Magma V2.8-10     Mon Apr  8 2002 18:21:01 on modular  [Seed = 1895717766]
Type ? for help.  Type <Ctrl>-D to quit.

Loading startup file "/home/was/magma/local/init.m"

Forming extension L.
Time: 0.000
L =  Univariate Quotient Polynomial Algebra in w over Univariate Quotient Polynomial Algebra in z over Finite field of size 13
with modulus z^36 + z^35 + z^34 + z^33 + z^32 + z^31 + z^30 + z^29 + z^28 + z^27 + z^26 + z^25 + z^24 + z^23 + z^22 + z^21 + z^20 + z^19 + z^18 + z^17 + z^16 + z^15 + z^14 + z^13 + z^12 + z^11 + z^10 + z^9 + z^8 + z^7 + z^6 + z^5 + z^4 + z^3 + z^2 + z + 1
with modulus w^37 + 11*z^35 + z^34 + 11*z^33 + 3*z^32 + 3*z^30 + 4*z^29 + 12*z^28 + 4*z^26 + 11*z^25 + 11*z^24 + 5*z^22 + 5*z^21 + 12*z^20 + z^19 + z^18 + 12*z^17 + 5*z^16 + 5*z^15 + 11*z^13 + 11*z^12 + 4*z^11 + 12*z^9 + 4*z^8 + 3*z^7 + 3*z^5 + 11*z^4 + z^3 + 11*z^2 + 9
Computing trace of random element (alpha = w
)
34 steps: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, Time: 0.200

Finished computing trace of random element.
Computing minimal polynomial of trace(alpha), as an element of K[X]
Time: 1.750
f =  X^37 + 10*X^34 + 9*X^33 + 11*X^32 + 3*X^31 + 8*X^30 + 7*X^29 + 3*X^28 + X^27 + X^26 + 7*X^25 + 3*X^24 + 3*X^22 + 10*X^21 + 11*X^20 + 12*X^19 + 12*X^18 + 11*X^17 + 3*X^16 + 9*X^15 + 11*X^14 + 3*X^13 + 5*X^12 + 2*X^11 + 11*X^10 + 7*X^9 + X^7 + 8*X^6 + 5*X^5 + 3*X^4 + 3*X^3 + 5*X + 9
g =  T^37 + 10*T^34 + 9*T^33 + 11*T^32 + 3*T^31 + 8*T^30 + 7*T^29 + 3*T^28 + T^27 + T^26 + 7*T^25 + 3*T^24 + 3*T^22 + 10*T^21 + 11*T^20 + 12*T^19 + 12*T^18 + 11*T^17 + 3*T^16 + 9*T^15 + 11*T^14 + 3*T^13 + 5*T^12 + 2*T^11 + 11*T^10 + 7*T^9 + T^7 + 8*T^6 + 5*T^5 + 3*T^4 + 3*T^3 + 5*T + 9
Forming extension L.
Time: 0.000
L =  Univariate Quotient Polynomial Algebra in w over Univariate Quotient Polynomial Algebra in z over Finite field of size 17
with modulus z^36 + z^35 + z^34 + z^33 + z^32 + z^31 + z^30 + z^29 + z^28 + z^27 + z^26 + z^25 + z^24 + z^23 + z^22 + z^21 + z^20 + z^19 + z^18 + z^17 + z^16 + z^15 + z^14 + z^13 + z^12 + z^11 + z^10 + z^9 + z^8 + z^7 + z^6 + z^5 + z^4 + z^3 + z^2 + z + 1
with modulus w^37 + 16*z^35 + 6*z^34 + 6*z^33 + 10*z^32 + 10*z^30 + 9*z^29 + 12*z^28 + 13*z^27 + 9*z^26 + 16*z^25 + 6*z^24 + 13*z^23 + 13*z^22 + 13*z^21 + 12*z^20 + 6*z^19 + 6*z^18 + 12*z^17 + 13*z^16 + 13*z^15 + 13*z^14 + 6*z^13 + 16*z^12 + 9*z^11 + 13*z^10 + 12*z^9 + 9*z^8 + 10*z^7 + 10*z^5 + 6*z^4 + 6*z^3 + 16*z^2
Computing trace of random element (alpha = w
)
34 steps: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, Time: 0.200

Finished computing trace of random element.
Computing minimal polynomial of trace(alpha), as an element of K[X]
Time: 1.760
f =  X^37 + 12*X^34 + 8*X^33 + 11*X^32 + 11*X^31 + X^30 + 6*X^28 + 16*X^27 + 4*X^26 + 14*X^25 + 14*X^24 + 6*X^23 + 13*X^22 + 4*X^21 + 2*X^20 + 12*X^19 + 2*X^18 + 5*X^17 + 4*X^16 + 9*X^15 + 8*X^14 + 2*X^13 + 9*X^12 + 5*X^11 + 10*X^10 + 4*X^9 + 12*X^8 + 8*X^6 + 14*X^5 + 4*X^4 + 12*X^3 + 11*X^2 + 6*X + 3
g =  T^37 + 12*T^34 + 8*T^33 + 11*T^32 + 11*T^31 + T^30 + 6*T^28 + 16*T^27 + 4*T^26 + 14*T^25 + 14*T^24 + 6*T^23 + 13*T^22 + 4*T^21 + 2*T^20 + 12*T^19 + 2*T^18 + 5*T^17 + 4*T^16 + 9*T^15 + 8*T^14 + 2*T^13 + 9*T^12 + 5*T^11 + 10*T^10 + 4*T^9 + 12*T^8 + 8*T^6 + 14*T^5 + 4*T^4 + 12*T^3 + 11*T^2 + 6*T + 3
Forming extension L.
Time: 0.000
L =  Univariate Quotient Polynomial Algebra in w over Univariate Quotient Polynomial Algebra in z over Finite field of size 19
with modulus z^36 + z^35 + z^34 + z^33 + z^32 + z^31 + z^30 + z^29 + z^28 + z^27 + z^26 + z^25 + z^24 + z^23 + z^22 + z^21 + z^20 + z^19 + z^18 + z^17 + z^16 + z^15 + z^14 + z^13 + z^12 + z^11 + z^10 + z^9 + z^8 + z^7 + z^6 + z^5 + z^4 + z^3 + z^2 + z + 1
with modulus w^37 + 3*z^35 + 4*z^34 + 4*z^33 + 5*z^32 + 5*z^30 + 13*z^29 + 7*z^27 + 13*z^26 + 3*z^25 + 4*z^24 + 7*z^23 + 3*z^22 + 3*z^21 + 4*z^19 + 4*z^18 + 3*z^16 + 3*z^15 + 7*z^14 + 4*z^13 + 3*z^12 + 13*z^11 + 7*z^10 + 13*z^8 + 5*z^7 + 5*z^5 + 4*z^4 + 4*z^3 + 3*z^2 + 17
Computing trace of random element (alpha = w
)
34 steps: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, Time: 0.190

Finished computing trace of random element.
Computing minimal polynomial of trace(alpha), as an element of K[X]
Time: 1.770
f =  X^37 + 14*X^34 + X^33 + 16*X^32 + 4*X^31 + 7*X^30 + 18*X^29 + 16*X^28 + 8*X^26 + 18*X^25 + 12*X^23 + 18*X^22 + 13*X^21 + 3*X^20 + 5*X^19 + 10*X^18 + 2*X^17 + 15*X^16 + 9*X^15 + 10*X^14 + X^13 + 11*X^12 + 11*X^11 + 5*X^10 + 16*X^9 + 11*X^8 + 5*X^7 + 2*X^6 + 3*X^3 + 8*X^2 + 11*X + 1
g =  T^37 + 14*T^34 + T^33 + 16*T^32 + 4*T^31 + 7*T^30 + 18*T^29 + 16*T^28 + 8*T^26 + 18*T^25 + 12*T^23 + 18*T^22 + 13*T^21 + 3*T^20 + 5*T^19 + 10*T^18 + 2*T^17 + 15*T^16 + 9*T^15 + 10*T^14 + T^13 + 11*T^12 + 11*T^11 + 5*T^10 + 16*T^9 + 11*T^8 + 5*T^7 + 2*T^6 + 3*T^3 + 8*T^2 + 11*T + 1
Forming extension L.
Time: 0.000
L =  Univariate Quotient Polynomial Algebra in w over Univariate Quotient Polynomial Algebra in z over Finite field of size 59
with modulus z^36 + z^35 + z^34 + z^33 + z^32 + z^31 + z^30 + z^29 + z^28 + z^27 + z^26 + z^25 + z^24 + z^23 + z^22 + z^21 + z^20 + z^19 + z^18 + z^17 + z^16 + z^15 + z^14 + z^13 + z^12 + z^11 + z^10 + z^9 + z^8 + z^7 + z^6 + z^5 + z^4 + z^3 + z^2 + z + 1
with modulus w^37 + 28*z^35 + 6*z^34 + 38*z^33 + 18*z^32 + 18*z^30 + 45*z^29 + 44*z^28 + 57*z^27 + 45*z^26 + 28*z^25 + 38*z^24 + 57*z^23 + 8*z^22 + 8*z^21 + 44*z^20 + 6*z^19 + 6*z^18 + 44*z^17 + 8*z^16 + 8*z^15 + 57*z^14 + 38*z^13 + 28*z^12 + 45*z^11 + 57*z^10 + 44*z^9 + 45*z^8 + 18*z^7 + 18*z^5 + 38*z^4 + 6*z^3 + 28*z^2 + 21
Computing trace of random element (alpha = w
)
34 steps: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, Time: 0.200

