/*
Generated by Allan Steel in Magma, 2010.

Field defining polynomial: x^4 - x^2 + 1 [Q(zeta_12)].

Traces:    [ 0, 3*w^2 - 3 ]
Density:   [ 0.0046296296, 0.90226337 ]
Numer max: [ 1, 25 ]
Numer av:  [ 0.0015003429, 2.5418488 ]
Denom max: [ 1, 135 ], [ [], [ <3, 3>, <5, 1> ] ]
Denom LCM: [ 1, 405 ], [ [], [ <3, 4>, <5, 1> ] ]

[Constructed by BB tensor R30*R40.]

Character:
( 216, -216, 0, -216*zeta(12)_3 - 216, 216*zeta(12)_3, 27*zeta(12)_3 + 27, 
    -27*zeta(12)_3, -27, 0, 0, 0, 0, 0, -216*zeta(12)_4, 216*zeta(12)_4, 0, 
    4*zeta(12)_4, -4, 4, -4*zeta(12)_4, 1, -216*zeta(12)_3, 216*zeta(12)_3 + 
    216, -27*zeta(12)_3 - 27, 27*zeta(12)_3, 27, 0, 0, 0, 0, 0, 0, -3*zeta(12)_3
    - 3, -3, 3*zeta(12)_3 + 3, -3*zeta(12)_3, 3*zeta(12)_3, 3, 0, 0, 0, 0, 0, 0,
    0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1,
    -216*zeta(12)_4*zeta(12)_3 - 216*zeta(12)_4, 216*zeta(12)_4*zeta(12)_3,
    -216*zeta(12)_4*zeta(12)_3, 216*zeta(12)_4*zeta(12)_3 + 216*zeta(12)_4,
    27*zeta(12)_4*zeta(12)_3, 27*zeta(12)_4*zeta(12)_3 + 27*zeta(12)_4,
    -27*zeta(12)_4*zeta(12)_3, -27*zeta(12)_4, 27*zeta(12)_4,
    -27*zeta(12)_4*zeta(12)_3 - 27*zeta(12)_4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
    4*zeta(12)_3, -4*zeta(12)_3 - 4, 4*zeta(12)_4*zeta(12)_3 + 4*zeta(12)_4,
    -4*zeta(12)_4*zeta(12)_3, 4*zeta(12)_3 + 4, -4*zeta(12)_4*zeta(12)_3 -
    4*zeta(12)_4, 4*zeta(12)_4*zeta(12)_3, -4*zeta(12)_3,
    3*zeta(12)_4*zeta(12)_3 + 3*zeta(12)_4, -3*zeta(12)_4*zeta(12)_3,
    -3*zeta(12)_4, 3*zeta(12)_4, -3*zeta(12)_4*zeta(12)_3 - 3*zeta(12)_4,
    3*zeta(12)_4*zeta(12)_3, 0, 0, 0, 0, 0, 0, 0, 0, -zeta(12)_4*zeta(12)_3 -
    zeta(12)_4, -1, zeta(12)_3 + 1, -zeta(12)_3 - 1, zeta(12)_3, 1,
    -zeta(12)_4, zeta(12)_4*zeta(12)_3 + zeta(12)_4,
    -zeta(12)_4*zeta(12)_3, zeta(12)_4*zeta(12)_3, zeta(12)_4,
    -zeta(12)_3, 1, 1, zeta(12)_3, -zeta(12)_3 - 1, 0, 0, 0, 0, 0, 0, 0,
    0, -zeta(12)_4, zeta(12)_4, -zeta(12)_3, zeta(12)_3 + 1, zeta(12)_3 +
    1, -zeta(12)_3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -zeta(12)_4, zeta(12)_4,
    zeta(12)_4, -zeta(12)_4, -zeta(12)_3, zeta(12)_3 + 1, 0, 0, 0, 0,
    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -zeta(12)_3 - 1, zeta(12)_3,
    -zeta(12)_3 - 1, zeta(12)_3, -zeta(12)_4*zeta(12)_3 - zeta(12)_4,
    zeta(12)_4*zeta(12)_3 + zeta(12)_4, -zeta(12)_4*zeta(12)_3,
