/*
Generated by Allan Steel in Magma, 2010.

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

Traces:    [ -5, 0 ]
Density:   [ 0.019022222, 0.95911111 ]
Numer max: [ 1, 519 ]
Numer av:  [ 0.0047555555, 19.055333 ]
Denom max: [ 1, 240 ], [ [], [ <2, 4>, <3, 1>, <5, 1> ] ]
Denom LCM: [ 1, 960 ], [ [], [ <2, 6>, <3, 1>, <5, 1> ] ]

Character:
( 75, -5, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -zeta(13)_13^6 - zeta(13)_13^5 - 
    zeta(13)_13^2, zeta(13)_13^11 + zeta(13)_13^9 + zeta(13)_13^8 + 
    zeta(13)_13^7 + zeta(13)_13^6 + zeta(13)_13^5 + zeta(13)_13^3 + 
    zeta(13)_13^2 + zeta(13)_13 + 1, -zeta(13)_13^11 - zeta(13)_13^8 - 
    zeta(13)_13^7, -zeta(13)_13^9 - zeta(13)_13^3 - zeta(13)_13, 0, 0, 0, 0 )
*/

G:=PermutationGroup(ATLASGroup("U34"));
M:=
GModule(G, [
    Matrix(SparseMatrix(K, 75, 75, [
    <1, 1, -1>,  <2, 2, -1>,  <3, 3, -1>,  <4, 4, -1>,  <5, 5, -1>,  <6, 6, 1>, 
    <7, 7, -1>,  <8, 8, 1>,  <9, 9, 1>,  <10, 10, -1>,  <11, 11, 1>,  <12, 12, 
    -1>,  <13, 17, -1>, <13, 18, 1>,  <14, 15, 1>, <14, 51, -1>,  <15, 14, 1>, 
    <15, 51, -1>,  <16, 34, -1>, <16, 36, 1>,  <17, 17, -1>,  <18, 13, 1>, <18, 
    17, -1>,  <19, 19, -1>,  <20, 21, 1>, <20, 22, -1>,  <21, 20, 1>, <21, 22, 
    -1>,  <22, 22, -1>,  <23, 19, -1>, <23, 24, 1>,  <24, 19, -1>, <24, 23, 1>, 
    <25, 28, -1>, <25, 29, 1>,  <26, 27, 1>, <26, 30, -1>,  <27, 26, 1>, <27, 
    30, -1>,  <28, 28, -1>,  <29, 25, 1>, <29, 28, -1>,  <30, 30, -1>,  <31, 32,
    -1>, <31, 33, 1>,  <32, 32, -1>,  <33, 31, 1>, <33, 32, -1>,  <34, 34, -1>, 
    <35, 49, 1>, <35, 58, -1>,  <36, 16, 1>, <36, 34, -1>,  <37, 37, -1>,  <38, 
    39, 1>, <38, 54, -1>,  <39, 38, 1>, <39, 54, -1>,  <40, 40, -1>,  <41, 37, 
    -1>, <41, 42, 1>,  <42, 37, -1>, <42, 41, 1>,  <43, 52, -1>, <43, 53, 1>,  
    <44, 40, -1>, <44, 45, 1>,  <45, 40, -1>, <45, 44, 1>,  <46, 46, -1>,  <47, 
    46, -1>, <47, 48, 1>,  <48, 46, -1>, <48, 47, 1>,  <49, 35, 1>, <49, 58, 
    -1>,  <50, 50, -1>,  <51, 51, -1>,  <52, 52, -1>,  <53, 43, 1>, <53, 52, 
    -1>,  <54, 54, -1>,  <55, 50, -1>, <55, 59, 1>,  <56, 57, 1>, <56, 60, -1>, 
    <57, 56, 1>, <57, 60, -1>,  <58, 58, -1>,  <59, 50, -1>, <59, 55, 1>,  <60, 
    60, -1>,  <61, 61, 1>,  <62, 62, 1>,  <63, 63, 1>,  <64, 64, 1>,  <65, 65, 
    1>,  <66, 66, 1>,  <67, 67, 1>,  <68, 68, 1>,  <69, 69, 1>,  <70, 70, 1>,  
    <71, 71, 1>,  <72, 72, 1>,  <73, 73, 1>,  <74, 74, 1>,  <75, 75, 1> ])),
