/*
Generated by Allan Steel in Magma, 2010.

Field defining polynomial: x^2 + x - 1 [optimized Q(sqrt(5)]].

Traces:    [ 0, 2 ]
Density:   [ 0.97735970, 0.037308673 ]
Numer max: [ 89, 3 ]
Numer av:  [ 3.8826531, 0.023596939 ]
Denom max: [ 40, 1 ], [ [ <2, 3>, <5, 1> ], [] ]
Denom LCM: [ 120, 1 ], [ [ <2, 3>, <3, 1>, <5, 1> ], [] ]

Character:
    ( 56, 0, 2, -2*zeta(5)_5^3 - 2*zeta(5)_5^2, 2*zeta(5)_5^3 +
    2*zeta(5)_5^2 + 2, 0, 0, 0, 0, 1, -zeta(5)_5^3 - zeta(5)_5^2 - 1,
    zeta(5)_5^3 + zeta(5)_5^2, -1, -1, -1 )
*/

G := PermutationGroup(ATLASGroup("J1"));
M :=
GModule(G, [
    Matrix(K, 56, 56,
        [ [ -1/3, -1/12 ], [ 1/24, -1/24 ], [ -1/12, -1/12 ], [ 5/24, 5/24 ], [ 
        5/24, 1/6 ], [ 1/8, 1/24 ], [ 0, -1/12 ], [ -1/24, 1/24 ], [ -1/12, 
        -1/12 ], [ 0, -1/24 ], [ 1/24, -1/24 ], [ -1/24, 1/24 ], [ -1/24, -1/24 
        ], [ -1/8, -1/24 ], [ -1/24, -1/24 ], [ 0, -1/24 ], [ 1/24, 1/24 ], [ 
        -1/12, 1/24 ], [ 1/24, -1/24 ], [ 1/12, 1/12 ], [ 1/15, 1/10 ], [ 1/15, 
        -1/30 ], [ -1/15, 0 ], [ 1/15, 1/30 ], [ -1/15, -1/10 ], [ 1/10, 1/15 ],
        [ -1/30, -1/30 ], [ 1/30, 1/10 ], [ -1/15, 1/10 ], [ 1/10, 1/30 ], [ 
        -1/10, 4/15 ], [ 1/5, -1/5 ], [ 1/5, 1/15 ], [ 0, 1/30 ], [ 0, -1/30 ], 
        [ -1/10, -1/30 ], [ 13/40, 1/20 ], [ 2/5, 3/40 ], [ 1/8, -3/40 ], [ 
        -1/4, 1/10 ], [ -3/40, -7/40 ], [ -1/10, -1/4 ], [ -5/8, -17/40 ], [ 
        -3/20, 3/40 ], [ -1/8, -1/8 ], [ 17/40, 1/4 ], [ 1/20, 1/10 ], [ 9/40, 
        -1/20 ], [ 1/20, -1/8 ], [ 0, -1/8 ], [ -1/10, -3/40 ], [ 17/40, 3/10 ],
        [ -1/40, -1/10 ], [ -7/20, -17/40 ], [ 1/10, 3/40 ], [ -1/40, 0 ], [ 0, 
        1/8 ], [ -5/12, -5/24 ], [ 0, 1/8 ], [ 1/4, -1/24 ], [ 1/6, 1/24 ], [ 
        1/24, -1/24 ], [ -1/8, 1/24 ], [ 1/24, 1/8 ], [ 1/24, -1/8 ], [ -1/24, 
        1/24 ], [ 1/24, -1/12 ], [ -1/24, 0 ], [ -1/8, -1/12 ], [ -1/24, 0 ], [ 
        -1/24, 1/12 ], [ 1/12, 0 ], [ -1/12, 0 ], [ 0, 0 ], [ -1/12, -1/12 ], [ 
        1/12, 1/12 ], [ -1/30, -2/15 ], [ -2/15, -1/30 ], [ 1/15, 1/10 ], [ 
        7/30, 1/10 ], [ 2/15, 1/30 ], [ 1/15, 1/15 ], [ -1/6, -1/15 ], [ -1/10, 
        -1/10 ], [ -1/5, 2/15 ], [ 1/30, 2/15 ], [ -1/6, 1/10 ], [ 3/10, -1/6 ],
        [ 1/15, -1/30 ], [ -1/30, 0 ], [ 0, -1/30 ], [ 0, 1/15 ], [ -3/20, -7/20
        ], [ -3/20, -1/20 ], [ 1/4, 1/10 ], [ 0, 7/40 ], [ 3/20, -3/40 ], [ 
        -3/40, -1/4 ], [ -2/5, -1/4 ], [ 1/10, 3/20 ], [ -3/10, -1/4 ], [ 3/8, 
