/*
Generated by Allan Steel in Magma, 2010.

Field defining polynomial: x^4 + x^3 + x^2 + x + 1 [Q(zeta_5)].

Traces:    [ -13, -1 ]
Density:   [ 0.44329104, 0.98539023 ]
Numer max: [ 13, 191 ]
Numer av:  [ 0.55209535, 14.190888 ]
Denom max: [ 1, 10 ], [ [], [ <2, 1>, <5, 1> ] ]
Denom LCM: [ 1, 10 ], [ [], [ <2, 1>, <5, 1> ] ]

Character:
( 51, -13, 3, 0, 3, 3, -1, -13*zeta(5)_5^3 - zeta(5)_5, -zeta(5)_5^2 - 
    13*zeta(5)_5, zeta(5)_5^3 - 12*zeta(5)_5^2 + zeta(5)_5 + 1, 12*zeta(5)_5^3 +
    13*zeta(5)_5^2 + 13*zeta(5)_5 + 13, -3*zeta(5)_5^3 - 3*zeta(5)_5^2 - 3, 
    3*zeta(5)_5^3 + 3*zeta(5)_5^2, -zeta(5)_5^3 - zeta(5)_5^2 + 3, zeta(5)_5^3 +
    zeta(5)_5^2 + 4, -zeta(5)_5^3 + 3*zeta(5)_5 - 1, 3*zeta(5)_5^2 - zeta(5)_5 -
    1, -3*zeta(5)_5^3 - 4*zeta(5)_5^2 - 3*zeta(5)_5 - 4, 4*zeta(5)_5^3 + 
    zeta(5)_5^2 + zeta(5)_5, 1, -1, 0, -4*zeta(5)_5^3 - 3*zeta(5)_5^2 - 
    3*zeta(5)_5 - 3, zeta(5)_5^3 + 4*zeta(5)_5^2 + zeta(5)_5 + 1, 3*zeta(5)_5^3 
    - zeta(5)_5, -zeta(5)_5^2 + 3*zeta(5)_5, -zeta(5)_5^3 + 3*zeta(5)_5^2, 
    zeta(5)_5^3 + zeta(5)_5^2 + 4*zeta(5)_5 + 1, -3*zeta(5)_5^3 - 3*zeta(5)_5^2 
    - 4*zeta(5)_5 - 3, 3*zeta(5)_5^3 - zeta(5)_5^2, zeta(5)_5^3 + zeta(5)_5^2, 
    -zeta(5)_5^3 - zeta(5)_5^2 - 1, zeta(5)_5^2 + zeta(5)_5, zeta(5)_5^3 + 
    zeta(5)_5, -zeta(5)_5^3 - zeta(5)_5 - 1, -zeta(5)_5^2 - zeta(5)_5 - 1, 
    -zeta(5)_5^3 - zeta(5)_5^2, zeta(5)_5^3 + zeta(5)_5^2 + 1, -1, -1, -1, -1, 
    3*zeta(5)_5^2, -3*zeta(5)_5^3 - 3*zeta(5)_5^2 - 3*zeta(5)_5 - 3, 
    3*zeta(5)_5^3, 3*zeta(5)_5, zeta(5)_5^2 + zeta(5)_5 + 1, -zeta(5)_5^3 - 
    zeta(5)_5, -zeta(5)_5^2 - zeta(5)_5, zeta(5)_5^3 + zeta(5)_5 + 1, 
    -zeta(5)_5^3 - zeta(5)_5^2, zeta(5)_5^3 + zeta(5)_5^2 + 1, zeta(5)_5^3 + 
    zeta(5)_5^2 + zeta(5)_5, -zeta(5)_5^3 - 1, -zeta(5)_5 - 1, -zeta(5)_5^2 - 1,
    0, 0, 0, 0, 0, 0, zeta(5)_5^3 + zeta(5)_5 + 1, -zeta(5)_5^2 - zeta(5)_5, 
    zeta(5)_5^2 + zeta(5)_5 + 1, -zeta(5)_5^3 - zeta(5)_5, zeta(5)_5^3 + 
    zeta(5)_5^2 + zeta(5)_5 + 1, -zeta(5)_5^3, -zeta(5)_5^2, -zeta(5)_5, 0, 0, 