Finished computing trace of random element.
Computing minimal polynomial of trace(alpha), as an element of K[X]
Time: 1.890
f =  X^37 + 44*X^34 + 43*X^33 + 11*X^32 + 46*X^31 + 52*X^30 + 13*X^29 + 4*X^28 + 15*X^27 + 42*X^26 + 51*X^25 + 38*X^24 + 56*X^23 + 26*X^22 + 12*X^21 + 29*X^20 + 10*X^19 + 52*X^18 + 47*X^17 + 20*X^16 + 22*X^15 + 5*X^14 + 53*X^13 + 2*X^12 + 15*X^11 + 22*X^10 + 42*X^9 + 39*X^8 + 57*X^7 + 42*X^6 + 7*X^5 + 49*X^4 + 13*X^3 + 18*X^2 + 48*X + 30
g =  T^37 + 44*T^34 + 43*T^33 + 11*T^32 + 46*T^31 + 52*T^30 + 13*T^29 + 4*T^28 + 15*T^27 + 42*T^26 + 51*T^25 + 38*T^24 + 56*T^23 + 26*T^22 + 12*T^21 + 29*T^20 + 10*T^19 + 52*T^18 + 47*T^17 + 20*T^16 + 22*T^15 + 5*T^14 + 53*T^13 + 2*T^12 + 15*T^11 + 22*T^10 + 42*T^9 + 39*T^8 + 57*T^7 + 42*T^6 + 7*T^5 + 49*T^4 + 13*T^3 + 18*T^2 + 48*T + 30
Forming extension L.
Time: 0.000
L =  Univariate Quotient Polynomial Algebra in w over Univariate Quotient Polynomial Algebra in z over Finite field of size 61
with modulus z^36 + z^35 + z^34 + z^33 + z^32 + z^31 + z^30 + z^29 + z^28 + z^27 + z^26 + z^25 + z^24 + z^23 + z^22 + z^21 + z^20 + z^19 + z^18 + z^17 + z^16 + z^15 + z^14 + z^13 + z^12 + z^11 + z^10 + z^9 + z^8 + z^7 + z^6 + z^5 + z^4 + z^3 + z^2 + z + 1
with modulus w^37 + 3*z^35 + 51*z^34 + 17*z^33 + 36*z^32 + 36*z^30 + 51*z^29 + 50*z^28 + 13*z^27 + 51*z^26 + 3*z^25 + 17*z^24 + 13*z^23 + 44*z^22 + 44*z^21 + 50*z^20 + 51*z^19 + 51*z^18 + 50*z^17 + 44*z^16 + 44*z^15 + 13*z^14 + 17*z^13 + 3*z^12 + 51*z^11 + 13*z^10 + 50*z^9 + 51*z^8 + 36*z^7 + 36*z^5 + 17*z^4 + 51*z^3 + 3*z^2 + 42
Computing trace of random element (alpha = w
)
34 steps: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, Time: 0.220

Finished computing trace of random element.
Computing minimal polynomial of trace(alpha), as an element of K[X]
Time: 1.870
f =  X^37 + 45*X^34 + 48*X^33 + 55*X^32 + 2*X^31 + X^30 + 39*X^29 + 60*X^28 + 55*X^27 + 53*X^26 + 46*X^25 + 37*X^24 + 19*X^23 + 43*X^22 + 51*X^21 + 43*X^20 + 54*X^19 + 19*X^18 + 47*X^17 + 27*X^16 + 42*X^15 + 18*X^14 + 26*X^13 + 25*X^12 + X^11 + 10*X^10 + 38*X^9 + 17*X^8 + 15*X^7 + 29*X^6 + 3*X^5 + 14*X^4 + 5*X^3 + 8*X^2 + 38*X + 27
g =  T^37 + 45*T^34 + 48*T^33 + 55*T^32 + 2*T^31 + T^30 + 39*T^29 + 60*T^28 + 55*T^27 + 53*T^26 + 46*T^25 + 37*T^24 + 19*T^23 + 43*T^22 + 51*T^21 + 43*T^20 + 54*T^19 + 19*T^18 + 47*T^17 + 27*T^16 + 42*T^15 + 18*T^14 + 26*T^13 + 25*T^12 + T^11 + 10*T^10 + 38*T^9 + 17*T^8 + 15*T^7 + 29*T^6 + 3*T^5 + 14*T^4 + 5*T^3 + 8*T^2 + 38*T + 27
CRT step --  10.21
So far:   [ -4493233, 842509, -1752400, -24944, -2771948, -7176281, 5746229, 2916486, -2363855, 3012523, 1756688, -4332768, -1729996, 1956906, -3496807, 575272, 7437147, -7140369, -2725217, 7016762, 5020221, 2786287, -3680453, -5992987, -1650074, 2017438, 6425732, -5280898, 6969615, 1132931, 4437324, -4533396, 1499496, 3222800, -6483584, 0, 0, 1 ]
Forming extension L.
Time: 0.000
L =  Univariate Quotient Polynomial Algebra in w over Univariate Quotient Polynomial Algebra in z over Finite field of size 79
with modulus z^36 + z^35 + z^34 + z^33 + z^32 + z^31 + z^30 + z^29 + z^28 + z^27 + z^26 + z^25 + z^24 + z^23 + z^22 + z^21 + z^20 + z^19 + z^18 + z^17 + z^16 + z^15 + z^14 + z^13 + z^12 + z^11 + z^10 + z^9 + z^8 + z^7 + z^6 + z^5 + z^4 + z^3 + z^2 + z + 1
with modulus w^37 + 29*z^35 + 55*z^34 + 48*z^33 + 8*z^32 + 8*z^30 + 59*z^29 + 2*z^28 + 73*z^27 + 59*z^26 + 29*z^25 + 48*z^24 + 73*z^23 + 12*z^22 + 12*z^21 + 2*z^20 + 55*z^19 + 55*z^18 + 2*z^17 + 12*z^16 + 12*z^15 + 73*z^14 + 48*z^13 + 29*z^12 + 59*z^11 + 73*z^10 + 2*z^9 + 59*z^8 + 8*z^7 + 8*z^5 + 48*z^4 + 55*z^3 + 29*z^2 + 26
Computing trace of random element (alpha = w
)
34 steps: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, Time: 0.270

Finished computing trace of random element.
Computing minimal polynomial of trace(alpha), as an element of K[X]
Time: 2.320
f =  X^37 + 25*X^34 + 70*X^33 + 13*X^32 + 53*X^31 + 32*X^30 + 39*X^29 + 33*X^28 + 76*X^27 + 62*X^26 + 53*X^25 + 40*X^24 + 21*X^23 + 67*X^22 + 49*X^21 + 34*X^20 + 23*X^19 + 78*X^18 + 44*X^17 + 60*X^16 + 51*X^15 + 39*X^14 + 59*X^13 + 21*X^12 + 32*X^11 + 25*X^10 + 43*X^9 + 34*X^8 + 78*X^7 + 39*X^6 + 62*X^5 + 74*X^3 + 32*X^2 + 27*X + 60
g =  T^37 + 25*T^34 + 70*T^33 + 13*T^32 + 53*T^31 + 32*T^30 + 39*T^29 + 33*T^28 + 76*T^27 + 62*T^26 + 53*T^25 + 40*T^24 + 21*T^23 + 67*T^22 + 49*T^21 + 34*T^20 + 23*T^19 + 78*T^18 + 44*T^17 + 60*T^16 + 51*T^15 + 39*T^14 + 59*T^13 + 21*T^12 + 32*T^11 + 25*T^10 + 43*T^9 + 34*T^8 + 78*T^7 + 39*T^6 + 62*T^5 + 74*T^3 + 32*T^2 + 27*T + 60
Forming extension L.
Time: 0.000
L =  Univariate Quotient Polynomial Algebra in w over Univariate Quotient Polynomial Algebra in z over Finite field of size 89
with modulus z^36 + z^35 + z^34 + z^33 + z^32 + z^31 + z^30 + z^29 + z^28 + z^27 + z^26 + z^25 + z^24 + z^23 + z^22 + z^21 + z^20 + z^19 + z^18 + z^17 + z^16 + z^15 + z^14 + z^13 + z^12 + z^11 + z^10 + z^9 + z^8 + z^7 + z^6 + z^5 + z^4 + z^3 + z^2 + z + 1
with modulus w^37 + 40*z^35 + z^34 + 21*z^33 + 3*z^32 + 3*z^30 + 35*z^29 + 77*z^27 + 35*z^26 + 40*z^25 + 21*z^24 + 77*z^23 + 32*z^22 + 32*z^21 + z^19 + z^18 + 32*z^16 + 32*z^15 + 77*z^14 + 21*z^13 + 40*z^12 + 35*z^11 + 77*z^10 + 35*z^8 + 3*z^7 + 3*z^5 + 21*z^4 + z^3 + 40*z^2 + 63
Computing trace of random element (alpha = w
)
34 steps: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, Time: 0.240

Finished computing trace of random element.
Computing minimal polynomial of trace(alpha), as an element of K[X]
Time: 1.180
f =  X^37 + 66*X^34 + 29*X^33 + 4*X^32 + 5*X^31 + 2*X^30 + 46*X^29 + 69*X^28 + 55*X^27 + 47*X^26 + 79*X^25 + 78*X^24 + 2*X^23 + 24*X^22 + 83*X^21 + 64*X^20 + 33*X^19 + 42*X^18 + 80*X^17 + 35*X^16 + 56*X^15 + 42*X^14 + 29*X^13 + 34*X^12 + 2*X^11 + X^10 + 40*X^9 + 47*X^8 + 84*X^7 + 55*X^6 + 16*X^5 + 61*X^4 + 38*X^3 + 31*X^2 + 63*X + 84
g =  T^37 + 66*T^34 + 29*T^33 + 4*T^32 + 5*T^31 + 2*T^30 + 46*T^29 + 69*T^28 + 55*T^27 + 47*T^26 + 79*T^25 + 78*T^24 + 2*T^23 + 24*T^22 + 83*T^21 + 64*T^20 + 33*T^19 + 42*T^18 + 80*T^17 + 35*T^16 + 56*T^15 + 42*T^14 + 29*T^13 + 34*T^12 + 2*T^11 + T^10 + 40*T^9 + 47*T^8 + 84*T^7 + 55*T^6 + 16*T^5 + 61*T^4 + 38*T^3 + 31*T^2 + 63*T + 84
Forming extension L.
Time: 0.000
L =  Univariate Quotient Polynomial Algebra in w over Univariate Quotient Polynomial Algebra in z over Finite field of size 109
with modulus z^36 + z^35 + z^34 + z^33 + z^32 + z^31 + z^30 + z^29 + z^28 + z^27 + z^26 + z^25 + z^24 + z^23 + z^22 + z^21 + z^20 + z^19 + z^18 + z^17 + z^16 + z^15 + z^14 + z^13 + z^12 + z^11 + z^10 + z^9 + z^8 + z^7 + z^6 + z^5 + z^4 + z^3 + z^2 + z + 1
with modulus w^37 + 13*z^35 + 67*z^34 + 106*z^33 + 3*z^32 + 3*z^30 + 11*z^29 + 38*z^28 + 52*z^27 + 11*z^26 + 13*z^25 + 106*z^24 + 52*z^23 + 74*z^22 + 74*z^21 + 38*z^20 + 67*z^19 + 67*z^18 + 38*z^17 + 74*z^16 + 74*z^15 + 52*z^14 + 106*z^13 + 13*z^12 + 11*z^11 + 52*z^10 + 38*z^9 + 11*z^8 + 3*z^7 + 3*z^5 + 106*z^4 + 67*z^3 + 13*z^2 + 22
Computing trace of random element (alpha = w
)
34 steps: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, Time: 0.110