        9/40 ], [ 1/8, 1/40 ], [ 7/40, -3/40 ], [ -1/40, -3/40 ], [ -3/40, -1/8 
        ], [ -1/40, 1/40 ], [ 1/2, 9/40 ], [ -1/20, -9/40 ], [ -21/40, -3/8 ], [
        7/40, -1/40 ], [ 0, 1/40 ], [ -1/8, -1/8 ], [ 0, 0 ], [ -1/24, 1/6 ], [ 
        1/8, 1/24 ], [ 1/8, 0 ], [ 1/6, -1/12 ], [ 1/24, 1/24 ], [ -1/12, 1/24 
        ], [ -1/12, -1/6 ], [ 0, 1/24 ], [ 1/8, 1/24 ], [ -1/24, -1/24 ], [ 
        -5/24, -5/24 ], [ -1/24, -1/24 ], [ 1/24, 1/8 ], [ 1/8, 1/24 ], [ -1/12,
        -1/24 ], [ -1/12, 0 ], [ -1/24, -1/24 ], [ 0, 0 ], [ -1/15, -1/6 ], [ 
        1/6, 1/6 ], [ 4/15, 4/15 ], [ -2/15, -1/30 ], [ 1/6, -1/15 ], [ -2/15, 0
        ], [ -3/10, -1/6 ], [ 1/15, 1/15 ], [ -7/30, -3/10 ], [ 4/15, 1/6 ], [ 
        1/30, 2/15 ], [ 1/30, -1/15 ], [ 0, 1/30 ], [ 1/15, 1/10 ], [ 1/15, 
        -1/30 ], [ -1/30, -2/15 ], [ 1/4, -7/40 ], [ 13/40, 1/5 ], [ 17/40, 9/40
        ], [ -1/40, 3/8 ], [ 1/5, -3/20 ], [ -1/20, -7/20 ], [ -13/20, -9/20 ], 
        [ -1/8, -3/40 ], [ -11/40, -9/40 ], [ 3/10, 7/40 ], [ 1/8, 1/10 ], [ 
        7/40, 0 ], [ -1/20, -1/40 ], [ 0, -1/40 ], [ -1/20, -3/40 ], [ 19/40, 
        3/10 ], [ -1/40, -3/20 ], [ -7/20, -13/40 ], [ 1/20, -1/40 ], [ -1/40, 0
        ], [ -1/12, 1/6 ], [ 0, -5/24 ], [ -1/6, -1/24 ], [ 1/8, 1/6 ], [ 1/4, 
        1/12 ], [ 1/12, 1/12 ], [ 1/12, 1/24 ], [ 1/12, 1/8 ], [ -1/24, -1/12 ],
        [ -1/12, -1/12 ], [ 1/12, -1/12 ], [ -1/6, 0 ], [ 0, -1/12 ], [ 0, 1/12 
        ], [ -1/12, 0 ], [ 0, 0 ], [ -1/8, -1/24 ], [ -1/24, 1/24 ], [ 0, -1/24 
        ], [ 1/12, 0 ], [ -2/15, -1/10 ], [ 2/15, 1/15 ], [ 0, 1/5 ], [ 1/30, 
        -1/30 ], [ -1/30, -1/30 ], [ -1/6, 1/30 ], [ 0, 1/30 ], [ 7/30, 0 ], [ 
        -2/15, 1/15 ], [ 3/10, 0 ], [ -1/10, 1/10 ], [ 1/15, 0 ], [ 1/30, 1/30 
        ], [ -1/15, -1/30 ], [ 1/6, 1/15 ], [ 1/30, -1/15 ], [ 3/10, -1/20 ], [ 
        1/10, 11/40 ], [ 1/5, 13/40 ], [ 0, 3/20 ], [ 1/4, -3/40 ], [ -1/20, 
        -11/40 ], [ 3/40, 0 ], [ 0, 1/10 ], [ 1/10, -1/40 ], [ 9/40, 3/20 ], [ 
        3/20, 0 ], [ 1/20, 1/40 ], [ -1/20, 1/10 ], [ 0, -1/20 ], [ -3/20, 0 ], 
        [ 3/20, 1/10 ], [ 1/5, 0 ], [ -1/5, -1/4 ], [ 1/10, -1/20 ], [ 1/20, 
        1/20 ], [ -1/12, 1/6 ], [ -1/8, -1/6 ], [ -1/12, -1/24 ], [ 1/6, 1/8 ], 
        [ 3/8, 1/12 ], [ 1/12, 0 ], [ 1/8, 1/12 ], [ 0, 1/24 ], [ -1/12, -1/24 
        ], [ -1/8, -1/12 ], [ 1/12, -1/12 ], [ -1/12, 0 ], [ 0, -1/12 ], [ -1/6,