    0, 0, 0, 0, 0, 0, -zeta(5)_5^3, -zeta(5)_5, zeta(5)_5^3 + zeta(5)_5^2 + 
    zeta(5)_5 + 1, -zeta(5)_5^2, -zeta(5)_5^3, -zeta(5)_5, zeta(5)_5^3 + 
    zeta(5)_5^2 + zeta(5)_5 + 1, -zeta(5)_5^2, -zeta(5)_5^3, -zeta(5)_5, 
    zeta(5)_5^3 + zeta(5)_5^2 + zeta(5)_5 + 1, -zeta(5)_5^2, -zeta(5)_5, 
    zeta(5)_5^3 + zeta(5)_5^2 + zeta(5)_5 + 1, -zeta(5)_5^2, -zeta(5)_5^3 )
*/

// G := c9Group("u44p");
G := PermutationGroup(ATLASGroup("U44"));
M :=
GModule(G, [
    Matrix(SparseMatrix(K, 51, 51, [
    <1, 2, -3*w^3 - 3*w^2 - 1>, <1, 3, 3*w^3 + 3*w^2 + 9>, <1, 5, 5>, <1, 7, 
    -2*w^3 - 2*w^2 - 5>, <1, 8, 7*w^3 + 7*w^2 + 6>, <1, 9, -4*w^3 - 4*w^2 - 8>, 
    <1, 10, -3*w^3 - 3*w^2>, <1, 11, w^3 + w^2 - 1>, <1, 12, -4*w^3 - 4*w^2 - 
    3>, <1, 13, -2*w^3 - 2*w^2 + 6>, <1, 14, w^3 + w^2 + 2>, <1, 15, 2*w^3 + 
    2*w^2 - 2>, <1, 16, 1>, <1, 17, 5*w^3 + 5*w^2 + 4>, <1, 18, w^3 + w^2 - 3>, 
    <1, 19, -w^3 - w^2 - 1>, <1, 20, -2*w^3 - 2*w^2>, <1, 21, 2*w^3 + 2*w^2 - 
    3>, <1, 22, w^3 + w^2 - 6>, <1, 23, -6*w^3 - 6*w^2 - 6>, <1, 24, -2>, <1, 
    25, 1>, <1, 27, -2*w^3 - 2*w^2 - 1>, <1, 29, -2*w^3 - 2*w^2 - 2>, <1, 30, 
    w^3 + w^2 + 1>, <1, 31, w^3 + w^2 - 3>, <1, 32, w^3 + w^2 - 1>, <1, 35, w^3 
    + w^2 + 1>, <1, 36, w^3 + w^2 + 2>, <1, 37, 3>, <1, 38, -2*w^3 - 2*w^2>, <1,
    40, w^3 + w^2 - 1>, <1, 41, w^3 + w^2>, <1, 42, 3*w^3 + 3*w^2 + 3>, <1, 43, 
    w^3 + w^2 + 4>, <1, 44, w^3 + w^2 - 1>, <1, 45, w^3 + w^2>, <1, 47, -2*w^3 -
    2*w^2>, <1, 48, w^3 + w^2 + 2>, <1, 49, 3*w^3 + 3*w^2 + 2>, <1, 50, -3*w^3 -
    3*w^2 - 6>, <1, 51, w^3 + w^2 + 1>,  <2, 2, -1>, <2, 7, w^3 + w^2 + 2>, <2, 
    8, w^3 + w^2>, <2, 9, 1>, <2, 13, 1>, <2, 17, -1>, <2, 19, -w^3 - w^2>, <2, 
    21, 1>, <2, 23, 1>, <2, 27, -w^3 - w^2>, <2, 28, -1>, <2, 30, -1>, <2, 36, 
    -1>, <2, 43, -w^3 - w^2 - 1>, <2, 50, w^3 + w^2 + 1>,  <3, 3, -1>, <3, 5, 
    -1>, <3, 7, w^3 + w^2 + 1>, <3, 8, -w^3 - w^2>, <3, 9, 2*w^3 + 2*w^2 + 1>, 
    <3, 14, -1>, <3, 17, -w^3 - w^2 - 1>, <3, 19, w^3 + w^2>, <3, 21, w^3 + 
    w^2>, <3, 22, w^3 + w^2>, <3, 23, w^3 + w^2 + 1>, <3, 27, w^3 + w^2>, <3, 
