/*
Generated by Allan Steel in Magma, 2010.

Field defining polynomial: x^8 + 3*x^6 + 5*x^4 + 12*x^2 + 16.

Traces:    [ 0, 1/20*(3*w^7 + 5*w^5 - 5*w^3 + 16*w) ]
Density:   [ 0.032777778, 0.75777778 ]
Numer max: [ 36, 2704 ]
Numer av:  [ 0.085937500, 47.701632 ]
Denom max: [ 40, 3200 ], [ [ <2, 3>, <5, 1> ], [ <2, 7>, <5, 2> ] ]
Denom LCM: [ 40, 9600 ], [ [ <2, 3>, <5, 1> ], [ <2, 7>, <3, 1>, <5, 2> ] ]

Character:
( 60, -60, 0, 60*zeta(84)_3, -60*zeta(84)_3 - 60, 0, 60*zeta(84)_4, 
    -60*zeta(84)_4, 0, -2*zeta(84)_4, 2*zeta(84)_4, -2, 2, 0, 0, -60*zeta(84)_3,
    60*zeta(84)_3 + 60, 0, 0, 0, zeta(84)_7^4 + zeta(84)_7^2 + zeta(84)_7 + 1, 
    -zeta(84)_7^4 - zeta(84)_7^2 - zeta(84)_7, 0, 0, 0, 0, 
    60*zeta(84)_4*zeta(84)_3 + 60*zeta(84)_4, -60*zeta(84)_4*zeta(84)_3 - 
    60*zeta(84)_4, 60*zeta(84)_4*zeta(84)_3, -60*zeta(84)_4*zeta(84)_3, 0, 0, 
    -2*zeta(84)_4*zeta(84)_3 - 2*zeta(84)_4, 2*zeta(84)_3 + 2, -2*zeta(84)_3, 
    2*zeta(84)_3, -2*zeta(84)_3 - 2, 2*zeta(84)_4*zeta(84)_3, 
    -2*zeta(84)_4*zeta(84)_3, 2*zeta(84)_4*zeta(84)_3 + 2*zeta(84)_4, 0, 0, 
    -zeta(84)_7^4 - zeta(84)_7^2 - zeta(84)_7 - 1, zeta(84)_7^4 + zeta(84)_7^2 +
    zeta(84)_7, 0, 0, 0, 0, 0, 0, 0, 0, -zeta(84)_3*zeta(84)_7^4 - 
    zeta(84)_3*zeta(84)_7^2 - zeta(84)_3*zeta(84)_7 - zeta(84)_3 - zeta(84)_7^4 
    - zeta(84)_7^2 - zeta(84)_7 - 1, -zeta(84)_3*zeta(84)_7^4 - 
    zeta(84)_3*zeta(84)_7^2 - zeta(84)_3*zeta(84)_7, zeta(84)_3*zeta(84)_7^4 + 
    zeta(84)_3*zeta(84)_7^2 + zeta(84)_3*zeta(84)_7 + zeta(84)_7^4 + 
    zeta(84)_7^2 + zeta(84)_7, zeta(84)_3*zeta(84)_7^4 + zeta(84)_3*zeta(84)_7^2
    + zeta(84)_3*zeta(84)_7 + zeta(84)_3, 0, 0, 0, 0, -zeta(84)_4*zeta(84)_7^4 -
    zeta(84)_4*zeta(84)_7^2 - zeta(84)_4*zeta(84)_7 - zeta(84)_4, 
    -zeta(84)_4*zeta(84)_7^4 - zeta(84)_4*zeta(84)_7^2 - zeta(84)_4*zeta(84)_7, 
    zeta(84)_4*zeta(84)_7^4 + zeta(84)_4*zeta(84)_7^2 + zeta(84)_4*zeta(84)_7, 
    zeta(84)_4*zeta(84)_7^4 + zeta(84)_4*zeta(84)_7^2 + zeta(84)_4*zeta(84)_7 + 
    zeta(84)_4, 0, 0, 0, 0, zeta(84)_3*zeta(84)_7^4 + zeta(84)_3*zeta(84)_7^2 + 
    zeta(84)_3*zeta(84)_7 + zeta(84)_3 + zeta(84)_7^4 + zeta(84)_7^2 + 
    zeta(84)_7 + 1, -zeta(84)_3*zeta(84)_7^4 - zeta(84)_3*zeta(84)_7^2 - 
    zeta(84)_3*zeta(84)_7 - zeta(84)_3, zeta(84)_3*zeta(84)_7^4 + 
    zeta(84)_3*zeta(84)_7^2 + zeta(84)_3*zeta(84)_7, -zeta(84)_3*zeta(84)_7^4 - 
    zeta(84)_3*zeta(84)_7^2 - zeta(84)_3*zeta(84)_7 - zeta(84)_7^4 - 
