w^3 + 
    w - 2)>, <32, 30, 2>, <32, 31, 1/2*(-w^3 + w + 2)>, <32, 32, 1/2*(-w^3 + 
    w)>, <32, 33, 1/2*(-w^3 + w + 2)>, <32, 34, 1/2*(-w^3 + w + 2)>, <32, 35, 
    1/2*(w^3 - w + 2)>, <32, 37, 1/2*(-w^3 + w - 2)>, 
    <33, 26, 1/2*(-w^3 + w)>, <33, 27, 1>, <33, 29, 1>, <33, 35, 1/2*(w^3 - w - 
    2)>, <33, 37, -1>, 
    <34, 25, 1/2*(-w^3 + w)>, <34, 26, 1/2*(-w^3 + w)>, <34, 27, 1/2*(w^3 - w + 
    2)>, <34, 29, 1/2*(w^3 - w + 2)>, <34, 30, -1>, <34, 31, 1/2*(w^3 - w - 2)>,
    <34, 32, 1/2*(w^3 - w)>, <34, 33, 1/2*(w^3 - w - 2)>, <34, 34, 1/2*(w^3 - w 
    - 2)>, <34, 35, -1>, <34, 37, 1/2*(w^3 - w + 2)>, 
    <35, 26, 1/2*(-w^3 + w)>, <35, 27, 1>, <35, 29, 1>, <35, 33, 1/2*(w^3 - w)>,
    <35, 35, -1>, <35, 37, 1>, 
    <36, 28, 1/2*(-w^3 + w)>, <36, 35, 1/2*(w^3 - w)>, <36, 38, 1/2*(-w^3 + w)>,
    <36, 40, 1/2*(-w^3 + w)>, 
    <37, 33, -1>, <37, 35, 1>, <37, 37, 1/2*(w^3 - w)>, 
    <38, 26, 1/2*(-w^3 + w - 2)>, <38, 27, 1>, <38, 28, -1>, <38, 29, 1>, <38, 
    30, -2>, <38, 31, 1/2*(w^3 - w)>, <38, 32, 1/2*(w^3 - w + 2)>, <38, 33, 
    1/2*(w^3 - w)>, <38, 34, 1/2*(w^3 - w)>, <38, 36, 1/2*(w^3 - w)>, <38, 37, 
    1>, <38, 39, 1/2*(-w^3 + w)>, <38, 40, -1>, 
    <39, 26, 1/2*(w^3 - w)>, <39, 39, -1>, 
    <40, 29, 1>, <40, 30, 1/2*(w^3 - w + 2)>, <40, 32, 1/2*(-w^3 + w)>, <40, 33,
    1/2*(w^3 - w)>, <40, 35, -1>, <40, 37, 1>, <40, 39, 1/2*(w^3 - w)>, <40, 40,
    1>, 
    <41, 42, -1>, <41, 48, 1>, <41, 49, -1>, <41, 52, -1>, <41, 54, 1/2*(-w^3 + 
    w + 2)>, <41, 57, -1>, 
    <42, 42, 1/2*(-w^3 + w)>, <42, 54, 1>, <42, 55, 1/2*(-w^3 + w + 2)>, <42, 
    57, 1/2*(-w^3 + w - 2)>, 
    <43, 46, 1/2*(-w^3 + w + 2)>, <43, 47, 1/2*(w^3 - w)>, <43, 54, 1/2*(-w^3 + 
    w)>, <43, 55, -1>, <43, 59, 1>, 
    <44, 42, -1>, <44, 44, 1/2*(w^3 - w)>, <44, 45, 1/2*(-w^3 + w)>, <44, 50, 
    1>, <44, 54, -1>, <44, 55, 1/2*(w^3 - w - 2)>, <44, 57, 1/2*(w^3 - w)>, 
    <45, 42, 1/2*(w^3 - w)>, <45, 45, -1>, <45, 50, 1/2*(-w^3 + w)>, <45, 51, 
    -1>, <45, 54, 1/2*(w^3 - w - 2)>, <45, 55, 1/2*(w^3 - w)>, <45, 57, 1/2*(w^3
    - w + 2)>, 
    <46, 42, 1>, <46, 43, 1/2*(-w^3 + w - 2)>, <46, 53, 1/2*(w^3 - w - 2)>, <46,