    30, -w^3 - w^2>, <3, 36, -w^3 - w^2>, <3, 43, -w^3 - w^2 - 1>, <3, 50, w^3 +
    w^2 + 1>,  <4, 1, w^3 + w^2 + 1>, <4, 2, -w^3 - w^2 - 1>, <4, 3, 1>, <4, 4, 
    -w^3 - w^2 - 1>, <4, 5, w^3 + w^2 + 1>, <4, 6, 1>, <4, 7, 6*w^3 + 6*w^2 + 
    9>, <4, 8, -w^3 - w^2 - 1>, <4, 9, 2*w^3 + 2*w^2 + 4>, <4, 11, w^3 + w^2 + 
    2>, <4, 12, w^3 + w^2 + 2>, <4, 13, 2*w^3 + 2*w^2 + 2>, <4, 15, -w^3 - w^2 -
    1>, <4, 16, w^3 + w^2 - 1>, <4, 17, -2*w^3 - 2*w^2 - 2>, <4, 18, -w^3 - w^2 
    - 1>, <4, 20, w^3 + w^2>, <4, 21, 2*w^3 + 2*w^2 + 2>, <4, 22, w^3 + w^2 + 
    3>, <4, 23, 3*w^3 + 3*w^2 + 4>, <4, 24, w^3 + w^2 + 2>, <4, 26, 1>, <4, 29, 
    1>, <4, 30, -w^3 - w^2 - 2>, <4, 31, w^3 + w^2 + 1>, <4, 35, w^3 + w^2 + 2>,
    <4, 36, -w^3 - w^2 - 1>, <4, 37, w^3 + w^2>, <4, 38, w^3 + w^2 + 1>, <4, 39,
    w^3 + w^2 + 1>, <4, 40, -1>, <4, 41, -w^3 - w^2>, <4, 42, -w^3 - w^2>, <4, 
    43, -w^3 - w^2 - 2>, <4, 44, -w^3 - w^2 - 1>, <4, 46, -w^3 - w^2 - 2>, <4, 
    47, 1>, <4, 48, -w^3 - w^2 - 1>, <4, 49, -w^3 - w^2 - 2>, <4, 50, 2*w^3 + 
    2*w^2 + 4>, <4, 51, -1>,  <5, 14, 1>,  <6, 1, w^3 + w^2 + 1>, <6, 2, -w^3 - 
    w^2 - 1>, <6, 3, 1>, <6, 4, -w^3 - w^2>, <6, 5, w^3 + w^2 + 1>, <6, 7, 6*w^3
    + 6*w^2 + 9>, <6, 8, -w^3 - w^2 - 1>, <6, 9, 2*w^3 + 2*w^2 + 4>, <6, 11, w^3
    + w^2 + 2>, <6, 12, w^3 + w^2 + 2>, <6, 13, 2*w^3 + 2*w^2 + 2>, <6, 15, -w^3
    - w^2 - 1>, <6, 16, w^3 + w^2 - 1>, <6, 17, -2*w^3 - 2*w^2 - 2>, <6, 18, 
    -w^3 - w^2 - 1>, <6, 20, w^3 + w^2>, <6, 21, 2*w^3 + 2*w^2 + 2>, <6, 22, w^3
    + w^2 + 3>, <6, 23, 3*w^3 + 3*w^2 + 4>, <6, 24, w^3 + w^2 + 2>, <6, 26, 1>, 
    <6, 29, 1>, <6, 30, -w^3 - w^2 - 2>, <6, 31, w^3 + w^2 + 1>, <6, 35, w^3 + 
    w^2 + 2>, <6, 36, -w^3 - w^2 - 1>, <6, 37, w^3 + w^2>, <6, 38, w^3 + w^2 + 
    1>, <6, 39, w^3 + w^2 + 1>, <6, 40, -1>, <6, 41, -w^3 - w^2>, <6, 42, -w^3 -
    w^2>, <6, 43, -w^3 - w^2 - 2>, <6, 44, -w^3 - w^2 - 1>, <6, 46, -w^3 - w^2 -
    2>, <6, 47, 1>, <6, 48, -w^3 - w^2 - 1>, <6, 49, -w^3 - w^2 - 2>, <6, 50, 