    zeta(84)_7^2 - zeta(84)_7, 0, 0, 0, 0, 0, 0, 0, 0, 
    zeta(84)_4*zeta(84)_3*zeta(84)_7^4 + zeta(84)_4*zeta(84)_3*zeta(84)_7^2 + 
    zeta(84)_4*zeta(84)_3*zeta(84)_7 + zeta(84)_4*zeta(84)_7^4 + 
    zeta(84)_4*zeta(84)_7^2 + zeta(84)_4*zeta(84)_7, 
    -zeta(84)_4*zeta(84)_3*zeta(84)_7^4 - zeta(84)_4*zeta(84)_3*zeta(84)_7^2 - 
    zeta(84)_4*zeta(84)_3*zeta(84)_7 - zeta(84)_4*zeta(84)_7^4 - 
    zeta(84)_4*zeta(84)_7^2 - zeta(84)_4*zeta(84)_7, 
    -zeta(84)_4*zeta(84)_3*zeta(84)_7^4 - zeta(84)_4*zeta(84)_3*zeta(84)_7^2 - 
    zeta(84)_4*zeta(84)_3*zeta(84)_7 - zeta(84)_4*zeta(84)_3 - 
    zeta(84)_4*zeta(84)_7^4 - zeta(84)_4*zeta(84)_7^2 - zeta(84)_4*zeta(84)_7 - 
    zeta(84)_4, zeta(84)_4*zeta(84)_3*zeta(84)_7^4 + 
    zeta(84)_4*zeta(84)_3*zeta(84)_7^2 + zeta(84)_4*zeta(84)_3*zeta(84)_7 + 
    zeta(84)_4*zeta(84)_3, -zeta(84)_4*zeta(84)_3*zeta(84)_7^4 - 
    zeta(84)_4*zeta(84)_3*zeta(84)_7^2 - zeta(84)_4*zeta(84)_3*zeta(84)_7, 
    zeta(84)_4*zeta(84)_3*zeta(84)_7^4 + zeta(84)_4*zeta(84)_3*zeta(84)_7^2 + 
    zeta(84)_4*zeta(84)_3*zeta(84)_7, zeta(84)_4*zeta(84)_3*zeta(84)_7^4 + 
    zeta(84)_4*zeta(84)_3*zeta(84)_7^2 + zeta(84)_4*zeta(84)_3*zeta(84)_7 + 
    zeta(84)_4*zeta(84)_3 + zeta(84)_4*zeta(84)_7^4 + zeta(84)_4*zeta(84)_7^2 + 
    zeta(84)_4*zeta(84)_7 + zeta(84)_4, -zeta(84)_4*zeta(84)_3*zeta(84)_7^4 - 
    zeta(84)_4*zeta(84)_3*zeta(84)_7^2 - zeta(84)_4*zeta(84)_3*zeta(84)_7 - 
    zeta(84)_4*zeta(84)_3 )

*/

G:=c9Group("12bl34p");
M:=
GModule(G, [
    Matrix(SparseMatrix(K, 60, 60, [
    <1, 3, 1/40*(-w^7 + 5*w^5 - 5*w^3 - 12*w)>, <1, 4, 1/40*(-3*w^7 - 5*w^5 + 
    5*w^3 - 16*w)>, <1, 5, 1/20*(3*w^6 + 5*w^4 + 15*w^2 + 16)>, <1, 6, 1>, 
    <2, 2, 1>, <2, 4, 1/40*(3*w^7 + 5*w^5 - 5*w^3 + 16*w)>, <2, 5, 1/20*(3*w^6 +
    5*w^4 + 15*w^2 + 36)>, 
    <3, 1, 1/10*(-w^7 - 7*w)>, <3, 4, 1/20*(3*w^6 + 5*w^4 + 15*w^2 + 16)>, <3, 
    5, 1/40*(w^7 - 5*w^5 + 5*w^3 + 12*w)>, <3, 6, 1/10*(w^7 + 7*w)>, 
    <4, 5, 1/10*(w^7 + 7*w)>, 
    <5, 4, 1/40*(w^7 - 5*w^5 + 5*w^3 + 12*w)>, 
    <6, 6, 1>, 
    <7, 7, -1>, 
    <8, 12, 1>, 
    <9, 10, 1/20*(3*w^6 + 5*w^4 + 15*w^2 + 36)>, 
    <10, 9, 1/20*(-3*w^6 - 5*w^4 - 15*w^2 - 16)>, 
    <11, 11, -1>, 
    <12, 8, 1>, 
    <13, 17, 1/20*(3*w^6 + 5*w^4 + 15*w^2 + 16)>, <13, 19, 1/40*(w^7 - 5*w^5 + 
    5*w^3 + 12*w)>, <13, 21, 1>, 
    <14, 17, 1/20*(3*w^6 + 5*w^4 + 15*w^2 + 36)>, <14, 19, 1/40*(3*w^7 + 5*w^5 -
    5*w^3 + 16*w)>, 