    Matrix(K, 75, 75,
        [ [ 9/20, -49/120, -9/40, -17/120 ], [ 3/20, 3/40, 3/40, 1/40 ], [ 1/10,
        -1/24, -1/20, -1/30 ], [ 2/5, -1/24, -3/40, -7/120 ], [ 1/60, -31/120, 
        -17/120, -1/15 ], [ 1/8, -19/120, 1/5, -1/24 ], [ -3/40, 1/20, 1/40, 0 
        ], [ 1/30, -1/20, -1/30, 1/40 ], [ -3/40, 9/40, 1/20, -3/40 ], [ 1/12, 
        -1/4, -2/15, -3/40 ], [ 1/15, 1/24, -11/120, -1/60 ], [ -7/40, 1/30, 
        -1/40, 1/60 ], [ 1/10, -1/15, 0, 1/24 ], [ 3/20, -37/120, 1/20, 1/30 ], 
        [ -1/8, 1/120, -1/40, -19/120 ], [ -1/10, 29/120, -1/20, 1/12 ], [ 
        -3/40, 1/120, 1/20, 1/24 ], [ -1/20, 1/5, -3/40, -1/40 ], [ 0, 0, 0, 0 
        ], [ -1/20, 1/20, -1/40, 0 ], [ 3/8, -11/60, -1/40, 13/120 ], [ -3/20, 
        -1/30, 1/10, 7/120 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 0 ], [ 0, -1/24, 1/40, 
        -1/120 ], [ -1/4, 11/30, 0, 1/120 ], [ 1/8, -31/120, 0, -7/60 ], [ 
        -7/40, 3/20, 1/20, -3/20 ], [ 3/10, -1/15, 1/40, 17/120 ], [ 9/40, 
        -7/20, 3/20, 1/40 ], [ -3/40, 1/30, 0, 1/24 ], [ 3/40, 7/120, 0, 1/24 ],
        [ -3/20, 3/40, 1/40, 1/20 ], [ -1/10, -11/60, 11/40, -1/24 ], [ -11/40, 
        1/4, 1/40, -1/10 ], [ 3/20, -1/30, -1/40, -1/60 ], [ 1/8, -11/120, 
        -3/40, -1/12 ], [ 0, 7/120, 1/20, -1/30 ], [ -1/4, 2/5, -3/10, 3/40 ], [
        -1/40, -7/120, -1/20, 1/120 ], [ 1/20, 1/30, 3/20, 1/60 ], [ -1/8, 
        13/120, -1/10, 7/60 ], [ -3/20, 13/40, 1/40, -1/40 ], [ 3/40, -1/40, 0, 
        1/20 ], [ 1/8, -7/60, 3/40, -7/120 ], [ 1/10, 1/24, 1/40, 1/120 ], [ 0, 
        -1/120, 1/5, 7/120 ], [ -13/40, 17/60, -11/40, -7/120 ], [ -1/8, 1/6, 
        -1/20, 13/120 ], [ 1/20, -11/120, -1/10, -1/30 ], [ -9/40, 13/60, -1/40,
        7/120 ], [ 0, -11/120, 0, 1/60 ], [ 7/40, -13/120, 0, 1/120 ], [ 1/40, 
        1/30, -1/20, -7/120 ], [ -3/40, 1/12, 1/10, 1/24 ], [ 1/10, 0, -3/20, 
        -1/20 ], [ 1/10, -3/10, 1/10, 3/40 ], [ 1/20, -1/4, 1/40, -1/40 ], [ 0, 
        1/30, -1/20, -1/120 ], [ -1/20, 7/40, 3/40, 0 ], [ 0, -13/96, -3/32, 
        -1/48 ], [ 1/4, -7/96, -1/8, -1/12 ], [ 3/16, -1/4, -3/16, -3/32 ], [ 
        1/16, 3/32, 1/32, 1/32 ], [ -3/32, 7/48, 3/32, 1/24 ], [ -7/32, 1/6, 
        3/32, 5/96 ], [ 3/32, 7/48, 1/8, 1/96 ], [ -1/32, -1/48, 0, 1/48 ], [ 0,
        0, 0, 0 ], [ -5/32, 3/32, 3/32, 1/16 ], [ -5/32, 25/96, 3/16, 1/12 ], [ 