    2*w^3 + 2*w^2 + 4>, <6, 51, -1>,  <7, 13, 1>, <7, 23, -w^3 - w^2>,  <8, 8, 
    1>, <8, 17, 1>, <8, 27, -1>, <8, 30, -w^3 - w^2>, <8, 36, -w^3 - w^2>,  <9, 
    19, 1>,  <10, 2, w^3 + w^2 + 2>, <10, 3, -2*w^3 - 2*w^2 - 3>, <10, 5, -w^3 -
    w^2 - 1>, <10, 7, 2*w^3 + 2*w^2 + 4>, <10, 8, -2*w^3 - 2*w^2 - 5>, <10, 9, 
    3*w^3 + 3*w^2 + 5>, <10, 10, 1>, <10, 11, w^3 + w^2>, <10, 12, 2*w^3 + 2*w^2
    + 3>, <10, 13, -w^3 - w^2>, <10, 14, -w^3 - w^2 - 1>, <10, 15, -1>, <10, 16,
    -w^3 - w^2 - 1>, <10, 17, -w^3 - w^2 - 3>, <10, 18, -1>, <10, 19, 1>, <10, 
    20, 1>, <10, 21, 1>, <10, 22, 2*w^3 + 2*w^2 + 2>, <10, 23, 2*w^3 + 2*w^2 + 
    4>, <10, 24, w^3 + w^2 + 1>, <10, 25, -w^3 - w^2>, <10, 27, 1>, <10, 29, w^3
    + w^2 + 1>, <10, 30, -w^3 - w^2 - 1>, <10, 31, w^3 + w^2 + 1>, <10, 36, -2>,
    <10, 37, -w^3 - w^2 - 1>, <10, 38, 1>, <10, 42, -w^3 - w^2 - 2>, <10, 43, 
    -w^3 - w^2 - 2>, <10, 47, w^3 + w^2 + 1>, <10, 48, -w^3 - w^2 - 1>, <10, 49,
    -w^3 - w^2 - 2>, <10, 50, 2*w^3 + 2*w^2 + 3>, <10, 51, -w^3 - w^2 - 1>,  
    <11, 2, -1>, <11, 3, -1>, <11, 5, -1>, <11, 7, w^3 + w^2 + 2>, <11, 9, w^3 +
    w^2 + 1>, <11, 11, -1>, <11, 12, -1>, <11, 17, -w^3 - w^2 - 1>, <11, 18, 1>,
    <11, 21, 1>, <11, 22, w^3 + w^2>, <11, 23, 1>, <11, 25, -w^3 - w^2>, <11, 
    28, -1>, <11, 30, -w^3 - w^2>, <11, 36, -1>, <11, 43, -w^3 - w^2 - 1>, <11, 
    50, w^3 + w^2 + 1>,  <12, 2, -w^3 - w^2 - 2>, <12, 3, 2*w^3 + 2*w^2 + 3>, 
    <12, 5, w^3 + w^2 + 1>, <12, 7, -3*w^3 - 3*w^2 - 5>, <12, 8, 2*w^3 + 2*w^2 +
    5>, <12, 9, -4*w^3 - 4*w^2 - 6>, <12, 10, -2>, <12, 11, -w^3 - w^2>, <12, 
    12, -2*w^3 - 2*w^2 - 4>, <12, 13, w^3 + w^2>, <12, 14, w^3 + w^2 + 1>, <12, 
    15, 1>, <12, 16, w^3 + w^2 + 1>, <12, 17, w^3 + w^2 + 4>, <12, 18, 1>, <12, 
    19, -1>, <12, 20, -1>, <12, 21, -w^3 - w^2 - 1>, <12, 22, -3*w^3 - 3*w^2 - 
    2>, <12, 23, -3*w^3 - 3*w^2 - 5>, <12, 24, -w^3 - w^2 - 1>, <12, 25, w^3 + 
    w^2>, <12, 27, -1>, <12, 28, 1>, <12, 29, -w^3 - w^2 - 1>, <12, 30, w^3 + 
    w^2 + 2>, <12, 31, -w^3 - w^2 - 1>, <12, 36, w^3 + w^2 + 2>, <12, 37, w^3 + 