Finished computing trace of random element.
Computing minimal polynomial of trace(alpha), as an element of K[X]
Time: 0.930
f =  X^37 + 63*X^34 + 8*X^33 + 40*X^32 + 100*X^31 + 67*X^30 + 89*X^29 + 20*X^28 + 80*X^27 + 66*X^26 + X^25 + 56*X^24 + 103*X^23 + 6*X^22 + 15*X^21 + 30*X^20 + 91*X^19 + 11*X^18 + 69*X^17 + 64*X^16 + 26*X^15 + 19*X^14 + 2*X^13 + 43*X^12 + 68*X^11 + 67*X^10 + 83*X^9 + 41*X^8 + 38*X^7 + 27*X^6 + 38*X^5 + 81*X^4 + 3*X^3 + X^2 + 75*X + 33
g =  T^37 + 63*T^34 + 8*T^33 + 40*T^32 + 100*T^31 + 67*T^30 + 89*T^29 + 20*T^28 + 80*T^27 + 66*T^26 + T^25 + 56*T^24 + 103*T^23 + 6*T^22 + 15*T^21 + 30*T^20 + 91*T^19 + 11*T^18 + 69*T^17 + 64*T^16 + 26*T^15 + 19*T^14 + 2*T^13 + 43*T^12 + 68*T^11 + 67*T^10 + 83*T^9 + 41*T^8 + 38*T^7 + 27*T^6 + 38*T^5 + 81*T^4 + 3*T^3 + T^2 + 75*T + 33
Forming extension L.
Time: 0.000
L =  Univariate Quotient Polynomial Algebra in w over Univariate Quotient Polynomial Algebra in z over Finite field of size 113
with modulus z^36 + z^35 + z^34 + z^33 + z^32 + z^31 + z^30 + z^29 + z^28 + z^27 + z^26 + z^25 + z^24 + z^23 + z^22 + z^21 + z^20 + z^19 + z^18 + z^17 + z^16 + z^15 + z^14 + z^13 + z^12 + z^11 + z^10 + z^9 + z^8 + z^7 + z^6 + z^5 + z^4 + z^3 + z^2 + z + 1
with modulus w^37 + 58*z^35 + 24*z^34 + 91*z^33 + 49*z^32 + 49*z^30 + 86*z^29 + 102*z^28 + 56*z^27 + 86*z^26 + 58*z^25 + 91*z^24 + 56*z^23 + 56*z^22 + 56*z^21 + 102*z^20 + 24*z^19 + 24*z^18 + 102*z^17 + 56*z^16 + 56*z^15 + 56*z^14 + 91*z^13 + 58*z^12 + 86*z^11 + 56*z^10 + 102*z^9 + 86*z^8 + 49*z^7 + 49*z^5 + 91*z^4 + 24*z^3 + 58*z^2 + 90
Computing trace of random element (alpha = w
)
34 steps: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, Time: 0.100

Finished computing trace of random element.
Computing minimal polynomial of trace(alpha), as an element of K[X]
Time: 0.920
f =  X^37 + 17*X^34 + 53*X^33 + 61*X^32 + 67*X^31 + 73*X^30 + 66*X^29 + 92*X^28 + 28*X^27 + 46*X^26 + 40*X^25 + 75*X^24 + X^23 + 58*X^22 + 3*X^21 + 20*X^20 + 63*X^19 + 63*X^18 + 100*X^17 + 55*X^16 + 7*X^15 + 81*X^14 + 86*X^13 + 87*X^12 + 99*X^11 + 79*X^10 + 74*X^9 + 23*X^8 + 100*X^7 + 109*X^6 + 89*X^5 + 75*X^4 + 95*X^3 + 81*X^2 + 22*X + 73
g =  T^37 + 17*T^34 + 53*T^33 + 61*T^32 + 67*T^31 + 73*T^30 + 66*T^29 + 92*T^28 + 28*T^27 + 46*T^26 + 40*T^25 + 75*T^24 + T^23 + 58*T^22 + 3*T^21 + 20*T^20 + 63*T^19 + 63*T^18 + 100*T^17 + 55*T^16 + 7*T^15 + 81*T^14 + 86*T^13 + 87*T^12 + 99*T^11 + 79*T^10 + 74*T^9 + 23*T^8 + 100*T^7 + 109*T^6 + 89*T^5 + 75*T^4 + 95*T^3 + 81*T^2 + 22*T + 73
Forming extension L.
Time: 0.000
L =  Univariate Quotient Polynomial Algebra in w over Univariate Quotient Polynomial Algebra in z over Finite field of size 131
with modulus z^36 + z^35 + z^34 + z^33 + z^32 + z^31 + z^30 + z^29 + z^28 + z^27 + z^26 + z^25 + z^24 + z^23 + z^22 + z^21 + z^20 + z^19 + z^18 + z^17 + z^16 + z^15 + z^14 + z^13 + z^12 + z^11 + z^10 + z^9 + z^8 + z^7 + z^6 + z^5 + z^4 + z^3 + z^2 + z + 1
with modulus w^37 + 83*z^35 + 70*z^34 + 100*z^33 + 61*z^32 + 61*z^30 + 90*z^29 + 102*z^28 + 100*z^27 + 90*z^26 + 83*z^25 + 100*z^24 + 100*z^23 + 16*z^22 + 16*z^21 + 102*z^20 + 70*z^19 + 70*z^18 + 102*z^17 + 16*z^16 + 16*z^15 + 100*z^14 + 100*z^13 + 83*z^12 + 90*z^11 + 100*z^10 + 102*z^9 + 90*z^8 + 61*z^7 + 61*z^5 + 100*z^4 + 70*z^3 + 83*z^2 + 48
Computing trace of random element (alpha = w
)
34 steps: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, Time: 0.110

Finished computing trace of random element.
Computing minimal polynomial of trace(alpha), as an element of K[X]
Time: 0.950
f =  X^37 + 130*X^34 + 104*X^33 + 36*X^32 + 64*X^31 + 42*X^30 + 130*X^29 + 96*X^28 + 32*X^27 + 86*X^26 + 72*X^25 + 86*X^24 + 3*X^23 + 58*X^22 + 113*X^21 + X^20 + 11*X^19 + 13*X^18 + 41*X^17 + 119*X^16 + 24*X^15 + 106*X^14 + 99*X^13 + 113*X^12 + 107*X^11 + 7*X^10 + 90*X^9 + 33*X^8 + 103*X^7 + 74*X^6 + 49*X^5 + 88*X^4 + 10*X^3 + 40*X^2 + 118*X + 123
g =  T^37 + 130*T^34 + 104*T^33 + 36*T^32 + 64*T^31 + 42*T^30 + 130*T^29 + 96*T^28 + 32*T^27 + 86*T^26 + 72*T^25 + 86*T^24 + 3*T^23 + 58*T^22 + 113*T^21 + T^20 + 11*T^19 + 13*T^18 + 41*T^17 + 119*T^16 + 24*T^15 + 106*T^14 + 99*T^13 + 113*T^12 + 107*T^11 + 7*T^10 + 90*T^9 + 33*T^8 + 103*T^7 + 74*T^6 + 49*T^5 + 88*T^4 + 10*T^3 + 40*T^2 + 118*T + 123
CRT step --  7.381
So far:   [ -80836533286084697, 66975563345854857, 11386057713100772, -71805543500898880, -17719410116834202, -85606231403767368, -81015051182520668, -28049887250629581, 54808687005980427, -17903549832058169, 82545037454991174, -40280302088041351, -60413319556376730, 31306766626319811, -34924345508252449, 81856318539096058, -64127040240441591, -82701333283509215, 84917620727847933, -45619682822865711, 62947702402846571, 16391888204680362, 68382141997723193, -17342592435595375, 69744392611215208, -6953203077586616, 63129662250715074, -40796532230514306, 71847730592145342, 8296194355663598, -39812753188183955, -7894900273815552, -123335506765824, -118234637824, -6483584, 0, 0, 1 ]
Forming extension L.
Time: 0.000
L =  Univariate Quotient Polynomial Algebra in w over Univariate Quotient Polynomial Algebra in z over Finite field of size 163
with modulus z^36 + z^35 + z^34 + z^33 + z^32 + z^31 + z^30 + z^29 + z^28 + z^27 + z^26 + z^25 + z^24 + z^23 + z^22 + z^21 + z^20 + z^19 + z^18 + z^17 + z^16 + z^15 + z^14 + z^13 + z^12 + z^11 + z^10 + z^9 + z^8 + z^7 + z^6 + z^5 + z^4 + z^3 + z^2 + z + 1
with modulus w^37 + 135*z^35 + 143*z^34 + 37*z^33 + 144*z^32 + 144*z^30 + 27*z^29 + 139*z^27 + 27*z^26 + 135*z^25 + 37*z^24 + 139*z^23 + 109*z^22 + 109*z^21 + 143*z^19 + 143*z^18 + 109*z^16 + 109*z^15 + 139*z^14 + 37*z^13 + 135*z^12 + 27*z^11 + 139*z^10 + 27*z^8 + 144*z^7 + 144*z^5 + 37*z^4 + 143*z^3 + 135*z^2 + 59
Computing trace of random element (alpha = w
)
34 steps: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, Time: 0.110