    <15, 13, 1/10*(-w^7 - 7*w)>, <15, 15, -1>, <15, 21, 1/10*(-w^7 - 7*w)>, 
    <16, 13, 1/10*(-w^7 - 7*w)>, <16, 14, 1/10*(w^7 + 7*w)>, <16, 15, 
    1/20*(3*w^6 + 5*w^4 + 15*w^2 + 16)>, <16, 18, 1>, <16, 19, -1>, <16, 20, 
    1/40*(w^7 - 5*w^5 + 5*w^3 + 12*w)>, <16, 21, 1/10*(-w^7 - 7*w)>, 
    <17, 14, 1/20*(-3*w^6 - 5*w^4 - 15*w^2 - 36)>, <17, 17, 1/20*(3*w^6 + 5*w^4 
    + 15*w^2 + 36)>, <17, 19, 1/10*(w^7 + 7*w)>, 
    <18, 13, 1/10*(w^7 + 7*w)>, <18, 14, 1/10*(-w^7 - 7*w)>, <18, 18, -1>, <18, 
    19, 1>, <18, 21, 1/10*(w^7 + 7*w)>, 
    <19, 14, 1/10*(-w^7 - 7*w)>, <19, 17, 1/40*(w^7 - 5*w^5 + 5*w^3 + 12*w)>, 
    <19, 19, 1/20*(-3*w^6 - 5*w^4 - 15*w^2 - 16)>, 
    <20, 13, 1/20*(3*w^6 + 5*w^4 + 15*w^2 + 36)>, <20, 15, 1/40*(-3*w^7 - 5*w^5 
    + 5*w^3 - 16*w)>, <20, 16, 1/10*(w^7 + 7*w)>, <20, 18, 1/10*(w^7 + 7*w)>, 
    <20, 21, 1/20*(3*w^6 + 5*w^4 + 15*w^2 + 36)>, 
    <21, 13, 1>, <21, 17, 1/20*(-3*w^6 - 5*w^4 - 15*w^2 - 16)>, <21, 19, 
    1/40*(-w^7 + 5*w^5 - 5*w^3 - 12*w)>, 
    <22, 26, 1/20*(3*w^6 + 5*w^4 + 15*w^2 + 16)>, <22, 28, 1/40*(w^7 - 5*w^5 + 
    5*w^3 + 12*w)>, <22, 30, 1>, 
    <23, 26, 1/20*(3*w^6 + 5*w^4 + 15*w^2 + 36)>, <23, 28, 1/40*(3*w^7 + 5*w^5 -
    5*w^3 + 16*w)>, 
    <24, 22, 1/10*(-w^7 - 7*w)>, <24, 24, -1>, <24, 30, 1/10*(-w^7 - 7*w)>, 
    <25, 22, 1/10*(-w^7 - 7*w)>, <25, 23, 1/10*(w^7 + 7*w)>, <25, 24, 
    1/20*(3*w^6 + 5*w^4 + 15*w^2 + 16)>, <25, 27, 1>, <25, 28, -1>, <25, 29, 
    1/40*(w^7 - 5*w^5 + 5*w^3 + 12*w)>, <25, 30, 1/10*(-w^7 - 7*w)>, 
    <26, 23, 1/20*(-3*w^6 - 5*w^4 - 15*w^2 - 36)>, <26, 26, 1/20*(3*w^6 + 5*w^4 
    + 15*w^2 + 36)>, <26, 28, 1/10*(w^7 + 7*w)>, 
    <27, 22, 1/10*(w^7 + 7*w)>, <27, 23, 1/10*(-w^7 - 7*w)>, <27, 27, -1>, <27, 
    28, 1>, <27, 30, 1/10*(w^7 + 7*w)>, 
    <28, 23, 1/10*(-w^7 - 7*w)>, <28, 26, 1/40*(w^7 - 5*w^5 + 5*w^3 + 12*w)>, 
    <28, 28, 1/20*(-3*w^6 - 5*w^4 - 15*w^2 - 16)>, 
    <29, 22, 1/20*(3*w^6 + 5*w^4 + 15*w^2 + 36)>, <29, 24, 1/40*(-3*w^7 - 5*w^5 
    + 5*w^3 - 16*w)>, <29, 25, 1/10*(w^7 + 7*w)>, <29, 27, 1/10*(w^7 + 7*w)>, 
    <29, 30, 1/20*(3*w^6 + 5*w^4 + 15*w^2 + 36)>, 
    <30, 22, 1>, <30, 26, 1/20*(-3*w^6 - 5*w^4 - 15*w^2 - 16)>, <30, 28, 
    1/40*(-w^7 + 5*w^5 - 5*w^3 - 12*w)>, 
    <31, 31, 1>, 
    <32, 42, 1/20*(3*w^6 + 5*w^4 + 15*w^2 + 16)>, 
    <33, 39, 1/40*(-3*w^7 - 5*w^5 + 5*w^3 - 16*w)>, 
    <34, 38, 1/40*(-3*w^7 - 5*w^5 + 5*w^3 - 16*w)>, 
    <35, 43, 1/40*(-3*w^7 - 5*w^5 + 5*w^3 - 16*w)>, 
    <36, 36, -1>, 
    <37, 37, 1>, 