        -1/32, 1/96, 0, -1/96 ], [ 3/32, -13/96, -3/32, -5/96 ], [ -3/16, -1/32,
        0, 1/32 ], [ 0, -1/6, -3/32, -5/96 ], [ 1/20, -1/5, -1/10, -1/20 ], [ 
        -1/20, 1/12, 1/5, 1/15 ], [ 1/20, 1/20, -3/20, -1/20 ], [ 7/20, -1/12, 
        -1/20, -1/15 ], [ 3/20, -1/6, -1/20, -1/30 ], [ 1/20, -1/15, 1/10, -1/30
        ], [ -1/10, 1/30, -1/10, -1/12 ], [ 1/20, -1/15, -1/10, -1/30 ], [ 
        -7/20, 3/10, 0, 0 ], [ 3/20, -1/15, 0, -1/30 ], [ 1/20, 1/12, 0, 1/60 ],
        [ 1/10, -1/15, -1/4, -1/30 ], [ 1/40, -1/60, -1/20, 1/15 ], [ 1/40, 
        -1/12, -3/40, 1/30 ], [ -1/10, 1/15, 0, 7/120 ], [ 3/40, 3/40, -7/40, 
        9/40 ], [ -1/10, 7/24, 0, -1/6 ], [ -3/40, 1/30, -1/40, 7/60 ], [ 0, 0, 
        0, 0 ], [ 3/10, -13/40, 1/20, 1/40 ], [ -3/40, 1/40, -1/10, -1/20 ], [ 
        -3/10, 71/120, -1/8, 1/30 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 0 ], [ 0, 
        -23/120, 1/20, -13/120 ], [ -1/5, 7/24, -3/20, -1/60 ], [ -3/40, 13/60, 
        -3/20, 7/120 ], [ 9/40, -4/15, 7/40, -1/30 ], [ 1/10, -1/30, -1/10, 
        1/120 ], [ 9/40, -29/120, 3/20, -1/30 ], [ -3/20, 17/120, 0, -17/120 ], 
        [ -1/20, 1/10, 1/20, 9/40 ], [ 11/40, -29/60, 11/40, 1/12 ], [ 3/40, 
        -1/5, 1/4, -1/20 ], [ -1/40, 17/120, 0, -1/60 ], [ -1/40, 1/10, -1/20, 
        -7/40 ], [ 1/10, -31/120, 7/20, 1/30 ], [ 13/40, -13/60, 3/20, -7/120 ],
        [ 1/8, 1/24, -3/20, 7/30 ], [ -1/40, -1/12, 0, 5/24 ], [ 3/40, 11/60, 
        -1/8, 1/15 ], [ -1/5, -1/120, 3/40, -1/15 ], [ 0, -1/120, -13/40, 1/12 
        ], [ -3/40, 7/60, -1/20, -1/15 ], [ -3/40, 9/40, -1/40, -3/40 ], [ 1/10,
        -5/24, -1/20, 2/15 ], [ 1/10, 1/40, -1/40, 0 ], [ 7/40, -3/10, 1/4, 1/20
        ], [ 1/40, 1/40, -3/40, -3/40 ], [ -3/40, -13/120, 1/10, -7/60 ], [ 
        -1/10, 19/120, -1/5, 1/24 ], [ 3/20, -17/120, 0, 17/120 ], [ -11/40, 
        17/40, 1/20, -1/10 ], [ -1/20, -7/24, 3/20, 1/60 ], [ 3/10, -3/10, 1/10,
        3/40 ], [ -13/40, 11/40, -1/8, -1/40 ], [ 11/40, -17/120, 3/40, 1/15 ], 
        [ -1/10, 29/120, -1/5, -1/24 ], [ -9/40, 4/15, -1/10, -1/24 ], [ 1/8, 
        -7/30, 7/20, 1/120 ], [ 1/4, 1/48, 0, -1/48 ], [ 1/8, 1/24, 1/16, 1/48 
        ], [ -3/16, 1/8, 1/16, 1/16 ], [ 3/16, -1/48, -1/16, -1/24 ], [ 1/4, 
        -7/48, -1/16, -1/24 ], [ 1/16, 11/48, 1/8, 1/48 ], [ -3/16, 1/24, 1/16, 
        1/48 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 0 ], [ -1/4, -1/48, 0, 1/48 ], [ 0, 