Finished computing trace of random element.
Computing minimal polynomial of trace(alpha), as an element of K[X]
Time: 0.950
f =  X^37 + 67*X^34 + 127*X^33 + 69*X^32 + 100*X^31 + 58*X^30 + 160*X^29 + 40*X^28 + 2*X^27 + 89*X^26 + 112*X^25 + 9*X^24 + 25*X^23 + 9*X^22 + 131*X^21 + 74*X^20 + 17*X^19 + 97*X^18 + X^17 + 64*X^16 + 76*X^15 + 16*X^14 + 41*X^13 + 78*X^12 + 132*X^11 + 43*X^10 + 7*X^9 + 135*X^8 + 96*X^7 + 25*X^6 + 76*X^5 + 9*X^4 + 148*X^3 + 158*X^2 + 18*X + 123
g =  T^37 + 67*T^34 + 127*T^33 + 69*T^32 + 100*T^31 + 58*T^30 + 160*T^29 + 40*T^28 + 2*T^27 + 89*T^26 + 112*T^25 + 9*T^24 + 25*T^23 + 9*T^22 + 131*T^21 + 74*T^20 + 17*T^19 + 97*T^18 + T^17 + 64*T^16 + 76*T^15 + 16*T^14 + 41*T^13 + 78*T^12 + 132*T^11 + 43*T^10 + 7*T^9 + 135*T^8 + 96*T^7 + 25*T^6 + 76*T^5 + 9*T^4 + 148*T^3 + 158*T^2 + 18*T + 123
Forming extension L.
Time: 0.000
L =  Univariate Quotient Polynomial Algebra in w over Univariate Quotient Polynomial Algebra in z over Finite field of size 167
with modulus z^36 + z^35 + z^34 + z^33 + z^32 + z^31 + z^30 + z^29 + z^28 + z^27 + z^26 + z^25 + z^24 + z^23 + z^22 + z^21 + z^20 + z^19 + z^18 + z^17 + z^16 + z^15 + z^14 + z^13 + z^12 + z^11 + z^10 + z^9 + z^8 + z^7 + z^6 + z^5 + z^4 + z^3 + z^2 + z + 1
with modulus w^37 + 145*z^35 + 102*z^34 + 66*z^33 + 11*z^32 + 11*z^30 + 165*z^29 + 19*z^28 + 16*z^27 + 165*z^26 + 145*z^25 + 66*z^24 + 16*z^23 + 79*z^22 + 79*z^21 + 19*z^20 + 102*z^19 + 102*z^18 + 19*z^17 + 79*z^16 + 79*z^15 + 16*z^14 + 66*z^13 + 145*z^12 + 165*z^11 + 16*z^10 + 19*z^9 + 165*z^8 + 11*z^7 + 11*z^5 + 66*z^4 + 102*z^3 + 145*z^2 + 21
Computing trace of random element (alpha = w
)
34 steps: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, Time: 0.100

Finished computing trace of random element.
Computing minimal polynomial of trace(alpha), as an element of K[X]
Time: 0.950
f =  X^37 + 24*X^34 + 124*X^33 + 62*X^32 + 120*X^31 + 36*X^30 + 127*X^29 + 41*X^28 + 87*X^27 + 52*X^26 + 57*X^25 + 94*X^24 + 126*X^23 + 10*X^22 + 139*X^21 + 127*X^20 + 118*X^19 + 63*X^18 + 55*X^17 + 121*X^16 + 87*X^15 + 166*X^14 + 133*X^13 + 14*X^12 + 78*X^11 + 110*X^10 + 14*X^9 + 150*X^8 + 130*X^7 + 27*X^6 + 42*X^5 + 17*X^4 + 164*X^3 + 79*X^2 + 92*X + 134
g =  T^37 + 24*T^34 + 124*T^33 + 62*T^32 + 120*T^31 + 36*T^30 + 127*T^29 + 41*T^28 + 87*T^27 + 52*T^26 + 57*T^25 + 94*T^24 + 126*T^23 + 10*T^22 + 139*T^21 + 127*T^20 + 118*T^19 + 63*T^18 + 55*T^17 + 121*T^16 + 87*T^15 + 166*T^14 + 133*T^13 + 14*T^12 + 78*T^11 + 110*T^10 + 14*T^9 + 150*T^8 + 130*T^7 + 27*T^6 + 42*T^5 + 17*T^4 + 164*T^3 + 79*T^2 + 92*T + 134
Forming extension L.
Time: 0.000
L =  Univariate Quotient Polynomial Algebra in w over Univariate Quotient Polynomial Algebra in z over Finite field of size 227
with modulus z^36 + z^35 + z^34 + z^33 + z^32 + z^31 + z^30 + z^29 + z^28 + z^27 + z^26 + z^25 + z^24 + z^23 + z^22 + z^21 + z^20 + z^19 + z^18 + z^17 + z^16 + z^15 + z^14 + z^13 + z^12 + z^11 + z^10 + z^9 + z^8 + z^7 + z^6 + z^5 + z^4 + z^3 + z^2 + z + 1
with modulus w^37 + 108*z^35 + 206*z^34 + 5*z^33 + 190*z^32 + 190*z^30 + 31*z^29 + 143*z^28 + 142*z^27 + 31*z^26 + 108*z^25 + 5*z^24 + 142*z^23 + 185*z^22 + 185*z^21 + 143*z^20 + 206*z^19 + 206*z^18 + 143*z^17 + 185*z^16 + 185*z^15 + 142*z^14 + 5*z^13 + 108*z^12 + 31*z^11 + 142*z^10 + 143*z^9 + 31*z^8 + 190*z^7 + 190*z^5 + 5*z^4 + 206*z^3 + 108*z^2 + 74
Computing trace of random element (alpha = w
)
34 steps: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, Time: 0.130

Finished computing trace of random element.
Computing minimal polynomial of trace(alpha), as an element of K[X]
Time: 0.960
f =  X^37 + 217*X^34 + 148*X^33 + 2*X^32 + 15*X^31 + 133*X^30 + 138*X^29 + 192*X^28 + 8*X^27 + 124*X^26 + 218*X^25 + 79*X^24 + 199*X^23 + 99*X^22 + 193*X^21 + 212*X^20 + 185*X^19 + 226*X^18 + 112*X^17 + 144*X^16 + 22*X^15 + 171*X^14 + 98*X^13 + 213*X^12 + 208*X^11 + 13*X^10 + 150*X^9 + 191*X^8 + 126*X^7 + 93*X^6 + 74*X^5 + 57*X^4 + 197*X^3 + 203*X^2 + 59*X + 101
g =  T^37 + 217*T^34 + 148*T^33 + 2*T^32 + 15*T^31 + 133*T^30 + 138*T^29 + 192*T^28 + 8*T^27 + 124*T^26 + 218*T^25 + 79*T^24 + 199*T^23 + 99*T^22 + 193*T^21 + 212*T^20 + 185*T^19 + 226*T^18 + 112*T^17 + 144*T^16 + 22*T^15 + 171*T^14 + 98*T^13 + 213*T^12 + 208*T^11 + 13*T^10 + 150*T^9 + 191*T^8 + 126*T^7 + 93*T^6 + 74*T^5 + 57*T^4 + 197*T^3 + 203*T^2 + 59*T + 101
Forming extension L.
Time: 0.000
L =  Univariate Quotient Polynomial Algebra in w over Univariate Quotient Polynomial Algebra in z over Finite field of size 239
with modulus z^36 + z^35 + z^34 + z^33 + z^32 + z^31 + z^30 + z^29 + z^28 + z^27 + z^26 + z^25 + z^24 + z^23 + z^22 + z^21 + z^20 + z^19 + z^18 + z^17 + z^16 + z^15 + z^14 + z^13 + z^12 + z^11 + z^10 + z^9 + z^8 + z^7 + z^6 + z^5 + z^4 + z^3 + z^2 + z + 1
with modulus w^37 + 45*z^35 + 181*z^34 + 168*z^33 + 85*z^32 + 85*z^30 + 39*z^29 + 137*z^28 + 186*z^27 + 39*z^26 + 45*z^25 + 168*z^24 + 186*z^23 + 38*z^22 + 38*z^21 + 137*z^20 + 181*z^19 + 181*z^18 + 137*z^17 + 38*z^16 + 38*z^15 + 186*z^14 + 168*z^13 + 45*z^12 + 39*z^11 + 186*z^10 + 137*z^9 + 39*z^8 + 85*z^7 + 85*z^5 + 168*z^4 + 181*z^3 + 45*z^2 + 114
Computing trace of random element (alpha = w
)
34 steps: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, Time: 0.120

Finished computing trace of random element.
Computing minimal polynomial of trace(alpha), as an element of K[X]
Time: 0.970
f =  X^37 + 8*X^34 + 98*X^33 + 72*X^32 + 190*X^31 + 21*X^30 + 183*X^29 + 132*X^28 + 79*X^27 + 226*X^26 + 131*X^25 + 224*X^24 + 135*X^23 + 142*X^22 + 121*X^21 + 94*X^20 + 100*X^19 + 154*X^18 + 37*X^17 + 109*X^16 + 110*X^15 + 76*X^14 + 210*X^13 + 211*X^12 + 176*X^11 + 64*X^10 + 235*X^9 + 75*X^8 + 62*X^7 + 176*X^6 + 137*X^5 + 7*X^4 + 81*X^3 + 43*X^2 + 163*X + 87
g =  T^37 + 8*T^34 + 98*T^33 + 72*T^32 + 190*T^31 + 21*T^30 + 183*T^29 + 132*T^28 + 79*T^27 + 226*T^26 + 131*T^25 + 224*T^24 + 135*T^23 + 142*T^22 + 121*T^21 + 94*T^20 + 100*T^19 + 154*T^18 + 37*T^17 + 109*T^16 + 110*T^15 + 76*T^14 + 210*T^13 + 211*T^12 + 176*T^11 + 64*T^10 + 235*T^9 + 75*T^8 + 62*T^7 + 176*T^6 + 137*T^5 + 7*T^4 + 81*T^3 + 43*T^2 + 163*T + 87
Forming extension L.
Time: 0.000
L =  Univariate Quotient Polynomial Algebra in w over Univariate Quotient Polynomial Algebra in z over Finite field of size 241
with modulus z^36 + z^35 + z^34 + z^33 + z^32 + z^31 + z^30 + z^29 + z^28 + z^27 + z^26 + z^25 + z^24 + z^23 + z^22 + z^21 + z^20 + z^19 + z^18 + z^17 + z^16 + z^15 + z^14 + z^13 + z^12 + z^11 + z^10 + z^9 + z^8 + z^7 + z^6 + z^5 + z^4 + z^3 + z^2 + z + 1
with modulus w^37 + 164*z^35 + 200*z^34 + 180*z^33 + 222*z^32 + 222*z^30 + 109*z^29 + 229*z^28 + 95*z^27 + 109*z^26 + 164*z^25 + 180*z^24 + 95*z^23 + 23*z^22 + 23*z^21 + 229*z^20 + 200*z^19 + 200*z^18 + 229*z^17 + 23*z^16 + 23*z^15 + 95*z^14 + 180*z^13 + 164*z^12 + 109*z^11 + 95*z^10 + 229*z^9 + 109*z^8 + 222*z^7 + 222*z^5 + 180*z^4 + 200*z^3 + 164*z^2 + 126
Computing trace of random element (alpha = w
)
34 steps: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, Time: 0.080