    <38, 34, 1/40*(3*w^7 + 5*w^5 - 5*w^3 + 16*w)>, 
    <39, 33, 1/40*(3*w^7 + 5*w^5 - 5*w^3 + 16*w)>, 
    <40, 45, 1/40*(-w^7 + 5*w^5 - 5*w^3 - 12*w)>, 
    <41, 44, 1/10*(-w^7 - 7*w)>, 
    <42, 32, 1/20*(-3*w^6 - 5*w^4 - 15*w^2 - 36)>, 
    <43, 35, 1/40*(3*w^7 + 5*w^5 - 5*w^3 + 16*w)>, 
    <44, 41, 1/40*(-w^7 + 5*w^5 - 5*w^3 - 12*w)>, 
    <45, 40, 1/10*(-w^7 - 7*w)>, 
    <46, 46, 1>, 
    <47, 57, 1/20*(3*w^6 + 5*w^4 + 15*w^2 + 16)>, 
    <48, 54, 1/40*(-3*w^7 - 5*w^5 + 5*w^3 - 16*w)>, 
    <49, 53, 1/40*(-3*w^7 - 5*w^5 + 5*w^3 - 16*w)>, 
    <50, 58, 1/40*(-3*w^7 - 5*w^5 + 5*w^3 - 16*w)>, 
    <51, 51, -1>, 
    <52, 52, 1>, 
    <53, 49, 1/40*(3*w^7 + 5*w^5 - 5*w^3 + 16*w)>, 
    <54, 48, 1/40*(3*w^7 + 5*w^5 - 5*w^3 + 16*w)>, 
    <55, 60, 1/40*(-w^7 + 5*w^5 - 5*w^3 - 12*w)>, 
    <56, 59, 1/10*(-w^7 - 7*w)>, 
    <57, 47, 1/20*(-3*w^6 - 5*w^4 - 15*w^2 - 36)>, 
    <58, 50, 1/40*(3*w^7 + 5*w^5 - 5*w^3 + 16*w)>, 
    <59, 56, 1/40*(-w^7 + 5*w^5 - 5*w^3 - 12*w)>, 
    <60, 55, 1/10*(-w^7 - 7*w)>
    ])),
    Matrix(K, 60, 60,
        [ [ 31/150, 17/50, 1/15, 1/10, 1/30, 1/15, 1/50, 1/50 ], [ 4/75, 12/25, 
        -1/60, 1/5, 1/60, 2/15, 1/100, 1/25 ], [ 3/25, -3/100, 1/15, 1/80, 
        -1/30, -1/80, -1/150, -13/1200 ], [ -26/75, -2/25, -1/30, 1/48, -1/30, 
        1/80, -1/25, 17/1200 ], [ -11/75, 11/150, -13/120, 0, -11/120, 1/30, 
        -29/600, 1/50 ], [ -8/25, -7/50, -3/40, 1/80, -1/40, -1/80, -7/200, 
        -3/400 ], [ 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 
        0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 
        0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0 ], [ 6/25, -7/200, 3/20, 1/160, 1/20, 
        -1/160, 1/50, 1/800 ], [ 0, 0, 0, 0, 0, 0, 0, 0 ], [ -1/50, -3/50, 1/80,
        1/40, -1/80, 1/40, 1/400, -1/200 ], [ 13/100, 1/25, 1/40, 1/40, 1/40, 
        -1/40, 3/200, -1/200 ], [ 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 
        0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0 ], [ 1/5, 
        -13/200, 1/16, 3/80, -1/80, 1/80, 1/80, -3/400 ], [ 4/25, 11/100, -1/40,
        13/160, -1/40, 3/160, 1/200, 9/800 ], [ 0, 0, 0, 0, 0, 0, 0, 0 ], [ 
        1/20, -7/100, 1/40, -1/80, 1/40, -3/80, 1/40, -9/400 ], [ 13/100, 0, 
        1/16, -3/80, 3/80, -1/80, 1/400, 1/80 ], [ 0, 0, 0, 0, 0, 0, 0, 0 ], [ 
        0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 
        0, 0, 0 ], [ 4/25, 1/10, 3/80, 9/160, 1/80, -1/160, 7/400, 1/160 ], [ 0,