    zeta(12)_4*zeta(12)_3, -zeta(12)_4*zeta(12)_3 - zeta(12)_4,
    -zeta(12)_4*zeta(12)_3, zeta(12)_4*zeta(12)_3, -zeta(12)_4*zeta(12)_3,
    zeta(12)_4*zeta(12)_3, zeta(12)_4*zeta(12)_3 + zeta(12)_4,
    -zeta(12)_4*zeta(12)_3 - zeta(12)_4, zeta(12)_4*zeta(12)_3 +
    zeta(12)_4 )

*/

G:=c9Group("12au43p");
M:=
GModule(G, [
    Matrix(SparseMatrix(K, 216, 216, [
    <1, 31, -w^2 + 1>,  <2, 22, -1>,  <3, 19, -w^3>,  <4, 24, -w>,  <5, 23, 1>, 
    <6, 33, -w^3>,  <7, 7, 1>,  <8, 34, -w^2>,  <9, 25, -w^2 + 1>,  <10, 18, 
    -w^2 + 1>,  <11, 13, -1>,  <12, 35, w^3>,  <13, 11, -1>,  <14, 14, 1>,  <15,
    26, w^2 - 1>,  <16, 36, 1>,  <17, 32, w^2 - 1>,  <18, 10, w^2>,  <19, 3, 
    w^3>,  <20, 21, 1>,  <21, 20, 1>,  <22, 2, -1>,  <23, 5, 1>,  <24, 4, w^3 - 
    w>,  <25, 9, w^2>,  <26, 15, -w^2>,  <27, 29, -w^2>,  <28, 28, -1>,  <29, 
    27, w^2 - 1>,  <30, 30, -1>,  <31, 1, w^2>,  <32, 17, -w^2>,  <33, 6, w^3>, 
    <34, 8, w^2 - 1>,  <35, 12, -w^3>,  <36, 16, 1>,  <37, 45, -1>,  <38, 89, 
    -w>,  <39, 46, w^3>,  <40, 84, -w^3>,  <41, 69, -w^3>,  <42, 59, -w^2 + 1>, 
    <43, 83, w^2>,  <44, 61, -w^2 + 1>,  <45, 37, -1>,  <46, 39, -w^3>,  <47, 
    76, w^2>,  <48, 79, -1>,  <49, 52, 1>,  <50, 87, w^2>,  <51, 77, -1>,  <52, 
    49, 1>,  <53, 53, 1>,  <54, 60, -w^3 + w>,  <55, 58, -w^3 + w>,  <56, 90, 
    -w^3 + w>,  <57, 85, -1>,  <58, 55, w>,  <59, 42, w^2>,  <60, 54, w>,  <61, 
    44, w^2>,  <62, 70, -1>,  <63, 88, -w^2 + 1>,  <64, 94, w^3 - w>,  <65, 71, 
    w>,  <66, 66, -1>,  <67, 75, -w^3 + w>,  <68, 74, -w^3>,  <69, 41, w^3>,  
    <70, 62, -1>,  <71, 65, -w^3 + w>,  <72, 95, -w^3 + w>,  <73, 78, w>,  <74, 
    68, w^3>,  <75, 67, w>,  <76, 47, -w^2 + 1>,  <77, 51, -1>,  <78, 73, -w^3 +
    w>,  <79, 48, -1>,  <80, 91, w^3 - w>,  <81, 81, 1>,  <82, 86, w^2 - 1>,  
    <83, 43, -w^2 + 1>,  <84, 40, w^3>,  <85, 57, -1>,  <86, 82, -w^2>,  <87, 
    50, -w^2 + 1>,  <88, 63, w^2>,  <89, 38, w^3 - w>,  <90, 56, w>,  <91, 80, 
    -w>,  <92, 92, -1>,  <93, 96, 1>,  <94, 64, -w>,  <95, 72, w>,  <96, 93, 1>,
    <97, 216, w^3 - w>,  <98, 206, 1>,  <99, 146, w^2 - 1>,  <100, 201, -1>,  
    <101, 179, w^2>,  <102, 155, -w^2>,  <103, 187, -w>,  <104, 124, -w^3>,  
    <105, 158, -w>,  <106, 173, -w^3>,  <107, 141, -w>,  <108, 215, w^2>,  <109,
    208, w^2 - 1>,  <110, 185, 1>,  <111, 191, -w^2 + 1>,  <112, 203, w^2>,  