Finished computing trace of random element.
Computing minimal polynomial of trace(alpha), as an element of K[X]
Time: 1.080
f =  X^37 + 39*X^34 + 13*X^33 + 16*X^32 + 38*X^31 + 89*X^30 + 22*X^29 + 16*X^28 + 152*X^27 + 100*X^26 + 103*X^25 + 124*X^24 + 163*X^23 + 175*X^22 + 232*X^21 + 196*X^20 + 109*X^19 + 132*X^18 + 173*X^17 + 156*X^16 + 84*X^15 + 107*X^14 + 83*X^13 + 59*X^12 + 200*X^11 + 66*X^10 + 78*X^9 + 215*X^8 + 215*X^7 + 153*X^6 + 176*X^5 + 144*X^4 + 27*X^3 + 39*X^2 + 235*X + 195
g =  T^37 + 39*T^34 + 13*T^33 + 16*T^32 + 38*T^31 + 89*T^30 + 22*T^29 + 16*T^28 + 152*T^27 + 100*T^26 + 103*T^25 + 124*T^24 + 163*T^23 + 175*T^22 + 232*T^21 + 196*T^20 + 109*T^19 + 132*T^18 + 173*T^17 + 156*T^16 + 84*T^15 + 107*T^14 + 83*T^13 + 59*T^12 + 200*T^11 + 66*T^10 + 78*T^9 + 215*T^8 + 215*T^7 + 153*T^6 + 176*T^5 + 144*T^4 + 27*T^3 + 39*T^2 + 235*T + 195
CRT step --  5.609
So far:   [ -17333804602389517722935223877, -563344211769880560547153803, -21414491000108207211865706220, -20617423538934842227684506401, -30197371353541307192817415470, -21195335327830830073273480148, -9075910991752992354531156221, -16545935079877558747115667969, 8140668110927212171260744977, 29005970811849012047343187970, -1522920495316332571426126512, 23877373216837475058552417357, -3317765599056758988164339256, 8635689714790290578150665840, 26942973820484439584131104162, 28565693170580777300824837605, 168973487006204869456419110, -28032581057462368300424006082, -8317172036590254822944556065, -17564704593385090887096527138, 14727410229375576758663272516, -6987157832237765045872476523, -15785465102497719342986528890, 1787570166600297610489162607, -4847332633054888656328495493, -20948472909143855749034147247, 14798699041715499710671432887, 27391104695281881340835547929, -2221784070205669762924544, -19612786666813992009728, -25584896141781024768, -7894900273815552, -123335506765824, -118234637824, -6483584, 0, 0, 1 ]
Forming extension L.
Time: 0.000
L =  Univariate Quotient Polynomial Algebra in w over Univariate Quotient Polynomial Algebra in z over Finite field of size 257
with modulus z^36 + z^35 + z^34 + z^33 + z^32 + z^31 + z^30 + z^29 + z^28 + z^27 + z^26 + z^25 + z^24 + z^23 + z^22 + z^21 + z^20 + z^19 + z^18 + z^17 + z^16 + z^15 + z^14 + z^13 + z^12 + z^11 + z^10 + z^9 + z^8 + z^7 + z^6 + z^5 + z^4 + z^3 + z^2 + z + 1
with modulus w^37 + 146*z^35 + 43*z^34 + 21*z^33 + 172*z^32 + 172*z^30 + 200*z^29 + 103*z^28 + 92*z^27 + 200*z^26 + 146*z^25 + 21*z^24 + 92*z^23 + 24*z^22 + 24*z^21 + 103*z^20 + 43*z^19 + 43*z^18 + 103*z^17 + 24*z^16 + 24*z^15 + 92*z^14 + 21*z^13 + 146*z^12 + 200*z^11 + 92*z^10 + 103*z^9 + 200*z^8 + 172*z^7 + 172*z^5 + 21*z^4 + 43*z^3 + 146*z^2 + 180
Computing trace of random element (alpha = w
)
34 steps: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, Time: 0.110

Finished computing trace of random element.
Computing minimal polynomial of trace(alpha), as an element of K[X]
Time: 1.080
f =  X^37 + 12*X^34 + 125*X^33 + 35*X^32 + 141*X^31 + 201*X^30 + 205*X^29 + 47*X^28 + 216*X^27 + 188*X^26 + 234*X^25 + 26*X^24 + 72*X^23 + 113*X^22 + 239*X^21 + 39*X^20 + 230*X^19 + 143*X^18 + 141*X^17 + 124*X^16 + 120*X^15 + 48*X^14 + 131*X^13 + 105*X^12 + 96*X^11 + 200*X^10 + 206*X^9 + 110*X^8 + 231*X^7 + 234*X^6 + 252*X^5 + 228*X^4 + 96*X^3 + 106*X^2 + 47*X + 100
g =  T^37 + 12*T^34 + 125*T^33 + 35*T^32 + 141*T^31 + 201*T^30 + 205*T^29 + 47*T^28 + 216*T^27 + 188*T^26 + 234*T^25 + 26*T^24 + 72*T^23 + 113*T^22 + 239*T^21 + 39*T^20 + 230*T^19 + 143*T^18 + 141*T^17 + 124*T^16 + 120*T^15 + 48*T^14 + 131*T^13 + 105*T^12 + 96*T^11 + 200*T^10 + 206*T^9 + 110*T^8 + 231*T^7 + 234*T^6 + 252*T^5 + 228*T^4 + 96*T^3 + 106*T^2 + 47*T + 100
Forming extension L.
Time: 0.000
L =  Univariate Quotient Polynomial Algebra in w over Univariate Quotient Polynomial Algebra in z over Finite field of size 277
with modulus z^36 + z^35 + z^34 + z^33 + z^32 + z^31 + z^30 + z^29 + z^28 + z^27 + z^26 + z^25 + z^24 + z^23 + z^22 + z^21 + z^20 + z^19 + z^18 + z^17 + z^16 + z^15 + z^14 + z^13 + z^12 + z^11 + z^10 + z^9 + z^8 + z^7 + z^6 + z^5 + z^4 + z^3 + z^2 + z + 1
with modulus w^37 + 17*z^35 + 271*z^34 + 155*z^33 + 202*z^32 + 202*z^30 + 34*z^29 + 255*z^28 + 19*z^27 + 34*z^26 + 17*z^25 + 155*z^24 + 19*z^23 + 172*z^22 + 172*z^21 + 255*z^20 + 271*z^19 + 271*z^18 + 255*z^17 + 172*z^16 + 172*z^15 + 19*z^14 + 155*z^13 + 17*z^12 + 34*z^11 + 19*z^10 + 255*z^9 + 34*z^8 + 202*z^7 + 202*z^5 + 155*z^4 + 271*z^3 + 17*z^2 + 20
Computing trace of random element (alpha = w
)
34 steps: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, Time: 0.090

Finished computing trace of random element.
Computing minimal polynomial of trace(alpha), as an element of K[X]
Time: 1.060
f =  X^37 + 155*X^34 + 72*X^33 + 73*X^32 + 250*X^31 + 84*X^30 + 111*X^29 + 170*X^28 + 73*X^27 + 186*X^26 + 62*X^25 + 150*X^24 + 172*X^23 + 96*X^22 + 212*X^21 + 170*X^20 + 92*X^19 + 53*X^18 + 240*X^17 + 7*X^16 + 270*X^15 + 53*X^14 + 200*X^13 + 139*X^12 + 113*X^11 + 172*X^10 + 216*X^9 + 158*X^8 + 219*X^7 + 275*X^6 + 58*X^5 + 255*X^4 + 142*X^3 + 129*X^2 + 108*X + 263
g =  T^37 + 155*T^34 + 72*T^33 + 73*T^32 + 250*T^31 + 84*T^30 + 111*T^29 + 170*T^28 + 73*T^27 + 186*T^26 + 62*T^25 + 150*T^24 + 172*T^23 + 96*T^22 + 212*T^21 + 170*T^20 + 92*T^19 + 53*T^18 + 240*T^17 + 7*T^16 + 270*T^15 + 53*T^14 + 200*T^13 + 139*T^12 + 113*T^11 + 172*T^10 + 216*T^9 + 158*T^8 + 219*T^7 + 275*T^6 + 58*T^5 + 255*T^4 + 142*T^3 + 129*T^2 + 108*T + 263
Forming extension L.
Time: 0.000
L =  Univariate Quotient Polynomial Algebra in w over Univariate Quotient Polynomial Algebra in z over Finite field of size 281
with modulus z^36 + z^35 + z^34 + z^33 + z^32 + z^31 + z^30 + z^29 + z^28 + z^27 + z^26 + z^25 + z^24 + z^23 + z^22 + z^21 + z^20 + z^19 + z^18 + z^17 + z^16 + z^15 + z^14 + z^13 + z^12 + z^11 + z^10 + z^9 + z^8 + z^7 + z^6 + z^5 + z^4 + z^3 + z^2 + z + 1
with modulus w^37 + 166*z^35 + 40*z^34 + 158*z^33 + 280*z^32 + 280*z^30 + 242*z^29 + 49*z^28 + 8*z^27 + 242*z^26 + 166*z^25 + 158*z^24 + 8*z^23 + 259*z^22 + 259*z^21 + 49*z^20 + 40*z^19 + 40*z^18 + 49*z^17 + 259*z^16 + 259*z^15 + 8*z^14 + 158*z^13 + 166*z^12 + 242*z^11 + 8*z^10 + 49*z^9 + 242*z^8 + 280*z^7 + 280*z^5 + 158*z^4 + 40*z^3 + 166*z^2 + 166
Computing trace of random element (alpha = w
)
34 steps: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, Time: 0.150