        0, 0, 0, 0, 0, 0, 0 ], [ -1/20, 1/20, -1/12, 1/96, 0, -1/96, 1/60, 
        -1/160 ], [ 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0 ], [ 
        11/30, -1/15, 1/8, 1/48, 1/24, -1/48, 7/120, -1/80 ], [ 0, 0, 0, 0, 0, 
        0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0 ], [ 
        -1/20, 11/120, -5/48, 1/16, -1/16, 1/48, -1/240, 1/240 ], [ 0, 0, 0, 0, 
        0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0 ], [ 
        -1/3, 23/60, -1/12, 1/16, -1/12, 5/48, -1/12, 11/240 ], [ -13/30, -7/40,
        -1/16, -17/96, -1/48, -7/96, -7/240, -17/480 ], [ -13/60, -7/60, -1/8, 
        -1/96, -1/8, 1/96, -1/40, -13/480 ], [ 0, 0, 0, 0, 0, 0, 0, 0 ], [ 1/5, 
        1/15, 0, 1/16, 0, 1/48, 1/60, 1/80 ], [ 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 
        0, 0, 0, 0, 0, 0, 0 ], [ -3/10, 7/60, -1/8, -1/48, -1/24, 1/48, -1/40, 
        -1/240 ], [ 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 
        0, 0, 0, 0, 0, 0, 0 ], [ 1/5, -1/12, 1/12, 0, 0, 0, 1/60, 0 ], [ 0, 0, 
        0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0
        ], [ 2/5, -3/20, 5/24, -1/12, 1/8, -1/12, 3/40, -1/30 ], [ 1/10, 1/12, 
        -1/24, 1/12, -1/24, 0, 1/120, 0 ], [ 4/15, -7/60, 1/8, -1/16, 1/24, 
        -1/48, 1/120, 1/240 ], [ -1/5, -37/150, -1/15, -1/16, -1/30, -3/80, 
        -1/30, -1/400 ], [ 41/150, -13/150, 7/60, -3/80, 1/12, -7/240, 11/300, 
        1/400 ], [ 0, 23/100, -1/60, -1/80, -1/60, 1/80, 1/60, 13/1200 ], [ 
        31/150, -17/100, -1/15, -1/12, 1/30, -1/20, 1/50, -2/75 ], [ -31/150, 
        1/15, 0, 9/80, 0, 1/48, 1/75, 1/80 ], [ 12/25, 19/75, 11/60, 1/16, 7/60,
        3/80, 17/300, 9/400 ], [ 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 
        0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 
        0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0 ], [ 1/100, 3/200, 0, 1/80,
        -1/20, 3/80, -1/50, 3/400 ], [ 0, 0, 0, 0, 0, 0, 0, 0 ], [ -1/20, 7/50, 
        -9/80, 13/160, -3/80, 3/160, -1/80, 1/800 ], [ -9/50, -21/200, -1/80, 
        -1/10, 1/80, -1/20, -1/400, -3/200 ], [ 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 
        0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 
        0, 0 ], [ 9/100, -13/200, 3/16, -1/20, 1/16, 0, 3/400, 1/200 ], [ -3/20,
        1/100, -1/20, 1/80, 0, -1/80, 0, -3/400 ], [ 0, 0, 0, 0, 0, 0, 0, 0 ], [
        -1/25, 0, 1/40, -7/160, 1/40, -1/160, 1/200, 1/160 ], [ 1/10, -1/40, 