    <113, 196, 1>,  <114, 174, -w^2 + 1>,  <115, 209, -w^2>,  <116, 135, -w^3 + 
    w>,  <117, 167, -w^2>,  <118, 186, -w^3>,  <119, 165, w^3>,  <120, 147, -w>,
    <121, 138, w^3>,  <122, 194, w^3 - w>,  <123, 210, -w^3 + w>,  <124, 104, 
    w^3>,  <125, 190, -w>,  <126, 142, w>,  <127, 180, w^2 - 1>,  <128, 140, 
    -w>,  <129, 130, -w^3>,  <130, 129, w^3>,  <131, 169, w^2 - 1>,  <132, 144, 
    -w^3>,  <133, 205, -1>,  <134, 213, -w^2>,  <135, 116, w>,  <136, 198, -w^2 
    + 1>,  <137, 177, -w>,  <138, 121, -w^3>,  <139, 183, w^3>,  <140, 128, w^3 
    - w>,  <141, 107, w^3 - w>,  <142, 126, -w^3 + w>,  <143, 170, -w^2>,  <144,
    132, w^3>,  <145, 214, w^3>,  <146, 99, -w^2>,  <147, 120, w^3 - w>,  <148, 
    211, -1>,  <149, 154, w>,  <150, 207, -w^3>,  <151, 189, -w>,  <152, 192, 
    -w^3 + w>,  <153, 199, -w^3 + w>,  <154, 149, -w^3 + w>,  <155, 102, w^2 - 
    1>,  <156, 188, -w^3>,  <157, 204, w^2>,  <158, 105, w^3 - w>,  <159, 166, 
    w^2>,  <160, 168, w^3 - w>,  <161, 193, -w^2>,  <162, 202, 1>,  <163, 184, 
    -w^2 + 1>,  <164, 181, w^2>,  <165, 119, -w^3>,  <166, 159, -w^2 + 1>,  
    <167, 117, w^2 - 1>,  <168, 160, -w>,  <169, 131, -w^2>,  <170, 143, w^2 - 
    1>,  <171, 212, w^2 - 1>,  <172, 197, -1>,  <173, 106, w^3>,  <174, 114, 
    w^2>,  <175, 195, -w^3>,  <176, 182, -w^2 + 1>,  <177, 137, w^3 - w>,  <178,
    200, -w^3>,  <179, 101, -w^2 + 1>,  <180, 127, -w^2>,  <181, 164, -w^2 + 1>,
    <182, 176, w^2>,  <183, 139, -w^3>,  <184, 163, w^2>,  <185, 110, 1>,  <186,
    118, w^3>,  <187, 103, w^3 - w>,  <188, 156, w^3>,  <189, 151, w^3 - w>,  
    <190, 125, w^3 - w>,  <191, 111, w^2>,  <192, 152, w>,  <193, 161, w^2 - 1>,
    <194, 122, -w>,  <195, 175, w^3>,  <196, 113, 1>,  <197, 172, -1>,  <198, 
    136, w^2>,  <199, 153, w>,  <200, 178, w^3>,  <201, 100, -1>,  <202, 162, 
    1>,  <203, 112, -w^2 + 1>,  <204, 157, -w^2 + 1>,  <205, 133, -1>,  <206, 
    98, 1>,  <207, 150, w^3>,  <208, 109, -w^2>,  <209, 115, w^2 - 1>,  <210, 
    123, w>,  <211, 148, -1>,  <212, 171, -w^2>,  <213, 134, w^2 - 1>,  <214, 
    145, -w^3>,  <215, 108, -w^2 + 1>,  <216, 97, -w> ])),
    Matrix(K, 216, 216,
        [ [ 0, -1/27, 0, -1/27 ], [ 0, 0, 0, 0 ], [ 2/27, 0, -1/27, 0 ], [ 0, 
        -2/27, 0, 1/27 ], [ 0, 0, 0, 0 ], [ 0, -2/27, 0, 1/27 ], [ -2/27, 0, 
        1/27, 0 ], [ 2/27, -2/27, 2/27, 4/27 ], [ 0, 0, 0, 0 ], [ 0, -2/27, 0, 