Finished computing trace of random element.
Computing minimal polynomial of trace(alpha), as an element of K[X]
Time: 1.060
f =  X^37 + 210*X^34 + 92*X^33 + 161*X^32 + 248*X^31 + 93*X^30 + 52*X^29 + 168*X^28 + 72*X^27 + 244*X^26 + 73*X^25 + 211*X^24 + 133*X^23 + 227*X^22 + 40*X^21 + 225*X^20 + 112*X^19 + 177*X^18 + 179*X^17 + 161*X^16 + 80*X^15 + 124*X^14 + 88*X^13 + 61*X^12 + 108*X^11 + 155*X^10 + 99*X^9 + 263*X^8 + 77*X^7 + 57*X^6 + 156*X^5 + 143*X^4 + 224*X^3 + 199*X^2 + 88*X + 64
g =  T^37 + 210*T^34 + 92*T^33 + 161*T^32 + 248*T^31 + 93*T^30 + 52*T^29 + 168*T^28 + 72*T^27 + 244*T^26 + 73*T^25 + 211*T^24 + 133*T^23 + 227*T^22 + 40*T^21 + 225*T^20 + 112*T^19 + 177*T^18 + 179*T^17 + 161*T^16 + 80*T^15 + 124*T^14 + 88*T^13 + 61*T^12 + 108*T^11 + 155*T^10 + 99*T^9 + 263*T^8 + 77*T^7 + 57*T^6 + 156*T^5 + 143*T^4 + 224*T^3 + 199*T^2 + 88*T + 64
Forming extension L.
Time: 0.000
L =  Univariate Quotient Polynomial Algebra in w over Univariate Quotient Polynomial Algebra in z over Finite field of size 283
with modulus z^36 + z^35 + z^34 + z^33 + z^32 + z^31 + z^30 + z^29 + z^28 + z^27 + z^26 + z^25 + z^24 + z^23 + z^22 + z^21 + z^20 + z^19 + z^18 + z^17 + z^16 + z^15 + z^14 + z^13 + z^12 + z^11 + z^10 + z^9 + z^8 + z^7 + z^6 + z^5 + z^4 + z^3 + z^2 + z + 1
with modulus w^37 + 97*z^35 + 198*z^34 + 109*z^33 + 47*z^32 + 47*z^30 + 10*z^29 + 41*z^28 + 20*z^27 + 10*z^26 + 97*z^25 + 109*z^24 + 20*z^23 + 117*z^22 + 117*z^21 + 41*z^20 + 198*z^19 + 198*z^18 + 41*z^17 + 117*z^16 + 117*z^15 + 20*z^14 + 109*z^13 + 97*z^12 + 10*z^11 + 20*z^10 + 41*z^9 + 10*z^8 + 47*z^7 + 47*z^5 + 109*z^4 + 198*z^3 + 97*z^2 + 158
Computing trace of random element (alpha = w
)
34 steps: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, Time: 0.120

Finished computing trace of random element.
Computing minimal polynomial of trace(alpha), as an element of K[X]
Time: 1.080
f =  X^37 + 229*X^34 + 96*X^33 + 279*X^32 + 157*X^31 + 228*X^30 + 229*X^29 + 39*X^28 + 282*X^27 + 4*X^26 + 126*X^25 + 138*X^24 + 81*X^23 + 114*X^22 + 183*X^21 + 101*X^20 + 193*X^19 + 6*X^18 + 168*X^17 + 210*X^16 + 120*X^15 + 187*X^14 + 32*X^13 + 54*X^12 + 178*X^11 + 28*X^10 + 125*X^9 + 8*X^8 + 9*X^7 + 223*X^6 + 140*X^5 + 40*X^4 + 166*X^3 + 59*X^2 + 118*X + 229
g =  T^37 + 229*T^34 + 96*T^33 + 279*T^32 + 157*T^31 + 228*T^30 + 229*T^29 + 39*T^28 + 282*T^27 + 4*T^26 + 126*T^25 + 138*T^24 + 81*T^23 + 114*T^22 + 183*T^21 + 101*T^20 + 193*T^19 + 6*T^18 + 168*T^17 + 210*T^16 + 120*T^15 + 187*T^14 + 32*T^13 + 54*T^12 + 178*T^11 + 28*T^10 + 125*T^9 + 8*T^8 + 9*T^7 + 223*T^6 + 140*T^5 + 40*T^4 + 166*T^3 + 59*T^2 + 118*T + 229
Forming extension L.
Time: 0.000
L =  Univariate Quotient Polynomial Algebra in w over Univariate Quotient Polynomial Algebra in z over Finite field of size 311
with modulus z^36 + z^35 + z^34 + z^33 + z^32 + z^31 + z^30 + z^29 + z^28 + z^27 + z^26 + z^25 + z^24 + z^23 + z^22 + z^21 + z^20 + z^19 + z^18 + z^17 + z^16 + z^15 + z^14 + z^13 + z^12 + z^11 + z^10 + z^9 + z^8 + z^7 + z^6 + z^5 + z^4 + z^3 + z^2 + z + 1
with modulus w^37 + 247*z^35 + 101*z^34 + 173*z^33 + 165*z^32 + 165*z^30 + 139*z^29 + 183*z^28 + 126*z^27 + 139*z^26 + 247*z^25 + 173*z^24 + 126*z^23 + 246*z^22 + 246*z^21 + 183*z^20 + 101*z^19 + 101*z^18 + 183*z^17 + 246*z^16 + 246*z^15 + 126*z^14 + 173*z^13 + 247*z^12 + 139*z^11 + 126*z^10 + 183*z^9 + 139*z^8 + 165*z^7 + 165*z^5 + 173*z^4 + 101*z^3 + 247*z^2 + 108
Computing trace of random element (alpha = w
)
34 steps: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, Time: 0.120

Finished computing trace of random element.
Computing minimal polynomial of trace(alpha), as an element of K[X]
Time: 1.080
f =  X^37 + 144*X^34 + 211*X^33 + 290*X^32 + 108*X^31 + 104*X^30 + 141*X^29 + 60*X^28 + 305*X^27 + 38*X^26 + 138*X^25 + 10*X^24 + 23*X^23 + 111*X^22 + 111*X^21 + 43*X^20 + 71*X^19 + 199*X^18 + 214*X^17 + 30*X^16 + 125*X^15 + 88*X^14 + 128*X^13 + 76*X^12 + 200*X^11 + 74*X^10 + 272*X^9 + 136*X^8 + 156*X^7 + 137*X^6 + 121*X^5 + 158*X^4 + 83*X^3 + 212*X^2 + 217*X + 33
g =  T^37 + 144*T^34 + 211*T^33 + 290*T^32 + 108*T^31 + 104*T^30 + 141*T^29 + 60*T^28 + 305*T^27 + 38*T^26 + 138*T^25 + 10*T^24 + 23*T^23 + 111*T^22 + 111*T^21 + 43*T^20 + 71*T^19 + 199*T^18 + 214*T^17 + 30*T^16 + 125*T^15 + 88*T^14 + 128*T^13 + 76*T^12 + 200*T^11 + 74*T^10 + 272*T^9 + 136*T^8 + 156*T^7 + 137*T^6 + 121*T^5 + 158*T^4 + 83*T^3 + 212*T^2 + 217*T + 33
CRT step --  6.111
So far:   [ -53094611856159223307416895355870823743433, -50694399744629490579105367204201792411460, -10291359783190481842059024030120033815423, 36932576072632696420777341935171691304330, 33965819674158032041265095229133249816841, -11799891484448211886335462024584390575972, 11498937725190597472577378744238234379031, -33671835863623384437538374408885320986000, -43653345477868980298726541985639435622400, -48880764854360744662849449533747331965369, -28971777296049448487792598296178663766030, 618938235019969414431714537841534589817, -26992318796263667010488409038823196228702, 12125182104303507260162649448308042519198, -9646248485594659675727994480586491617900, 41168803166767947625094918960196229687637, -17485245094372070393289080980330810783113, -12427979606936056771272370080957166462763, 1533258113986381204606371195456544992297, 28214929869904264585589393213777068229080, 9516802532259256827500248347495168444789, -51774382193476812748347140457217447374908, 46532997435075497705371944123250938106620, -3171787436319383501703813676940597919744, -13099755496539209311468832290825568256, -2249002615426863992005848511545344, -4805711697609190244214712041472, -33628014249666292632903483392, -2221784070205669762924544, -19612786666813992009728, -25584896141781024768, -7894900273815552, -123335506765824, -118234637824, -6483584, 0, 0, 1 ]
Forming extension L.
Time: 0.000
L =  Univariate Quotient Polynomial Algebra in w over Univariate Quotient Polynomial Algebra in z over Finite field of size 313
with modulus z^36 + z^35 + z^34 + z^33 + z^32 + z^31 + z^30 + z^29 + z^28 + z^27 + z^26 + z^25 + z^24 + z^23 + z^22 + z^21 + z^20 + z^19 + z^18 + z^17 + z^16 + z^15 + z^14 + z^13 + z^12 + z^11 + z^10 + z^9 + z^8 + z^7 + z^6 + z^5 + z^4 + z^3 + z^2 + z + 1
with modulus w^37 + 264*z^35 + 306*z^34 + 129*z^33 + 306*z^32 + 306*z^30 + 298*z^29 + 200*z^28 + 100*z^27 + 298*z^26 + 264*z^25 + 129*z^24 + 100*z^23 + 290*z^22 + 290*z^21 + 200*z^20 + 306*z^19 + 306*z^18 + 200*z^17 + 290*z^16 + 290*z^15 + 100*z^14 + 129*z^13 + 264*z^12 + 298*z^11 + 100*z^10 + 200*z^9 + 298*z^8 + 306*z^7 + 306*z^5 + 129*z^4 + 306*z^3 + 264*z^2 + 213
Computing trace of random element (alpha = w
)
34 steps: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, Time: 0.110