    w^2 + 1>, <12, 38, -1>, <12, 42, w^3 + w^2 + 2>, <12, 43, 2*w^3 + 2*w^2 + 
    3>, <12, 47, -w^3 - w^2 - 1>, <12, 48, w^3 + w^2 + 1>, <12, 49, w^3 + w^2 + 
    2>, <12, 50, -3*w^3 - 3*w^2 - 4>, <12, 51, w^3 + w^2 + 1>,  <13, 13, -1>,  
    <14, 5, 1>,  <15, 25, w^3 + w^2>, <15, 30, w^3 + w^2>,  <16, 2, 1>, <16, 3, 
    1>, <16, 5, 1>, <16, 8, -1>, <16, 9, 1>, <16, 12, 1>, <16, 13, 1>, <16, 15, 
    -1>, <16, 16, -1>, <16, 17, -1>, <16, 18, -1>, <16, 19, 1>, <16, 27, 1>,  
    <17, 2, -1>, <17, 3, -1>, <17, 5, -1>, <17, 12, -1>, <17, 13, -1>, <17, 15, 
    1>, <17, 18, 1>, <17, 21, -w^3 - w^2>, <17, 36, w^3 + w^2>,  <18, 2, -w^3 - 
    w^2 - 3>, <18, 3, 2*w^3 + 2*w^2 + 2>, <18, 5, w^3 + w^2>, <18, 7, -w^3 - w^2
    - 2>, <18, 8, 2*w^3 + 2*w^2 + 5>, <18, 9, -2*w^3 - 2*w^2 - 4>, <18, 10, -2>,
    <18, 11, -w^3 - w^2>, <18, 12, -2*w^3 - 2*w^2 - 4>, <18, 13, w^3 + w^2>, 
    <18, 14, w^3 + w^2 + 1>, <18, 15, 1>, <18, 16, w^3 + w^2 + 1>, <18, 17, 2>, 
    <18, 18, 1>, <18, 19, -1>, <18, 20, -1>, <18, 22, -2*w^3 - 2*w^2 - 2>, <18, 
    23, -2*w^3 - 2*w^2 - 3>, <18, 24, -w^3 - w^2 - 1>, <18, 27, -1>, <18, 29, 
    -w^3 - w^2 - 1>, <18, 30, 1>, <18, 31, -w^3 - w^2 - 1>, <18, 36, 1>, <18, 
    37, w^3 + w^2 + 1>, <18, 38, -1>, <18, 42, w^3 + w^2 + 2>, <18, 43, 1>, <18,
    47, -w^3 - w^2 - 1>, <18, 48, w^3 + w^2 + 1>, <18, 49, w^3 + w^2 + 2>, <18, 
    50, -w^3 - w^2 - 2>, <18, 51, w^3 + w^2 + 1>,  <19, 9, 1>,  <20, 5, w^3 + 
    w^2 + 1>, <20, 7, -w^3 - w^2 - 2>, <20, 8, 1>, <20, 9, -w^3 - w^2 - 3>, <20,
    14, w^3 + w^2 + 1>, <20, 17, w^3 + w^2 + 2>, <20, 19, -1>, <20, 20, -1>, 
    <20, 21, -1>, <20, 23, -w^3 - w^2 - 2>, <20, 27, -1>, <20, 30, 1>, <20, 36, 
    1>, <20, 43, w^3 + w^2 + 2>, <20, 50, -w^3 - w^2 - 2>,  <21, 27, -w^3 - w^2 
    - 1>,  <22, 22, 1>,  <23, 7, -w^3 - w^2 - 1>, <23, 13, -w^3 - w^2 - 1>,  
    <24, 2, -2*w^3 - 2*w^2 + 2>, <24, 3, -8*w^3 - 8*w^2 - 8>, <24, 4, -w^3 - 
    w^2>, <24, 5, -6*w^3 - 6*w^2 - 4>, <24, 6, 1>, <24, 7, 4*w^3 + 4*w^2 + 5>, 
    <24, 8, -w^3 - w^2 - 7>, <24, 9, 3*w^3 + 3*w^2 + 6>, <24, 10, -3*w^3 - 3*w^2