        1/27 ], [ 0, 0, 0, 0 ], [ -2/27, 0, 1/27, 0 ], [ 2/27, 0, -1/27, 0 ], [ 
        0, 0, 0, 0 ], [ -1/27, 0, 2/27, 0 ], [ 2/27, 0, -1/27, 0 ], [ 0, 0, 0, 0
        ], [ 0, 1/27, 0, 1/27 ], [ 0, -1/27, 0, 2/27 ], [ 0, -1/27, 0, -1/27 ], 
        [ 0, -1/27, 0, -1/27 ], [ 0, -2/27, 0, 1/27 ], [ 0, -1/27, 0, -1/27 ], [
        0, 1/27, 0, 1/27 ], [ 0, 0, 0, 0 ], [ 1/27, 0, 1/27, 0 ], [ -2/27, 0, 
        1/27, 0 ], [ -1/27, 0, 2/27, 0 ], [ 1/27, 0, -2/27, 0 ], [ 0, 0, 0, 0 ],
        [ 0, -1/27, 0, 2/27 ], [ 0, -1/27, 0, -1/27 ], [ 0, -2/27, 0, 1/27 ], [ 
        0, 0, 0, 0 ], [ 0, 0, 0, 0 ], [ 0, 1/27, 0, 1/27 ], [ -1/81, 1/81, 2/81,
        1/81 ], [ -8/81, -8/81, 4/81, 4/81 ], [ 0, 0, 0, 0 ], [ -2/81, -1/81, 
        1/81, 2/81 ], [ 0, 0, 0, 0 ], [ 2/81, 1/81, -1/81, -2/81 ], [ -1/81, 
        -2/81, -1/81, 1/81 ], [ 0, 0, 0, 0 ], [ -4/81, -5/81, 5/81, 7/81 ], [ 
        -2/81, -4/81, -2/81, 2/81 ], [ 4/81, 4/81, 4/81, 4/81 ], [ 1/81, -1/81, 
        -2/81, -1/81 ], [ 2/81, 5/81, 5/81, -1/81 ], [ -1/27, -2/81, 0, 1/81 ], 
        [ 1/81, 2/81, 4/81, 5/81 ], [ 0, 0, 0, 0 ], [ -2/81, -2/81, -2/81, -2/81
        ], [ 1/81, 1/81, 1/81, 1/81 ], [ -2/81, -4/81, -2/81, 2/81 ], [ 0, 1/81,
        1/27, 1/81 ], [ -2/81, -2/81, 1/81, 1/81 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 0
        ], [ -2/81, 2/81, 4/81, 2/81 ], [ 1/81, -1/81, -2/81, -1/81 ], [ -1/81, 
        1/81, 2/81, 1/81 ], [ 2/81, 1/27, -1/81, -1/27 ], [ -1/81, 1/81, 2/81, 
        1/81 ], [ -1/81, -1/81, 2/81, 2/81 ], [ 2/81, 4/81, 2/81, -2/81 ], [ 
        8/81, 8/81, -4/81, -4/81 ], [ -1/81, -1/81, -1/81, -1/81 ], [ 1/81, 0, 
        -2/81, -1/27 ], [ 2/81, 2/81, -4/81, -4/81 ], [ 2/81, -2/81, -4/81, 
        -2/81 ], [ 0, 1/81, 1/27, 1/81 ], [ 1/81, 2/81, 1/81, -1/81 ], [ -2/81, 
        -2/81, 4/81, 4/81 ], [ 4/81, 2/81, -2/81, -4/81 ], [ 0, 0, 0, 0 ], [ 0, 
        1/81, 1/27, 1/81 ], [ -2/81, -5/81, -5/81, 1/81 ], [ 0, 0, 0, 0 ], [ 
        2/81, 1/27, -1/81, -1/27 ], [ -1/81, -1/81, 2/81, 2/81 ], [ -1/81, 
        -1/81, -1/81, -1/81 ], [ 0, 0, 0, 0 ], [ -2/81, -1/27, 1/81, 1/27 ], [ 
        1/27, 1/81, -1/27, -2/81 ], [ -4/81, -4/81, 8/81, 8/81 ], [ -1/81, 0, 
        2/81, 1/27 ], [ 0, 0, 0, 0 ], [ -2/81, -4/81, -2/81, 2/81 ], [ -1/81, 
        -1/81, -1/81, -1/81 ], [ 2/81, 2/81, -1/81, -1/81 ], [ 1/81, 1/81, 1/81,