        1/20, 1/40, 0, 1/40, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 
        0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0 ], [ 
        7/100, -1/40, -1/80, 3/40, -3/80, 1/40, -1/400, 0 ], [ 0, 0, 0, 0, 0, 0,
        0, 0 ], [ -1/6, -5/24, -1/48, -7/96, -1/16, -1/96, -1/48, -1/32 ], [ 0, 
        0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0 ], [ 1/12, 13/120, 
        -1/48, 1/24, 1/48, 1/24, -1/48, 1/30 ], [ 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0,
        0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0 ], [ -1/4, 1/15, -1/24, 
        -1/32, -1/24, 1/32, -1/24, 1/480 ], [ 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 
        0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0 ], [ 7/20, -5/24, 11/48, 
        -1/24, 5/48, -1/24, 7/240, 0 ], [ 1/30, 31/120, -5/48, 7/96, 1/48, 1/96,
        -1/240, 7/480 ], [ -1/12, 19/60, -1/24, 3/32, -1/24, 7/96, -1/24, 7/160 
        ], [ 0, 0, 0, 0, 0, 0, 0, 0 ], [ 1/15, -1/30, 1/24, -1/16, 1/24, -1/48, 
        -1/120, 1/240 ], [ 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0 ],
        [ 7/30, -1/3, 1/6, -5/48, 1/12, -1/16, 1/30, -1/48 ], [ 0, 0, 0, 0, 0, 
        0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0 ], [ 
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        1/240, 1/80 ], [ 19/60, -1/24, 7/48, -5/96, 1/48, -1/32, 1/80, -1/96 ], 
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        -1/4, -1/24, -5/48, -1/24, -1/16, -7/120, -1/48 ], [ 0, 0, 0, 0, 0, 0, 
        0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0 ], [ -7/30, 1/20, -1/12, -7/96, -1/12, 
        -1/96, -1/30, -1/160 ], [ -1/20, -1/40, 1/48, 7/192, 1/48, 1/192, 
        -1/240, 1/320 ], [ -3/40, 1/40, -1/48, 1/48, -1/48, 1/48, 1/240, 1/80 ],
        [ 1/30, 7/48, 1/48, 1/32, -1/48, 1/96, -1/240, 1/96 ], [ 17/60, 1/4, 
        1/24, 5/48, 1/24, 1/16, 7/120, 1/48 ], [ 1/30, 7/48, 1/48, 1/32, -1/48, 
        1/96, -1/240, 1/96 ], [ 0, 0, 0, 0, 0, 0, 0, 0 ], [ 7/60, 1/12, 5/96, 
        5/96, 1/32, 1/32, 13/480, 1/96 ], [ -17/60, -1/4, -1/24, -5/48, -1/24, 
        -1/16, -7/120, -1/48 ], [ -7/30, 1/20, -1/12, -7/96, -1/12, -1/96, 
        -1/30, -1/160 ], [ 3/20, 7/30, 1/24, 1/16, 1/24, 1/48, -1/120, 1/80 ] ])
]: Check := false) where w := K.1 where K := ext<K|Polynomial(K, [16, 0, 12, 0, 5, 0, 3, 0, 1])> 
where K is RationalField();
K<w> := BaseRing(M);
K;
M;