Finished computing trace of random element.
Computing minimal polynomial of trace(alpha), as an element of K[X]
Time: 1.080
f =  X^37 + 211*X^34 + 87*X^33 + 167*X^32 + 269*X^31 + 245*X^30 + 253*X^29 + 192*X^28 + 300*X^27 + 283*X^26 + 75*X^25 + 297*X^24 + 199*X^23 + 230*X^22 + 184*X^21 + 248*X^20 + 210*X^19 + 182*X^18 + 139*X^17 + 259*X^16 + 43*X^15 + 223*X^14 + 115*X^13 + 310*X^12 + 167*X^11 + 159*X^10 + 202*X^9 + 43*X^8 + 114*X^7 + 265*X^6 + 95*X^5 + 18*X^4 + 276*X^3 + 115*X^2 + 2*X + 139
g =  T^37 + 211*T^34 + 87*T^33 + 167*T^32 + 269*T^31 + 245*T^30 + 253*T^29 + 192*T^28 + 300*T^27 + 283*T^26 + 75*T^25 + 297*T^24 + 199*T^23 + 230*T^22 + 184*T^21 + 248*T^20 + 210*T^19 + 182*T^18 + 139*T^17 + 259*T^16 + 43*T^15 + 223*T^14 + 115*T^13 + 310*T^12 + 167*T^11 + 159*T^10 + 202*T^9 + 43*T^8 + 114*T^7 + 265*T^6 + 95*T^5 + 18*T^4 + 276*T^3 + 115*T^2 + 2*T + 139
Forming extension L.
Time: 0.000
L =  Univariate Quotient Polynomial Algebra in w over Univariate Quotient Polynomial Algebra in z over Finite field of size 331
with modulus z^36 + z^35 + z^34 + z^33 + z^32 + z^31 + z^30 + z^29 + z^28 + z^27 + z^26 + z^25 + z^24 + z^23 + z^22 + z^21 + z^20 + z^19 + z^18 + z^17 + z^16 + z^15 + z^14 + z^13 + z^12 + z^11 + z^10 + z^9 + z^8 + z^7 + z^6 + z^5 + z^4 + z^3 + z^2 + z + 1
with modulus w^37 + 226*z^35 + 265*z^34 + 122*z^33 + 317*z^32 + 317*z^30 + 272*z^29 + 3*z^28 + 69*z^27 + 272*z^26 + 226*z^25 + 122*z^24 + 69*z^23 + 136*z^22 + 136*z^21 + 3*z^20 + 265*z^19 + 265*z^18 + 3*z^17 + 136*z^16 + 136*z^15 + 69*z^14 + 122*z^13 + 226*z^12 + 272*z^11 + 69*z^10 + 3*z^9 + 272*z^8 + 317*z^7 + 317*z^5 + 122*z^4 + 265*z^3 + 226*z^2 + 1
Computing trace of random element (alpha = w
)
34 steps: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, Time: 0.120

Finished computing trace of random element.
Computing minimal polynomial of trace(alpha), as an element of K[X]
Time: 1.070
f =  X^37 + 44*X^34 + 40*X^33 + 22*X^32 + 246*X^31 + 247*X^30 + 292*X^29 + 218*X^28 + 116*X^27 + 105*X^26 + 83*X^25 + 26*X^24 + 203*X^23 + 143*X^22 + 112*X^21 + 227*X^20 + 158*X^19 + 241*X^18 + 54*X^17 + 320*X^16 + 186*X^15 + 28*X^14 + 323*X^13 + 280*X^12 + 282*X^11 + 316*X^10 + 4*X^9 + 224*X^8 + 263*X^7 + 274*X^6 + 314*X^5 + 273*X^4 + 63*X^3 + 2*X^2 + 208*X + 258
g =  T^37 + 44*T^34 + 40*T^33 + 22*T^32 + 246*T^31 + 247*T^30 + 292*T^29 + 218*T^28 + 116*T^27 + 105*T^26 + 83*T^25 + 26*T^24 + 203*T^23 + 143*T^22 + 112*T^21 + 227*T^20 + 158*T^19 + 241*T^18 + 54*T^17 + 320*T^16 + 186*T^15 + 28*T^14 + 323*T^13 + 280*T^12 + 282*T^11 + 316*T^10 + 4*T^9 + 224*T^8 + 263*T^7 + 274*T^6 + 314*T^5 + 273*T^4 + 63*T^3 + 2*T^2 + 208*T + 258
Forming extension L.
Time: 0.000
L =  Univariate Quotient Polynomial Algebra in w over Univariate Quotient Polynomial Algebra in z over Finite field of size 353
with modulus z^36 + z^35 + z^34 + z^33 + z^32 + z^31 + z^30 + z^29 + z^28 + z^27 + z^26 + z^25 + z^24 + z^23 + z^22 + z^21 + z^20 + z^19 + z^18 + z^17 + z^16 + z^15 + z^14 + z^13 + z^12 + z^11 + z^10 + z^9 + z^8 + z^7 + z^6 + z^5 + z^4 + z^3 + z^2 + z + 1
with modulus w^37 + 111*z^35 + 13*z^34 + 96*z^33 + 42*z^32 + 42*z^30 + 27*z^29 + 200*z^28 + 7*z^27 + 27*z^26 + 111*z^25 + 96*z^24 + 7*z^23 + 333*z^22 + 333*z^21 + 200*z^20 + 13*z^19 + 13*z^18 + 200*z^17 + 333*z^16 + 333*z^15 + 7*z^14 + 96*z^13 + 111*z^12 + 27*z^11 + 7*z^10 + 200*z^9 + 27*z^8 + 42*z^7 + 42*z^5 + 96*z^4 + 13*z^3 + 111*z^2 + 302
Computing trace of random element (alpha = w
)
34 steps: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, Time: 0.150

Finished computing trace of random element.
Computing minimal polynomial of trace(alpha), as an element of K[X]
Time: 1.070
f =  X^37 + 320*X^34 + 77*X^33 + 202*X^32 + 39*X^31 + 215*X^30 + 258*X^29 + 328*X^28 + 180*X^27 + 151*X^26 + 258*X^25 + 230*X^24 + 231*X^23 + 338*X^22 + 347*X^21 + 208*X^20 + 259*X^19 + 27*X^18 + 306*X^17 + 68*X^16 + 146*X^15 + 319*X^14 + 200*X^13 + 181*X^12 + 160*X^11 + 233*X^10 + 72*X^9 + 205*X^8 + 31*X^7 + 77*X^6 + 310*X^5 + 237*X^4 + 144*X^3 + 345*X^2 + 142*X + 176
g =  T^37 + 320*T^34 + 77*T^33 + 202*T^32 + 39*T^31 + 215*T^30 + 258*T^29 + 328*T^28 + 180*T^27 + 151*T^26 + 258*T^25 + 230*T^24 + 231*T^23 + 338*T^22 + 347*T^21 + 208*T^20 + 259*T^19 + 27*T^18 + 306*T^17 + 68*T^16 + 146*T^15 + 319*T^14 + 200*T^13 + 181*T^12 + 160*T^11 + 233*T^10 + 72*T^9 + 205*T^8 + 31*T^7 + 77*T^6 + 310*T^5 + 237*T^4 + 144*T^3 + 345*T^2 + 142*T + 176
Forming extension L.
Time: 0.000
L =  Univariate Quotient Polynomial Algebra in w over Univariate Quotient Polynomial Algebra in z over Finite field of size 383
with modulus z^36 + z^35 + z^34 + z^33 + z^32 + z^31 + z^30 + z^29 + z^28 + z^27 + z^26 + z^25 + z^24 + z^23 + z^22 + z^21 + z^20 + z^19 + z^18 + z^17 + z^16 + z^15 + z^14 + z^13 + z^12 + z^11 + z^10 + z^9 + z^8 + z^7 + z^6 + z^5 + z^4 + z^3 + z^2 + z + 1
with modulus w^37 + 213*z^35 + 322*z^34 + 382*z^33 + 202*z^32 + 202*z^30 + 248*z^29 + 96*z^28 + 243*z^27 + 248*z^26 + 213*z^25 + 382*z^24 + 243*z^23 + 56*z^22 + 56*z^21 + 96*z^20 + 322*z^19 + 322*z^18 + 96*z^17 + 56*z^16 + 56*z^15 + 243*z^14 + 382*z^13 + 213*z^12 + 248*z^11 + 243*z^10 + 96*z^9 + 248*z^8 + 202*z^7 + 202*z^5 + 382*z^4 + 322*z^3 + 213*z^2 + 266
Computing trace of random element (alpha = w
)
34 steps: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, Time: 0.140

Finished computing trace of random element.
Computing minimal polynomial of trace(alpha), as an element of K[X]
Time: 1.070
f =  X^37 + 223*X^34 + 317*X^33 + 45*X^32 + 359*X^31 + 337*X^30 + 306*X^29 + 13*X^28 + 228*X^27 + 365*X^26 + 311*X^25 + 354*X^24 + 379*X^23 + 60*X^22 + 109*X^21 + 181*X^20 + 69*X^19 + 115*X^18 + 219*X^17 + 323*X^16 + 162*X^15 + 357*X^14 + 237*X^13 + 110*X^12 + 6*X^11 + 301*X^10 + 290*X^9 + 238*X^8 + 256*X^7 + 257*X^6 + 120*X^5 + 275*X^4 + 205*X^3 + 331*X^2 + 351*X + 195
g =  T^37 + 223*T^34 + 317*T^33 + 45*T^32 + 359*T^31 + 337*T^30 + 306*T^29 + 13*T^28 + 228*T^27 + 365*T^26 + 311*T^25 + 354*T^24 + 379*T^23 + 60*T^22 + 109*T^21 + 181*T^20 + 69*T^19 + 115*T^18 + 219*T^17 + 323*T^16 + 162*T^15 + 357*T^14 + 237*T^13 + 110*T^12 + 6*T^11 + 301*T^10 + 290*T^9 + 238*T^8 + 256*T^7 + 257*T^6 + 120*T^5 + 275*T^4 + 205*T^3 + 331*T^2 + 351*T + 195
Forming extension L.
Time: 0.000
L =  Univariate Quotient Polynomial Algebra in w over Univariate Quotient Polynomial Algebra in z over Finite field of size 389
with modulus z^36 + z^35 + z^34 + z^33 + z^32 + z^31 + z^30 + z^29 + z^28 + z^27 + z^26 + z^25 + z^24 + z^23 + z^22 + z^21 + z^20 + z^19 + z^18 + z^17 + z^16 + z^15 + z^14 + z^13 + z^12 + z^11 + z^10 + z^9 + z^8 + z^7 + z^6 + z^5 + z^4 + z^3 + z^2 + z + 1
with modulus w^37 + 257*z^35 + 192*z^34 + 27*z^33 + 185*z^32 + 185*z^30 + 291*z^29 + 119*z^28 + 16*z^27 + 291*z^26 + 257*z^25 + 27*z^24 + 16*z^23 + 30*z^22 + 30*z^21 + 119*z^20 + 192*z^19 + 192*z^18 + 119*z^17 + 30*z^16 + 30*z^15 + 16*z^14 + 27*z^13 + 257*z^12 + 291*z^11 + 16*z^10 + 119*z^9 + 291*z^8 + 185*z^7 + 185*z^5 + 27*z^4 + 192*z^3 + 257*z^2 + 226
Computing trace of random element (alpha = w
)
34 steps: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, Time: 0.100