    54, 1/2*(w^3 - w - 2)>, <46, 57, 1>, <46, 58, 1/2*(-w^3 + w)>, <46, 60, -1>,
    <47, 42, 1/2*(w^3 - w + 2)>, <47, 43, 1/2*(-w^3 + w + 2)>, <47, 53, -1>, 
    <47, 54, -1>, <47, 57, 1/2*(w^3 - w + 2)>, <47, 60, 1/2*(-w^3 + w)>, 
    <48, 41, 1/2*(w^3 - w + 2)>, <48, 48, 1/2*(-w^3 + w - 2)>, <48, 49, 1/2*(w^3
    - w)>, <48, 52, 2>, <48, 54, 1/2*(w^3 - w - 2)>, <48, 55, 1/2*(w^3 - w)>, 
    <48, 57, 1>, 
    <49, 48, -1>, <49, 52, 1/2*(-w^3 + w + 2)>, <49, 54, 1/2*(w^3 - w)>, <49, 
    57, 1>, 
    <50, 42, 1/2*(w^3 - w)>, <50, 44, 2>, <50, 45, 1/2*(-w^3 + w - 2)>, <50, 50,
    1/2*(-w^3 + w + 2)>, <50, 51, 1/2*(-w^3 + w)>, <50, 55, 1/2*(w^3 - w + 2)>, 
    <51, 42, 1/2*(-w^3 + w)>, <51, 44, -w^3 + w>, <51, 45, 1/2*(w^3 - w - 2)>, 
    <51, 50, -1>, <51, 54, 1>, <51, 55, 1/2*(-w^3 + w + 2)>, <51, 57, 1/2*(-w^3 
    + w - 2)>, 
    <52, 41, 1/2*(w^3 - w)>, <52, 42, 1>, <52, 48, 1/2*(-w^3 + w)>, <52, 49, 
    1/2*(w^3 - w)>, <52, 52, 1/2*(w^3 - w + 2)>, <52, 54, -1>, <52, 57, 1>, 
    <53, 42, 1/2*(-w^3 + w - 2)>, <53, 54, 1/2*(-w^3 + w)>, <53, 55, -1>, <53, 
    56, 1>, <53, 57, -1>, <53, 59, 1>, 
    <54, 54, 1>, <54, 55, 1/2*(-w^3 + w + 2)>, 
    <55, 55, -1>, 
    <56, 43, 1/2*(w^3 - w - 4)>, <56, 53, 1/2*(w^3 - w + 2)>, <56, 54, 1/2*(w^3 
    - w + 2)>, <56, 55, 1>, <56, 57, 1/2*(-w^3 + w)>, <56, 58, 1/2*(-w^3 + w - 
    2)>, <56, 60, 1/2*(w^3 - w)>, 
    <57, 42, 1/2*(w^3 - w - 2)>, <57, 54, 1/2*(-w^3 + w)>, <57, 55, -1>, <57, 
    57, 1/2*(w^3 - w)>, 
    <58, 42, 1/2*(-w^3 + w)>, <58, 46, 1/2*(w^3 - w)>, <58, 47, -1>, <58, 54, 
    2>, <58, 55, 1/2*(-w^3 + w + 2)>, <58, 56, 1/2*(w^3 - w)>, <58, 57, 
    1/2*(-w^3 + w - 2)>, <58, 59, 1/2*(w^3 - w)>, 
    <59, 43, 1/2*(-w^3 + w + 4)>, <59, 53, 1/2*(-w^3 + w)>, <59, 55, 1/2*(w^3 - 
    w)>, <59, 58, 1/2*(w^3 - w + 2)>, <59, 60, 1/2*(-w^3 + w)>, 
    <60, 46, -2>, <60, 47, 1>, <60, 55, 1>, <60, 56, 1/2*(w^3 - w)>, <60, 57, 
    -1>, <60, 59, -1>, 
    <61, 62, -1>, <61, 68, 1>, <61, 69, -1>, <61, 72, -1>, <61, 74, 1/2*(-w^3 + 
    w + 2)>, <61, 77, -1>, 
    <62, 62, 1/2*(-w^3 + w)>, <62, 74, 1>, <62, 75, 1/2*(-w^3 + w + 2)>, <62, 
    77, 1/2*(-w^3 + w - 2)>, 