        1/81 ], [ 8/81, 4/81, -4/81, -8/81 ], [ 1/81, -1/81, -2/81, -1/81 ], [ 
        -7/81, -4/81, 2/81, 5/81 ], [ 1/81, -1/81, -2/81, -1/81 ], [ 2/81, 
        -1/81, 2/81, 2/81 ], [ -8/81, -8/81, 1/81, 4/81 ], [ -4/81, -2/81, 
        -1/81, 10/81 ], [ 8/81, 5/81, -10/81, -1/81 ], [ -7/81, -4/81, 8/81, 
        8/81 ], [ 2/81, -2/81, -1/81, -2/81 ], [ -4/81, -1/81, 2/81, -1/81 ], [ 
        -1/81, -4/81, -7/81, -4/81 ], [ 2/27, 1/27, -2/27, 0 ], [ -4/81, -1/81, 
        2/81, -1/81 ], [ 5/81, 1/27, -1/81, -1/27 ], [ 4/81, 1/81, -2/81, 1/81 
        ], [ 2/81, -1/81, 2/81, 2/81 ], [ -10/81, -1/81, 2/81, -4/81 ], [ 2/27, 
        0, 0, 1/27 ], [ 4/81, 0, -5/81, -1/27 ], [ 1/81, 0, -5/81, 1/27 ], [ 
        -1/81, 4/81, 2/81, -2/81 ], [ 7/81, 4/81, -8/81, -8/81 ], [ 2/27, 1/27, 
        -2/27, 0 ], [ 0, 4/81, -1/27, 1/81 ], [ 4/81, 0, -5/81, -1/27 ], [ 1/27,
        0, 0, -2/27 ], [ 0, -2/27, -1/27, 2/27 ], [ 4/81, 1/81, -2/81, 1/81 ], [
        -4/81, -2/81, -1/81, 10/81 ], [ 2/27, 0, 0, 1/27 ], [ -1/81, -2/81, 
        -1/81, 4/81 ], [ -10/81, -1/81, 2/81, -4/81 ], [ -1/27, 0, 0, 2/27 ], [ 
        0, -1/81, -1/27, -4/81 ], [ 8/81, -4/81, -7/81, 8/81 ], [ -1/81, -2/81, 
        -1/81, 4/81 ], [ 8/81, 5/81, -10/81, -1/81 ], [ -2/81, 2/81, 1/81, 2/81 
        ], [ -1/81, 4/81, 2/81, -2/81 ], [ -8/81, -8/81, 1/81, 4/81 ], [ 4/81, 
        -7/81, 4/81, -1/81 ], [ -5/81, 8/81, 4/81, 2/81 ], [ 1/81, 4/81, 7/81, 
        4/81 ], [ -2/81, 4/81, -8/81, -5/81 ], [ 2/81, -2/81, -1/81, -2/81 ], [ 
        -2/27, 0, 0, -1/27 ], [ -4/81, -8/81, -4/81, 1/81 ], [ 2/81, -2/81, 
        -1/81, -2/81 ], [ 1/27, -5/81, 0, 4/81 ], [ 0, 2/27, 1/27, -2/27 ], [ 0,
        -4/81, 1/27, -1/81 ], [ -2/81, 1/81, -2/81, -2/81 ], [ -1/27, 2/27, 
        1/27, 0 ], [ -2/81, -2/81, 4/81, 1/81 ], [ -2/81, 2/81, 1/81, 2/81 ], [ 
        5/81, -8/81, -4/81, -2/81 ], [ -1/81, -2/81, -1/81, 4/81 ], [ -2/81, 
        2/81, 1/81, 2/81 ], [ 4/81, -10/81, -5/81, 2/81 ], [ 1/81, -10/81, 
        -5/81, 8/81 ], [ -4/81, 1/81, 8/81, -8/81 ], [ 0, 2/27, 1/27, -2/27 ], [
        -1/81, 0, 5/81, -1/27 ], [ -2/81, 1/81, -2/81, -2/81 ], [ 2/81, -2/81, 
        -1/81, -2/81 ], [ 4/81, -1/27, 1/81, 0 ], [ 1/81, 2/81, 1/81, -4/81 ], [
        -10/81, -1/81, 2/81, -4/81 ], [ 2/81, -2/81, -1/81, -2/81 ], [ -1/81, 