    + 1>, <24, 11, w^3 + w^2 - 1>, <24, 12, -w^3 - w^2 + 3>, <24, 13, -8*w^3 - 
    8*w^2 - 2>, <24, 14, -2*w^3 - 2*w^2 - 1>, <24, 15, 4*w^3 + 4*w^2 + 2>, <24, 
    16, w^3 + w^2>, <24, 17, w^3 + w^2 - 4>, <24, 18, 5*w^3 + 5*w^2 + 3>, <24, 
    19, -w^3 - w^2 + 2>, <24, 20, -w^3 - w^2 + 1>, <24, 21, 3*w^3 + 3*w^2 - 2>, 
    <24, 22, 5*w^3 + 5*w^2>, <24, 23, 3*w^3 + 3*w^2 + 9>, <24, 24, 3*w^3 + 3*w^2
    + 2>, <24, 25, -w^3 - w^2>, <24, 27, -w^3 - w^2 + 2>, <24, 29, w^3 + w^2 + 
    4>, <24, 30, -1>, <24, 31, 3*w^3 + 3*w^2>, <24, 32, 2*w^3 + 2*w^2 + 1>, <24,
    35, -w^3 - w^2 - 1>, <24, 36, -w^3 - w^2 - 1>, <24, 37, -2*w^3 - 2*w^2 - 2>,
    <24, 38, -w^3 - w^2 + 2>, <24, 40, 2*w^3 + 2*w^2 - 1>, <24, 41, -w^3 - w^2 -
    1>, <24, 42, -2*w^3 - 2*w^2 - 4>, <24, 43, -3*w^3 - 3*w^2 - 2>, <24, 44, w^3
    + w^2>, <24, 45, -1>, <24, 46, -1>, <24, 47, -2*w^3 - 2*w^2 + 1>, <24, 48, 
    -w^3 - w^2 - 1>, <24, 49, w^3 + w^2 - 2>, <24, 50, 4*w^3 + 4*w^2 + 5>, <24, 
    51, -1>,  <25, 2, w^3 + w^2 + 1>, <25, 3, w^3 + w^2 + 1>, <25, 5, w^3 + w^2 
    + 1>, <25, 12, w^3 + w^2 + 1>, <25, 13, w^3 + w^2 + 1>, <25, 18, -w^3 - w^2 
    - 1>,  <26, 2, 4*w^3 + 4*w^2 + 7>, <26, 3, -2*w^3 - 2*w^2 - 3>, <26, 5, 1>, 
    <26, 7, 2*w^3 + 2*w^2 + 3>, <26, 8, -6*w^3 - 6*w^2 - 10>, <26, 9, 7*w^3 + 
    7*w^2 + 11>, <26, 10, 2*w^3 + 2*w^2 + 4>, <26, 11, 3*w^3 + 3*w^2 + 4>, <26, 
    12, 7*w^3 + 7*w^2 + 12>, <26, 13, -w^3 - w^2 + 1>, <26, 14, -2*w^3 - 2*w^2 -
    3>, <26, 15, -2*w^3 - 2*w^2 - 4>, <26, 16, -w^3 - w^2 - 2>, <26, 17, -3*w^3 
    - 3*w^2 - 5>, <26, 18, -3*w^3 - 3*w^2 - 6>, <26, 19, w^3 + w^2 + 2>, <26, 
    20, w^3 + w^2 + 2>, <26, 21, 2*w^3 + 2*w^2 + 2>, <26, 22, 4*w^3 + 4*w^2 + 
    5>, <26, 23, 4*w^3 + 4*w^2 + 7>, <26, 24, w^3 + w^2 + 1>, <26, 27, w^3 + w^2
    + 2>, <26, 29, w^3 + w^2 + 2>, <26, 30, -2*w^3 - 2*w^2 - 3>, <26, 31, 2*w^3 
    + 2*w^2 + 3>, <26, 32, -1>, <26, 36, -2*w^3 - 2*w^2 - 3>, <26, 37, -w^3 - 
    w^2 - 2>, <26, 38, 1>, <26, 42, -2*w^3 - 2*w^2 - 4>, <26, 43, -3*w^3 - 3*w^2