    <63, 66, 1/2*(-w^3 + w + 2)>, <63, 67, 1/2*(w^3 - w)>, <63, 74, 1/2*(-w^3 + 
    w)>, <63, 75, -1>, <63, 79, 1>, 
    <64, 62, -1>, <64, 64, 1/2*(w^3 - w)>, <64, 65, 1/2*(-w^3 + w)>, <64, 70, 
    1>, <64, 74, -1>, <64, 75, 1/2*(w^3 - w - 2)>, <64, 77, 1/2*(w^3 - w)>, 
    <65, 62, 1/2*(w^3 - w)>, <65, 65, -1>, <65, 70, 1/2*(-w^3 + w)>, <65, 71, 
    -1>, <65, 74, 1/2*(w^3 - w - 2)>, <65, 75, 1/2*(w^3 - w)>, <65, 77, 1/2*(w^3
    - w + 2)>, 
    <66, 62, 1>, <66, 63, 1/2*(-w^3 + w - 2)>, <66, 73, 1/2*(w^3 - w - 2)>, <66,
    74, 1/2*(w^3 - w - 2)>, <66, 77, 1>, <66, 78, 1/2*(-w^3 + w)>, <66, 80, -1>,
    <67, 62, 1/2*(w^3 - w + 2)>, <67, 63, 1/2*(-w^3 + w + 2)>, <67, 73, -1>, 
    <67, 74, -1>, <67, 77, 1/2*(w^3 - w + 2)>, <67, 80, 1/2*(-w^3 + w)>, 
    <68, 61, 1/2*(w^3 - w + 2)>, <68, 68, 1/2*(-w^3 + w - 2)>, <68, 69, 1/2*(w^3
    - w)>, <68, 72, 2>, <68, 74, 1/2*(w^3 - w - 2)>, <68, 75, 1/2*(w^3 - w)>, 
    <68, 77, 1>, 
    <69, 68, -1>, <69, 72, 1/2*(-w^3 + w + 2)>, <69, 74, 1/2*(w^3 - w)>, <69, 
    77, 1>, 
    <70, 62, 1/2*(w^3 - w)>, <70, 64, 2>, <70, 65, 1/2*(-w^3 + w - 2)>, <70, 70,
    1/2*(-w^3 + w + 2)>, <70, 71, 1/2*(-w^3 + w)>, <70, 75, 1/2*(w^3 - w + 2)>, 
    <71, 62, 1/2*(-w^3 + w)>, <71, 64, -w^3 + w>, <71, 65, 1/2*(w^3 - w - 2)>, 
    <71, 70, -1>, <71, 74, 1>, <71, 75, 1/2*(-w^3 + w + 2)>, <71, 77, 1/2*(-w^3 
    + w - 2)>, 
    <72, 61, 1/2*(w^3 - w)>, <72, 62, 1>, <72, 68, 1/2*(-w^3 + w)>, <72, 69, 
    1/2*(w^3 - w)>, <72, 72, 1/2*(w^3 - w + 2)>, <72, 74, -1>, <72, 77, 1>, 
    <73, 62, 1/2*(-w^3 + w - 2)>, <73, 74, 1/2*(-w^3 + w)>, <73, 75, -1>, <73, 
    76, 1>, <73, 77, -1>, <73, 79, 1>, 
    <74, 74, 1>, <74, 75, 1/2*(-w^3 + w + 2)>, 
    <75, 75, -1>, 
    <76, 63, 1/2*(w^3 - w - 4)>, <76, 73, 1/2*(w^3 - w + 2)>, <76, 74, 1/2*(w^3 
    - w + 2)>, <76, 75, 1>, <76, 77, 1/2*(-w^3 + w)>, <76, 78, 1/2*(-w^3 + w - 
    2)>, <76, 80, 1/2*(w^3 - w)>, 
    <77, 62, 1/2*(w^3 - w - 2)>, <77, 74, 1/2*(-w^3 + w)>, <77, 75, -1>, <77, 
    77, 1/2*(w^3 - w)>, 
    <78, 62, 1/2*(-w^3 + w)>, <78, 66, 1/2*(w^3 - w)>, <78, 67, -1>, <78, 74, 
    2>, <78, 75, 1/2*(-w^3 + w + 2)>, <78, 76, 1/2*(w^3 - w)>, <78, 77, 
