/*
Generated by Allan Steel in Magma, 2010.

Field defining polynomial: x^2 + x + 1 [Q(zeta_3)].

Traces:    [ 11, 6 ]
Density:   [ 0.94282001, 0.0059505489 ]
Numer max: [ 28, 1 ]
Numer av:  [ 1.6759516, 0.0039841319 ]
Denom max: [ 120, 1 ], [ [ <2, 3>, <3, 1>, <5, 1> ], [] ]
Denom LCM: [ 480, 1 ], [ [ <2, 5>, <3, 1>, <5, 1> ], [] ]

Character:
( 171, 11, -171*zeta(3)_3 - 171, 171*zeta(3)_3, 6*zeta(3)_3, 6, -6*zeta(3)_3 - 
    6, 0, 3, 1, 1, -11*zeta(3)_3 - 11, 11*zeta(3)_3, 2*zeta(3)_3, -2*zeta(3)_3 -
    2, 2, -1, 0, 0, 0, 1, 1, 3*zeta(3)_3, -3*zeta(3)_3 - 3, 0, 0, 0, zeta(3)_3, 
    -zeta(3)_3 - 1, zeta(3)_3, -zeta(3)_3 - 1, -zeta(3)_3 - 1, 1, zeta(3)_3, 
    zeta(3)_3, -zeta(3)_3 - 1, 1, 1, 1, 0, 0, -zeta(3)_3, zeta(3)_3 + 1, 
    -zeta(3)_3 - 1, zeta(3)_3, zeta(3)_3, -zeta(3)_3 - 1, zeta(3)_3, -zeta(3)_3 
    - 1, zeta(3)_3, -zeta(3)_3 - 1, 0, 0, 0, 0 )
*/

G := c9Group("3j3p");
M :=
GModule(G, [
    Matrix(K, 171, 171,
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        ])    ,
    Matrix(SparseMatrix(K, 171, 171, [
    <1, 1, 1>,  <2, 2, -w - 1>,  <3, 3, 1>, <3, 5, w>,  <4, 5, -1>,  <5, 4, 1>, 
    <5, 5, -1>,  <6, 5, -1>, <6, 6, 1>,  <7, 11, 1>,  <8, 8, w>,  <9, 9, 1>,  
    <10, 7, -w - 1>,  <11, 10, w>,  <12, 16, 1>,  <13, 13, w>,  <14, 14, 1>,  
    <15, 12, -w - 1>,  <16, 15, w>,  <17, 21, w>,  <18, 18, 1>,  <19, 19, -w - 
    1>,  <20, 17, 1>,  <21, 20, -w - 1>,  <22, 31, 1>,  <23, 24, -w - 1>,  <24, 
    34, w + 1>,  <25, 36, w + 1>,  <26, 35, w + 1>,  <27, 27, -w - 1>,  <28, 28,
    -w - 1>,  <29, 29, -w - 1>,  <30, 25, w>,  <31, 32, w>,  <32, 22, -w - 1>,  
    <33, 26, -1>,  <34, 23, w + 1>,  <35, 33, w>,  <36, 30, -1>,  <37, 46, -1>, 
    <38, 39, -w>,  <39, 49, 1>,  <40, 51, 1>,  <41, 50, -w - 1>,  <42, 42, 1>,  
    <43, 43, 1>,  <44, 44, 1>,  <45, 40, -w>,  <46, 47, -w>,  <47, 37, -w - 1>, 
    <48, 41, w + 1>,  <49, 38, w + 1>,  <50, 48, w + 1>,  <51, 45, w + 1>,  <52,
    61, -1>,  <53, 54, -w>,  <54, 64, 1>,  <55, 66, 1>,  <56, 65, -w - 1>,  <57,
    57, 1>,  <58, 58, 1>,  <59, 59, 1>,  <60, 55, -w>,  <61, 62, -w>,  <62, 52, 
    -w - 1>,  <63, 56, w + 1>,  <64, 53, w + 1>,  <65, 63, w + 1>,  <66, 60, w +
    1>,  <67, 76, w>,  <68, 69, w>,  <69, 79, w>,  <70, 81, w>,  <71, 80, -w>,  
    <72, 72, w>,  <73, 73, w>,  <74, 74, w>,  <75, 70, -w>,  <76, 77, -w>,  <77,
    67, -w>,  <78, 71, -w - 1>,  <79, 68, w>,  <80, 78, -1>,  <81, 75, -w>,  
    <82, 101, -w - 1>,  <83, 110, -1>,  <84, 99, 1>,  <85, 114, w>,  <86, 115, 
    -w>,  <87, 82, -w - 1>,  <88, 93, -w - 1>,  <89, 91, -w - 1>,  <90, 83, -w -
    1>,  <91, 117, w>,  <92, 96, -w - 1>,  <93, 126, -1>,  <94, 98, -w - 1>,  
    <95, 118, -w>,  <96, 113, -w>,  <97, 123, -w>,  <98, 109, 1>,  <99, 102, w +
    1>,  <100, 95, -w - 1>,  <101, 87, -w - 1>,  <102, 84, -w>,  <103, 111, -1>,
    <104, 86, w>,  <105, 108, -w - 1>,  <106, 124, -w>,  <107, 125, w + 1>,  
    <108, 122, -w>,  <109, 94, w>,  <110, 90, -w>,  <111, 120, -w - 1>,  <112, 
    97, 1>,  <113, 92, -1>,  <114, 116, -1>,  <115, 104, -w>,  <116, 85, w + 1>,
    <117, 89, 1>,  <118, 100, -1>,  <119, 107, -w>,  <120, 103, -w>,  <121, 106,
    -1>,  <122, 105, -1>,  <123, 112, w + 1>,  <124, 121, -w - 1>,  <125, 119, 
    1>,  <126, 88, -w>,  <127, 146, -w - 1>,  <128, 155, -1>,  <129, 144, 1>,  
    <130, 159, w>,  <131, 160, -w>,  <132, 127, -w - 1>,  <133, 138, -w - 1>,  
    <134, 136, -w - 1>,  <135, 128, -w - 1>,  <136, 162, w>,  <137, 141, -w - 
    1>,  <138, 171, -1>,  <139, 143, -w - 1>,  <140, 163, -w>,  <141, 158, -w>, 
    <142, 168, -w>,  <143, 154, 1>,  <144, 147, w + 1>,  <145, 140, -w - 1>,  
    <146, 132, -w - 1>,  <147, 129, -w>,  <148, 156, -1>,  <149, 131, w>,  <150,
    153, -w - 1>,  <151, 169, -w>,  <152, 170, w + 1>,  <153, 167, -w>,  <154, 
    139, w>,  <155, 135, -w>,  <156, 165, -w - 1>,  <157, 142, 1>,  <158, 137, 
    -1>,  <159, 161, -1>,  <160, 149, -w>,  <161, 130, w + 1>,  <162, 134, 1>,  
    <163, 145, -1>,  <164, 152, -w>,  <165, 148, -w>,  <166, 151, -1>,  <167, 
    150, -1>,  <168, 157, w + 1>,  <169, 166, -w - 1>,  <170, 164, 1>,  <171, 
    133, -w> ]))
]: Check := false) where w := K.1 where K := CyclotomicField(3);
K<w> := BaseRing(M);
K;
M;