        1/6, 1/16, 1/48 ], [ 3/16, -7/24, -1/8, -1/12 ], [ -1/16, -7/48, -1/16, 
        -1/24 ], [ 1/16, -1/12, -1/8, -1/24 ], [ -5/16, 7/48, 1/8, 5/48 ], [ 
        1/20, 1/40, 1/40, 0 ], [ 3/20, 11/120, -1/40, -7/60 ], [ 1/40, -19/120, 
        -3/40, 7/120 ], [ -1/20, -1/40, -1/40, 0 ], [ -1/10, -1/30, 0, 1/120 ], 
        [ 1/20, -13/120, -1/20, 1/120 ], [ -3/20, 1/6, -3/40, 13/120 ], [ -2/15,
        -1/120, 7/120, 1/120 ], [ 1/10, 1/8, 3/20, 1/40 ], [ 1/20, -3/40, -1/40,
        -1/40 ], [ 2/15, -3/20, -1/30, -1/40 ], [ 0, -17/60, 3/40, 13/120 ], [ 
        -1/20, -1/20, 1/40, -1/20 ], [ -3/20, 3/40, 1/40, 1/20 ], [ 3/40, 7/120,
        0, 1/24 ], [ 1/8, -7/60, 3/40, -7/120 ], [ 1/8, -11/120, -3/40, -1/12 ],
        [ 1/20, 1/30, 3/20, 1/60 ], [ 0, 0, 0, 0 ], [ 1/20, -1/4, 1/40, -1/40 ],
        [ -11/40, 1/4, 1/40, -1/10 ], [ 7/20, -1/6, 0, 1/60 ], [ 0, 0, 0, 0 ], [
        0, 0, 0, 0 ], [ -9/40, 13/60, -1/40, 7/120 ], [ 1/40, -1/40, 1/20, 0 ], 
        [ 0, 1/30, -1/20, -1/120 ], [ 3/20, -37/120, 1/20, 1/30 ], [ -1/8, 
        1/120, -1/40, -19/120 ], [ 1/20, -11/120, -1/10, -1/30 ], [ 0, -1/24, 
        1/40, -1/120 ], [ 3/10, -1/15, 1/40, 17/120 ], [ -7/40, 3/20, 1/20, 
        -3/20 ], [ 3/40, -1/40, 0, 1/20 ], [ 7/40, -13/120, 0, 1/120 ], [ -1/40,
        -7/120, -1/20, 1/120 ], [ 1/10, 1/24, 1/40, 1/120 ], [ 1/8, -31/120, 0, 
        -7/60 ], [ 9/40, -7/20, 3/20, 1/40 ], [ -1/20, 7/40, 3/40, 0 ], [ 9/40, 
        -19/60, 1/20, -1/120 ], [ 0, -1/120, 1/5, 7/120 ], [ -3/20, -1/30, 1/10,
        7/120 ], [ -3/20, 1/8, -1/40, -1/40 ], [ 1/10, 0, -3/20, -1/20 ], [ 
        -3/40, 1/120, 1/20, 1/24 ], [ 1/40, -17/120, 1/40, -7/120 ], [ 1/10, 
        -1/15, 0, 1/24 ], [ -1/40, -1/8, -1/40, 0 ], [ -1/4, 2/5, -3/10, 3/40 ],
        [ -3/40, 1/30, 0, 1/24 ], [ -1/20, 1/20, -1/40, 0 ], [ 3/8, -11/60, 
        -1/40, 13/120 ], [ -1/4, 11/30, 0, 1/120 ], [ 9/40, -59/120, 3/10, 1/60 
        ], [ -1/10, 29/120, -1/20, 1/12 ], [ 1/20, -1/40, -1/5, -1/40 ], [ 0, 
        -11/120, 0, 1/60 ], [ 0, 7/120, 1/20, -1/30 ], [ 3/20, -1/30, -1/40, 
        -1/60 ], [ 3/16, -1/4, -3/16, -3/32 ], [ 3/32, -13/96, -3/32, -5/96 ], [
        1/16, 3/32, 1/32, 1/32 ], [ 0, -13/96, -3/32, -1/48 ], [ 0, -1/6, -3/32,
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        -1/32, 1/96, 0, -1/96 ], [ 0, 0, 0, 0 ], [ -5/32, 25/96, 3/16, 1/12 ], [