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        -1/24 ], [ 0, -1/24 ], [ -1/30, 0 ], [ 1/15, 1/30 ], [ 2/15, 1/30 ], [ 
        1/10, 1/30 ], [ 1/10, 1/15 ], [ -4/15, -1/6 ], [ 0, 1/30 ], [ -2/15, 
        -1/15 ], [ -1/6, 0 ], [ 1/5, -1/30 ], [ -1/15, 1/10 ], [ 2/5, 1/30 ], [ 
        0, 0 ], [ -1/15, 0 ], [ 1/15, -1/15 ], [ 0, -1/30 ], [ 1/10, 3/40 ], [ 
        3/8, 1/40 ], [ 17/40, 1/40 ], [ -1/10, 7/40 ], [ 3/40, -1/8 ], [ -1/40, 
        -9/40 ], [ -1/2, -3/10 ], [ -1/5, -1/10 ], [ -3/40, 1/40 ], [ 11/20, 1/4
        ], [ 3/20, 3/20 ], [ 11/40, 1/40 ], [ 0, -1/10 ], [ -3/20, -1/5 ], [ 
        1/10, 1/20 ], [ 2/5, 1/20 ], [ 1/20, -1/5 ], [ -3/10, -1/5 ], [ 1/10, 
        -1/20 ], [ 0, 0 ], [ -1/12, -5/24 ], [ -7/24, -1/8 ], [ 1/8, -1/4 ], [ 
        1/3, 3/8 ], [ 1/8, 1/12 ], [ 1/24, 1/24 ], [ 1/3, 1/24 ], [ -1/12, -1/12
        ], [ 1/24, 1/8 ], [ -1/12, -1/12 ], [ 1/8, 1/6 ], [ 1/24, 1/12 ], [ 
        -7/24, -1/6 ], [ 1/24, 0 ], [ -1/8, 0 ], [ -1/6, 0 ], [ -1/12, -1/8 ], [
        7/24, 1/12 ], [ 1/12, 0 ], [ 1/24, 1/12 ], [ -2/15, -3/10 ], [ -1/15, 
        1/30 ], [ 1/30, 1/15 ], [ 2/15, 2/15 ], [ 11/30, 1/6 ], [ -1/30, 1/30 ],
        [ 1/6, 1/10 ], [ -1/10, -1/10 ], [ 1/5, 0 ], [ -8/15, -2/15 ], [ -1/15, 
        -1/30 ], [ 3/10, 1/15 ], [ -1/30, -1/30 ], [ 1/6, 1/30 ], [ 1/10, 1/15 
        ], [ -1/15, -1/30 ], [ 3/40, 1/5 ], [ 1/5, 9/20 ], [ 3/20, 1/5 ], [ 
        -7/40, -11/40 ], [ -3/10, -11/40 ], [ -3/40, -1/20 ], [ -33/40, -9/20 ],
        [ -1/4, -3/10 ], [ -1/5, -1/20 ], [ -19/20, -5/8 ], [ -13/40, -1/8 ], [ 
        -17/40, -11/40 ], [ -7/40, 7/40 ], [ -3/40, 1/8 ], [ -7/40, -1/40 ], [ 
        1/10, -1/40 ], [ 7/20, -1/40 ], [ 1/8, 3/40 ], [ 7/40, -1/40 ], [ -1/10,
        -3/40 ], [ -1/6, -11/24 ], [ -5/8, -1/8 ], [ 1/6, -1/8 ], [ 3/8, 3/8 ], 
        [ 1/4, 1/6 ], [ 5/24, 1/24 ], [ 1/6, 1/24 ], [ -1/24, -1/8 ], [ 0, 1/8 
        ], [ 1/8, -1/12 ], [ 1/24, 1/12 ], [ 1/24, 1/12 ], [ -1/24, 1/12 ], [ 
        1/24, 0 ], [ -1/8, -1/4 ], [ -1/6, -1/12 ], [ -1/12, -1/8 ], [ 1/6, 1/12
        ], [ 1/12, 1/24 ], [ -1/24, 1/24 ], [ -1/3, -4/15 ], [ 2/15, 1/6 ], [ 
        1/6, 1/5 ], [ 0, -1/15 ], [ 3/10, 11/30 ], [ -17/30, -11/30 ], [ -1/3, 
        -7/30 ], [ 1/6, -1/15 ], [ 1/10, -2/15 ], [ 1/15, 0 ], [ 2/15, -2/15 ], 
        [ -1/5, 1/10 ], [ 2/15, 1/10 ], [ -1/6, -1/10 ], [ 0, 1/30 ], [ 1/30, 
        -1/10 ], [ -1/8, 9/40 ], [ 1/20, -1/40 ], [ 3/10, 1/8 ], [ -3/40, -1/4 