        -2/81, -1/81, 4/81 ], [ 0, 1/81, 1/27, 4/81 ], [ 4/81, -1/81, -8/81, 
        8/81 ], [ 0, 1/81, 1/27, 4/81 ], [ 2/27, 1/27, -2/27, 0 ], [ 1/81, 4/81,
        -8/81, 4/81 ], [ -1/27, 1/81, 1/27, -5/81 ], [ 1/81, 2/81, 1/81, -4/81 
        ], [ -4/81, 1/27, -1/81, 0 ], [ -2/81, 2/81, 1/81, 2/81 ], [ 1/81, 
        -4/81, -2/81, 2/81 ], [ 1/81, 2/81, 1/81, -4/81 ], [ 4/81, 2/81, 1/81, 
        -10/81 ], [ -4/81, -1/81, 2/81, -1/81 ], [ -1/27, 0, 0, 2/27 ], [ 2/81, 
        5/81, -10/81, -4/81 ], [ 8/81, -4/81, -7/81, 8/81 ], [ -1/81, 0, 5/81, 
        -1/27 ], [ -2/27, 0, 0, -1/27 ], [ -4/81, -1/81, 2/81, -1/81 ], [ 2/81, 
        2/81, -4/81, -1/81 ], [ -1/27, 2/27, 1/27, 0 ], [ -7/81, 8/81, -1/81, 
        -4/81 ], [ -2/27, 0, 0, -1/27 ], [ -2/27, 0, 0, -1/27 ], [ 1/81, 2/81, 
        1/81, -4/81 ], [ 4/81, 0, -5/81, -1/27 ], [ 8/81, 8/81, -1/81, -4/81 ], 
        [ -8/81, 8/81, 4/81, -7/81 ], [ -2/81, 1/81, -2/81, -2/81 ], [ -4/81, 
        1/81, 8/81, 7/81 ], [ 1/81, 8/81, 4/81, -10/81 ], [ 2/81, 2/81, -4/81, 
        -1/81 ], [ -1/81, -2/81, -1/81, 4/81 ], [ 1/81, 2/81, 1/81, -4/81 ], [ 
        -1/27, 2/27, 1/27, 0 ], [ 2/81, 2/81, -4/81, -1/81 ], [ -10/81, -1/81, 
        2/81, -4/81 ], [ -7/81, 8/81, -1/81, -4/81 ], [ -4/81, 1/81, 8/81, 7/81 
        ], [ -2/81, 1/81, -2/81, -2/81 ], [ -1/81, 0, 5/81, -1/27 ], [ 2/81, 
        5/81, -10/81, -4/81 ], [ 1/27, 0, 0, -2/27 ], [ 0, -1/81, -1/27, -4/81 
        ], [ -1/81, -1/27, -4/81, 0 ], [ 8/81, -1/81, 2/81, 5/81 ], [ -4/81, 
        10/81, 5/81, -2/81 ], [ 4/81, -7/81, 4/81, -1/81 ], [ -2/81, -2/81, 
        4/81, 1/81 ], [ -10/81, -4/81, 8/81, -1/81 ], [ -1/27, 2/27, 1/27, 0 ], 
        [ 0, 1/81, 1/27, 4/81 ], [ 1/81, 2/81, 1/81, -4/81 ], [ 0, -1/27, 0, 
        -1/27 ], [ 1/27, 0, -2/27, 0 ], [ 0, 0, 0, 0 ], [ 0, -2/27, 0, 1/27 ], [
        -2/27, 0, 1/27, 0 ], [ 0, 0, 0, 0 ], [ 0, -1/27, 0, -1/27 ], [ 1/27, 0, 
        1/27, 0 ], [ 0, 1/27, 0, 1/27 ], [ 0, 2/27, 0, -1/27 ], [ 0, 0, 0, 0 ], 
        [ 0, 0, 0, 0 ], [ 0, 1/27, 0, 1/27 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 0 ], [ 
        0, 1/27, 0, 1/27 ], [ 1/27, 0, 1/27, 0 ], [ 0, -1/27, 0, -1/27 ], [ 
        1/27, 0, 1/27, 0 ], [ -2/27, 0, 1/27, 0 ], [ 0, 0, 0, 0 ], [ -1/27, 0, 
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]: Check := false) where w := K.1 where K := CyclotomicField(12);
K<w> := BaseRing(M);
M;
K;