        3/16, -5/48, -1/32, -1/48 ], [ -3/16, -1/32, 0, 1/32 ], [ -7/32, 1/6, 
        3/32, 5/96 ], [ -1/32, -1/48, 0, 1/48 ], [ 3/32, 7/48, 1/8, 1/96 ], [ 
        1/10, 3/10, 3/20, 1/20 ], [ -1/4, 1/5, 3/20, 1/10 ], [ -1/10, 13/60, 
        1/20, 1/30 ], [ -3/20, 11/60, 3/20, 1/15 ], [ 1/3, -1/4, -1/30, -1/20 ],
        [ -1/20, -1/60, 1/10, 1/15 ], [ -1/10, -1/60, 0, -1/30 ], [ 1/30, 1/20, 
        -1/30, 0 ], [ -3/20, 1/30, 1/10, 1/60 ], [ 13/60, -1/20, 1/30, -1/20 ], 
        [ -1/30, 2/15, 1/30, 1/60 ], [ 1/20, -1/10, -3/20, -1/20 ], [ 7/40, 
        -3/10, 1/4, 1/20 ], [ 9/40, -4/15, 7/40, -1/30 ], [ 1/10, -1/30, -1/10, 
        1/120 ], [ -13/40, 11/40, -1/8, -1/40 ], [ 1/10, -5/24, -1/20, 2/15 ], [
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        ], [ -11/40, 17/40, 1/20, -1/10 ], [ 0, -1/120, -13/40, 1/12 ], [ 0, 0, 
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        -3/40, 1/30 ], [ -3/40, 1/10, -3/10, -1/20 ], [ -3/40, 1/40, -1/10, 
        -1/20 ], [ 1/8, -7/30, 7/20, 1/120 ], [ -1/10, 7/24, 0, -1/6 ], [ -9/40,
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        -1/20, -7/40 ], [ -3/40, 1/30, -1/40, 7/60 ], [ 3/20, -37/120, 3/40, 
        -1/60 ], [ 1/10, -49/120, 11/40, 2/15 ], [ 3/40, -1/5, 1/4, -1/20 ], [ 
        3/40, 3/40, -7/40, 9/40 ], [ 1/10, -31/120, 7/20, 1/30 ], [ -1/5, 
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        -13/120 ], [ -1/10, 29/120, -1/5, -1/24 ], [ -1/40, 17/120, 0, -1/60 ], 
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        9/40, -1/40, -3/40 ], [ 7/40, -31/120, 3/40, -1/15 ], [ 3/10, -13/40, 
        1/20, 1/40 ], [ -3/40, 13/60, -3/20, 7/120 ], [ -1/40, -1/12, 0, 5/24 ],
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        0, -1/48 ], [ -3/16, 1/8, 1/16, 1/16 ], [ -3/16, 1/24, 1/16, 1/48 ], [ 
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        ], [ 0, 0, 0, 0 ], [ 1/5, -3/20, -1/8, 3/40 ], [ -1/8, 4/15, -1/10, 
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        7/120, -1/8, 1/60 ], [ -11/40, 7/20, -1/10, 1/20 ], [ 1/5, -13/40, 1/4, 
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        ], [ 7/64, -23/192, -7/64, -5/96 ], [ -7/64, 1/6, 5/64, 7/192 ], [ 
        -1/64, -1/96, -1/32, 1/96 ] ])
]: Check := false) where w := K.1 where K := ext<K|Polynomial(K, [3, -4, 2, 1, 1])> where K is 
RationalField();
K<w>:=BaseRing(M);
K;
M;