    1/2*(-w^3 + w - 2)>, <78, 79, 1/2*(w^3 - w)>, 
    <79, 63, 1/2*(-w^3 + w + 4)>, <79, 73, 1/2*(-w^3 + w)>, <79, 75, 1/2*(w^3 - 
    w)>, <79, 78, 1/2*(w^3 - w + 2)>, <79, 80, 1/2*(-w^3 + w)>, 
    <80, 66, -2>, <80, 67, 1>, <80, 75, 1>, <80, 76, 1/2*(w^3 - w)>, <80, 77, 
    -1>, <80, 79, -1>
    ])),
    Matrix(K, 80, 80,
        [ [ -11/45, 1/15, 4/45, -1/45 ], [ 1/9, 1/10, -4/45, -1/90 ], [ 17/45, 
        -7/90, -8/45, 1/30 ], [ -22/45, -1/45, 4/15, -1/45 ], [ 0, 0, 0, 0 ], [ 
        0, -1/9, -1/45, 2/45 ], [ -2/45, -2/45, 1/15, 1/45 ], [ 2/15, 1/9, 
        -13/90, -7/90 ], [ -7/15, -31/90, 23/90, 13/45 ], [ -2/5, -1/45, 1/3, 
        1/15 ], [ -7/15, -67/90, -4/15, 7/90 ], [ 16/9, 13/15, -34/45, -22/45 ],
        [ -59/45, -31/30, -1/90, 8/45 ], [ -16/15, -26/45, 37/90, -1/30 ], [ 
        3/5, 1/18, -4/15, -1/90 ], [ -1/5, 11/90, 1/45, 1/10 ], [ 77/45, 77/90, 
        -41/45, -47/90 ], [ 1, 23/90, -32/45, -11/30 ], [ 34/45, 3/5, -16/45, 
        -4/15 ], [ -1/5, -7/30, -7/45, 1/18 ], [ 7/45, -11/90, -8/15, -3/10 ], [
        2/9, -7/15, -14/45, 1/15 ], [ 8/15, -1/15, -17/90, -7/90 ], [ -19/45, 
        -1/18, 13/90, -1/9 ], [ 1/15, 7/30, 2/15, -1/18 ], [ 1/3, 1/18, -1/45, 
        -1/90 ], [ -11/45, -49/90, 29/90, 1/5 ], [ -1/9, -43/90, -22/45, 1/30 ],
        [ -32/45, -3/5, 5/9, 17/45 ], [ 17/45, -59/90, 13/90, 22/45 ], [ 1/9, 
        1/6, -13/90, -2/45 ], [ -1/9, 11/18, 1/6, -1/3 ], [ -1/15, -7/30, -5/18,
        -2/45 ], [ -4/9, -16/45, 1/30, 1/10 ], [ -14/45, -14/45, -1/15, 1/9 ], [
        -32/45, -11/45, 17/90, 11/90 ], [ -22/45, -5/9, 11/90, 17/90 ], [ -2/3, 
        -1/9, 7/45, 7/45 ], [ -14/45, 1/45, -7/90, -7/90 ], [ 1/9, -1/90, 1/45, 
        7/90 ], [ 29/18, -31/36, -2/3, 19/36 ], [ -1/18, 1/4, -1/3, 1/12 ], [ 
        -5/18, 17/36, -2/9, -1/36 ], [ -5/9, 10/9, 1/9, -4/9 ], [ 5/6, -13/12, 
        -1/3, 5/12 ], [ -7/18, -11/36, 1/3, -1/4 ], [ 7/9, 1/18, -4/9, 1/6 ], [ 
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]: Check := false) where w := K.1 where K := ext<K|Polynomial(K, [4, 0, -3, 0, 1])> where K is 
RationalField();
K<w> := BaseRing(M);
K;
M;