    - 4>, <26, 45, w^3 + w^2 + 1>, <26, 47, w^3 + w^2 + 2>, <26, 48, -2*w^3 - 
    2*w^2 - 3>, <26, 49, -3*w^3 - 3*w^2 - 5>, <26, 50, 4*w^3 + 4*w^2 + 6>, <26, 
    51, -w^3 - w^2 - 2>,  <27, 21, -w^3 - w^2>,  <28, 28, 1>,  <29, 2, 1>, <29, 
    3, 1>, <29, 5, 1>, <29, 8, 1>, <29, 12, 1>, <29, 13, 1>, <29, 15, -1>, <29, 
    18, -1>, <29, 21, w^3 + w^2>, <29, 27, -1>, <29, 29, -1>, <29, 30, -w^3 - 
    w^2>, <29, 36, -w^3 - w^2>,  <30, 2, -w^3 - w^2 - 1>, <30, 3, -w^3 - w^2 - 
    1>, <30, 5, -w^3 - w^2 - 1>, <30, 12, -w^3 - w^2 - 1>, <30, 13, -w^3 - w^2 -
    1>, <30, 15, w^3 + w^2 + 1>, <30, 18, w^3 + w^2 + 1>,  <31, 2, 7>, <31, 3, 
    -4*w^3 - 4*w^2>, <31, 5, -3*w^3 - 3*w^2 + 3>, <31, 7, -2>, <31, 8, -7>, <31,
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    -w^3 - w^2 - 1>, <38, 36, -2*w^3 - 2*w^2 - 4>, <38, 37, -w^3 - w^2 - 3>, 
    <38, 38, 2*w^3 + 2*w^2 + 1>, <38, 39, 1>, <38, 40, -w^3 - w^2 + 1>, <38, 42,
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    -w^3 - w^2>, <39, 31, -w^3 - w^2 + 1>, <39, 37, w^3 + w^2>, <39, 38, 1>, 
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    -4*w^3 - 4*w^2 - 7>, <40, 10, 3*w^3 + 3*w^2 - 2>, <40, 11, -w^3 - w^2 + 1>, 
    <40, 12, -5>, <40, 13, 9*w^3 + 9*w^2 + 3>, <40, 14, 3*w^3 + 3*w^2 + 3>, <40,
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    26, 1>, <40, 27, -3>, <40, 29, -w^3 - w^2 - 4>, <40, 30, -w^3 - w^2 + 1>, 
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    50, -4*w^3 - 4*w^2 - 5>, <40, 51, 1>,  <41, 1, -1>, <41, 2, -2*w^3 - 2*w^2 +
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    -8*w^3 - 8*w^2 - 2>, <41, 14, -4*w^3 - 4*w^2 - 3>, <41, 15, 4*w^3 + 4*w^2 - 
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    w^3 + w^2 + 1>, <41, 25, 1>, <41, 26, w^3 + w^2 - 1>, <41, 27, 4>, <41, 29, 
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    -1>,  <42, 1, -w^3 - w^2 - 1>, <42, 2, -2>, <42, 3, -3*w^3 - 3*w^2 - 6>, 
    <42, 5, -2*w^3 - 2*w^2 - 4>, <42, 7, -2*w^3 - 2*w^2 - 2>, <42, 9, -w^3 - w^2