        ], [ -1/20, -1/10 ], [ 1/40, 1/40 ], [ -19/20, -21/40 ], [ -1/5, -1/10 
        ], [ -11/20, -13/40 ], [ -7/40, -1/10 ], [ -1/40, 7/40 ], [ -9/40, -3/20
        ], [ -1/8, 1/8 ], [ -1/8, -1/40 ], [ -1/40, 1/8 ], [ 3/10, 1/40 ], [ 
        -3/20, -7/40 ], [ -1/40, 1/40 ], [ 7/40, -1/40 ], [ -1/10, -3/40 ], [ 
        -1/4, -1/4 ], [ 0, 1/8 ], [ -1/24, -7/24 ], [ 3/8, 3/8 ], [ 0, 1/24 ], [
        0, 1/12 ], [ 1/6, -1/24 ], [ -1/24, -5/24 ], [ 1/24, 5/24 ], [ 0, -1/24 
        ], [ 0, 1/6 ], [ -1/12, -1/12 ], [ -1/6, 0 ], [ -1/6, -1/4 ], [ 1/4, 1/6
        ], [ -1/12, 0 ], [ -1/8, -1/24 ], [ 5/24, 1/12 ], [ 1/24, 0 ], [ -1/24, 
        -1/24 ], [ -4/15, -2/15 ], [ 1/30, 1/10 ], [ 7/30, 1/10 ], [ -1/5, -1/5 
        ], [ 7/30, 1/3 ], [ -7/15, -7/30 ], [ -4/15, -1/6 ], [ 1/2, 1/30 ], [ 
        -2/15, -1/10 ], [ -1/30, -1/15 ], [ -1/6, 2/15 ], [ 3/10, -1/5 ], [ 
        1/10, -1/10 ], [ -1/30, -1/30 ], [ 1/10, 1/6 ], [ -4/15, -1/10 ], [ 
        -5/8, -11/40 ], [ -1/40, 1/5 ], [ 3/8, 1/5 ], [ 17/40, -1/8 ], [ 11/40, 
        3/10 ], [ -1/40, 1/4 ], [ -9/5, -11/10 ], [ -11/20, -7/20 ], [ -5/8, 
        -7/20 ], [ 1/10, -1/20 ], [ 1/5, 3/20 ], [ -9/40, -3/20 ], [ -1/10, 1/20
        ], [ 0, 0 ], [ -3/20, 0 ], [ -1/2, -9/20 ], [ 17/20, 9/20 ], [ 1/2, 7/20
        ], [ 1/10, -1/20 ], [ -1/20, -1/20 ], [ -1/6, -7/24 ], [ -1/12, 0 ], [ 
        -5/24, -3/8 ], [ 1/3, 5/24 ], [ 1/24, 5/24 ], [ 1/6, 1/12 ], [ 1/4, 1/24
        ], [ 1/8, 1/12 ], [ 0, 0 ], [ -5/24, -1/12 ], [ 0, 1/8 ], [ 0, -1/8 ], [
        -1/12, 1/24 ], [ -1/6, -1/8 ], [ 0, -1/24 ], [ -1/3, -1/8 ], [ 1/24, 0 
        ], [ 1/6, 1/12 ], [ 0, -1/8 ], [ 1/12, 1/12 ], [ -2/5, -4/15 ], [ 1/3, 
        1/3 ], [ 2/15, 0 ], [ 1/3, 1/5 ], [ 2/15, 2/15 ], [ -13/15, -8/15 ], [ 
        1/6, 1/30 ], [ 2/15, -1/30 ], [ 2/5, -1/3 ], [ -4/15, -1/5 ], [ -7/30, 
        -2/15 ], [ 1/30, 11/30 ], [ 0, 0 ], [ 1/15, 1/15 ], [ 2/15, 1/30 ], [ 
        -1/10, 0 ], [ 1/8, 1/5 ], [ 23/40, 11/40 ], [ 7/20, 1/40 ], [ 7/20, -1/8
        ], [ 1/20, 1/10 ], [ -1/4, 1/20 ], [ -1/2, -1/4 ], [ -1/10, -1/40 ], [ 
        -3/20, -1/8 ], [ -11/40, -3/10 ], [ -1/40, 7/40 ], [ -11/40, -13/40 ], [
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        1/12, 0 ], [ 11/24, 1/24 ], [ 1/24, -1/24 ], [ -1/12, 1/24 ], [ -1/3, 
        -1/12 ], [ 5/24, 5/24 ], [ 1/8, 1/24 ], [ -7/24, 1/24 ], [ -1/8, -1/8 ],
        [ -1/8, -1/8 ], [ -1/8, -1/24 ], [ 0, 1/24 ], [ 1/6, 1/24 ], [ 1/6, 1/12