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    -2>, <43, 14, -w^3 - w^2 - 2>, <43, 16, w^3 + w^2 - 1>, <43, 17, -w^3 - w^2 
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    w^3 + w^2 + 3>, <43, 23, 3*w^3 + 3*w^2 + 4>, <43, 24, 1>, <43, 27, w^3 + w^2
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    38, w^3 + w^2>, <43, 41, -w^3 - w^2>, <43, 42, -2*w^3 - 2*w^2 - 2>, <43, 43,
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    49, -w^3 - w^2 - 2>, <43, 50, w^3 + w^2 + 2>, <43, 51, -1>,  <44, 2, w^3 + 
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    + 2>, <44, 8, -w^3 - w^2>, <44, 9, 2*w^3 + 2*w^2 + 2>, <44, 10, w^3 + w^2>, 
    <44, 12, w^3 + w^2>, <44, 13, w^3 + w^2 - 1>, <44, 14, -1>, <44, 15, -w^3 - 
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    2>, <44, 23, 2*w^3 + 2*w^2 + 1>, <44, 26, -w^3 - w^2>, <44, 28, -w^3 - w^2 -
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    37, w^3 + w^2>, <44, 40, -w^3 - w^2>, <44, 43, -w^3 - w^2 - 2>, <44, 47, w^3
    + w^2>, <44, 49, -w^3 - w^2>, <44, 50, w^3 + w^2 + 2>,  <45, 1, -1>, <45, 2,
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    + 2*w^2 + 4>, <45, 8, -7*w^3 - 7*w^2 - 6>, <45, 9, 5*w^3 + 5*w^2 + 8>, <45, 
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    - 2*w^2 + 3>, <45, 22, -w^3 - w^2 + 6>, <45, 23, 7*w^3 + 7*w^2 + 6>, <45, 
    24, 2>, <45, 25, -1>, <45, 27, 2*w^3 + 2*w^2 + 1>, <45, 29, 2*w^3 + 2*w^2 + 
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    + 1>, <45, 35, -w^3 - w^2 - 1>, <45, 36, -w^3 - w^2 - 2>, <45, 37, -3>, <45,
    38, 2*w^3 + 2*w^2>, <45, 40, -w^3 - w^2 + 1>, <45, 41, -w^3 - w^2>, <45, 42,
    -3*w^3 - 3*w^2 - 3>, <45, 43, -w^3 - w^2 - 4>, <45, 44, -w^3 - w^2 + 1>, 
    <45, 45, -w^3 - w^2 - 1>, <45, 47, 2*w^3 + 2*w^2>, <45, 48, -w^3 - w^2 - 2>,
    <45, 49, -3*w^3 - 3*w^2 - 2>, <45, 50, 3*w^3 + 3*w^2 + 6>, <45, 51, -w^3 - 
    w^2 - 1>,  <46, 1, w^3 + w^2>, <46, 2, -2*w^3 - 2*w^2 - 2>, <46, 3, w^3 + 
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]: Check := false) where w := K.1 where K := CyclotomicField(5);
K<w> := BaseRing(M);
K;
M;