        ], [ -1/24, -1/24 ], [ -1/15, 1/15 ], [ -2/15, -1/30 ], [ 7/30, 7/30 ], 
        [ 1/30, -1/6 ], [ 7/15, 3/10 ], [ -2/3, -3/10 ], [ -13/30, -1/3 ], [ 
        2/5, 1/6 ], [ 13/30, 1/6 ], [ -2/15, -1/10 ], [ -1/15, -2/15 ], [ -1/30,
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        -7/20, -1/5 ], [ -1/8, -1/8 ], [ 1/40, 3/20 ], [ -1/20, -9/40 ], [ -1/5,
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        ], [ 1/6, 0 ], [ 2/15, 2/15 ], [ -2/15, -1/15 ], [ 3/40, -1/10 ], [ 
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        1/10 ], [ -1/8, 0 ], [ 3/40, 1/40 ], [ -1/6, 1/8 ], [ -1/8, 0 ], [ 1/6, 
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    <11, 15, -1>,  <12, 13, 1>, <12, 15, -1>,  <13, 14, 1>, <13, 15, -1>,  <14, 
    12, 1>, <14, 15, -1>,  <15, 11, 1>, <15, 15, -1>,  <16, 20, -1>,  <17, 18, 
    1>, <17, 20, -1>,  <18, 19, 1>, <18, 20, -1>,  <19, 17, 1>, <19, 20, -1>,  
    <20, 16, 1>, <20, 20, -1>,  <21, 21, 1>, <21, 23, -1>,  <22, 23, -1>,  <23, 
    22, 1>, <23, 23, -1>,  <24, 23, -1>, <24, 24, 1>,  <25, 25, 1>, <25, 27, 
    -1>,  <26, 27, -1>,  <27, 26, 1>, <27, 27, -1>,  <28, 27, -1>, <28, 28, 1>, 
    <29, 29, 1>, <29, 31, -1>,  <30, 31, -1>,  <31, 30, 1>, <31, 31, -1>,  <32, 
    31, -1>, <32, 32, 1>,  <33, 33, 1>, <33, 35, -1>,  <34, 35, -1>,  <35, 34, 
    1>, <35, 35, -1>,  <36, 35, -1>, <36, 36, 1>,  <37, 37, -1>, <37, 38, -w>, 
    <37, 39, 1>,  <38, 37, w>, <38, 38, 1>, <38, 39, -w>,  <39, 37, -w - 1>, 
    <39, 38, -w - 1>,  <40, 40, -1>, <40, 41, -w>, <40, 42, 1>,  <41, 40, w>, 
    <41, 41, 1>, <41, 42, -w>,  <42, 40, -w - 1>, <42, 41, -w - 1>,  <43, 43, -w
    - 2>, <43, 44, -1>, <43, 45, -1>,  <44, 43, w + 2>, <44, 44, w + 1>, <44, 
    45, 1>,  <45, 43, 2*w + 3>, <45, 44, w + 1>, <45, 45, 1>,  <46, 46, -w - 2>,
    <46, 47, -1>, <46, 48, -1>,  <47, 46, w + 2>, <47, 47, w + 1>, <47, 48, 1>, 
    <48, 46, 2*w + 3>, <48, 47, w + 1>, <48, 48, 1>,  <49, 49, w - 1>, <49, 50, 
    -1>, <49, 51, -1>,  <50, 49, -w + 1>, <50, 50, -w>, <50, 51, 1>,  <51, 49, 
    -2*w + 1>, <51, 50, -w>, <51, 51, 1>,  <52, 52, -1>, <52, 53, w + 1>, <52, 
    54, 1>,  <53, 52, -w - 1>, <53, 53, 1>, <53, 54, w + 1>,  <54, 52, w>, <54, 
    53, w>,  <55, 55, 1>,  <56, 56, 1> ]))
]: Check := false) where w := K.1 where K := ext<K|Polynomial(K, [-1, 1, 1])> where K is 
RationalField();
K<w>:=BaseRing(M);
K;
M;