Finished computing trace of random element.
Computing minimal polynomial of trace(alpha), as an element of K[X]
Time: 1.070
f =  X^37 + 268*X^34 + 241*X^33 + 66*X^32 + 119*X^31 + 80*X^30 + 152*X^29 + 17*X^28 + 386*X^27 + 46*X^26 + 322*X^25 + 66*X^24 + 297*X^23 + 285*X^22 + 34*X^21 + 110*X^20 + 213*X^19 + 71*X^18 + 107*X^17 + 194*X^16 + 11*X^15 + 253*X^14 + 333*X^13 + 348*X^12 + 302*X^11 + 15*X^10 + 201*X^9 + 146*X^8 + 10*X^7 + 65*X^6 + 388*X^5 + 379*X^4 + 294*X^3 + 193*X^2 + 110*X + 5
g =  T^37 + 268*T^34 + 241*T^33 + 66*T^32 + 119*T^31 + 80*T^30 + 152*T^29 + 17*T^28 + 386*T^27 + 46*T^26 + 322*T^25 + 66*T^24 + 297*T^23 + 285*T^22 + 34*T^21 + 110*T^20 + 213*T^19 + 71*T^18 + 107*T^17 + 194*T^16 + 11*T^15 + 253*T^14 + 333*T^13 + 348*T^12 + 302*T^11 + 15*T^10 + 201*T^9 + 146*T^8 + 10*T^7 + 65*T^6 + 388*T^5 + 379*T^4 + 294*T^3 + 193*T^2 + 110*T + 5
CRT step --  6.15
So far:   [ -19973173574015627316425977783154605933216859494232103, -197315566572895526045244926513713014618751027162826190, -178374021886003559975009090972133615193548443488058997, -252418980143895340138242083962585614658444953286458198, -79140564787698573609498752725434609893918015182528033, 176695333515622217486492120680278006989960306875400562, -21794041357593844324277177428418190380161447233030465, -102350376747351330750211951362330947911912136990898020, -132253654386288796438541556825137046698134209880851466, 103537319349210194933861899939821086143635479338275471, -28894465742055655952735677767397314490234033410502527, -152409728647560363912381895698891413471647721076471449, 94096218855548489687945474197671253660868809287268990, 263890114711583537051887458040425745420921009023841688, 95905472397423231077148221994623652646815080956298370, -271925580393724419581794752919585150484435760332495141, -265263078155323383399912129046056554703909846974365642, 16561872303084043896295392808448299892745285385552541, -286691716814546343801495841401510603556115510829416671, -80268638062435074559599184759300711777564488630272, -331493134727514939719441018060252656606965137408, -1396232608839552259966984463923520026947092480, 476259323830076662111107898811789814530048, -3171787436319383501703813676940597919744, -13099755496539209311468832290825568256, -2249002615426863992005848511545344, -4805711697609190244214712041472, -33628014249666292632903483392, -2221784070205669762924544, -19612786666813992009728, -25584896141781024768, -7894900273815552, -123335506765824, -118234637824, -6483584, 0, 0, 1 ]
Forming extension L.
Time: 0.000
L =  Univariate Quotient Polynomial Algebra in w over Univariate Quotient Polynomial Algebra in z over Finite field of size 409
with modulus z^36 + z^35 + z^34 + z^33 + z^32 + z^31 + z^30 + z^29 + z^28 + z^27 + z^26 + z^25 + z^24 + z^23 + z^22 + z^21 + z^20 + z^19 + z^18 + z^17 + z^16 + z^15 + z^14 + z^13 + z^12 + z^11 + z^10 + z^9 + z^8 + z^7 + z^6 + z^5 + z^4 + z^3 + z^2 + z + 1
with modulus w^37 + 306*z^35 + 53*z^34 + 394*z^33 + 360*z^32 + 360*z^30 + 328*z^29 + 268*z^28 + 206*z^27 + 328*z^26 + 306*z^25 + 394*z^24 + 206*z^23 + 346*z^22 + 346*z^21 + 268*z^20 + 53*z^19 + 53*z^18 + 268*z^17 + 346*z^16 + 346*z^15 + 206*z^14 + 394*z^13 + 306*z^12 + 328*z^11 + 206*z^10 + 268*z^9 + 328*z^8 + 360*z^7 + 360*z^5 + 394*z^4 + 53*z^3 + 306*z^2 + 122
Computing trace of random element (alpha = w
)
34 steps: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, Time: 0.100

Finished computing trace of random element.
Computing minimal polynomial of trace(alpha), as an element of K[X]
Time: 1.000
f =  X^37 + 293*X^34 + 381*X^33 + 242*X^32 + 102*X^31 + 310*X^30 + 158*X^29 + 156*X^28 + 293*X^27 + 48*X^26 + 261*X^25 + 128*X^24 + 159*X^23 + 254*X^22 + 88*X^21 + 132*X^20 + 189*X^19 + 326*X^18 + 51*X^17 + 365*X^16 + 279*X^15 + 176*X^14 + 281*X^13 + 216*X^12 + 71*X^11 + 268*X^10 + 57*X^9 + 244*X^8 + 227*X^7 + 323*X^6 + 30*X^5 + 164*X^4 + 52*X^3 + 29*X^2 + 175*X + 37
g =  T^37 + 293*T^34 + 381*T^33 + 242*T^32 + 102*T^31 + 310*T^30 + 158*T^29 + 156*T^28 + 293*T^27 + 48*T^26 + 261*T^25 + 128*T^24 + 159*T^23 + 254*T^22 + 88*T^21 + 132*T^20 + 189*T^19 + 326*T^18 + 51*T^17 + 365*T^16 + 279*T^15 + 176*T^14 + 281*T^13 + 216*T^12 + 71*T^11 + 268*T^10 + 57*T^9 + 244*T^8 + 227*T^7 + 323*T^6 + 30*T^5 + 164*T^4 + 52*T^3 + 29*T^2 + 175*T + 37
Forming extension L.
Time: 0.000
L =  Univariate Quotient Polynomial Algebra in w over Univariate Quotient Polynomial Algebra in z over Finite field of size 431
with modulus z^36 + z^35 + z^34 + z^33 + z^32 + z^31 + z^30 + z^29 + z^28 + z^27 + z^26 + z^25 + z^24 + z^23 + z^22 + z^21 + z^20 + z^19 + z^18 + z^17 + z^16 + z^15 + z^14 + z^13 + z^12 + z^11 + z^10 + z^9 + z^8 + z^7 + z^6 + z^5 + z^4 + z^3 + z^2 + z + 1
with modulus w^37 + 108*z^35 + 308*z^34 + 377*z^33 + 26*z^32 + 26*z^30 + 262*z^29 + 367*z^28 + 12*z^27 + 262*z^26 + 108*z^25 + 377*z^24 + 12*z^23 + 295*z^22 + 295*z^21 + 367*z^20 + 308*z^19 + 308*z^18 + 367*z^17 + 295*z^16 + 295*z^15 + 12*z^14 + 377*z^13 + 108*z^12 + 262*z^11 + 12*z^10 + 367*z^9 + 262*z^8 + 26*z^7 + 26*z^5 + 377*z^4 + 308*z^3 + 108*z^2 + 293
Computing trace of random element (alpha = w
)
34 steps: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, Time: 0.110

Finished computing trace of random element.
Computing minimal polynomial of trace(alpha), as an element of K[X]
Time: 0.960
f =  X^37 + 380*X^34 + 62*X^33 + 345*X^32 + 104*X^31 + 376*X^30 + 107*X^29 + 220*X^28 + 336*X^27 + 202*X^26 + 346*X^25 + 9*X^24 + 45*X^23 + 385*X^22 + 92*X^21 + 77*X^19 + 16*X^18 + 222*X^17 + 45*X^16 + 174*X^15 + 391*X^14 + 262*X^13 + 3*X^12 + 92*X^11 + 223*X^10 + 9*X^9 + 418*X^8 + 172*X^7 + 133*X^6 + 13*X^5 + 349*X^4 + 101*X^3 + 58*X^2 + 185*X + 263
g =  T^37 + 380*T^34 + 62*T^33 + 345*T^32 + 104*T^31 + 376*T^30 + 107*T^29 + 220*T^28 + 336*T^27 + 202*T^26 + 346*T^25 + 9*T^24 + 45*T^23 + 385*T^22 + 92*T^21 + 77*T^19 + 16*T^18 + 222*T^17 + 45*T^16 + 174*T^15 + 391*T^14 + 262*T^13 + 3*T^12 + 92*T^11 + 223*T^10 + 9*T^9 + 418*T^8 + 172*T^7 + 133*T^6 + 13*T^5 + 349*T^4 + 101*T^3 + 58*T^2 + 185*T + 263
Forming extension L.
Time: 0.000
L =  Univariate Quotient Polynomial Algebra in w over Univariate Quotient Polynomial Algebra in z over Finite field of size 439
with modulus z^36 + z^35 + z^34 + z^33 + z^32 + z^31 + z^30 + z^29 + z^28 + z^27 + z^26 + z^25 + z^24 + z^23 + z^22 + z^21 + z^20 + z^19 + z^18 + z^17 + z^16 + z^15 + z^14 + z^13 + z^12 + z^11 + z^10 + z^9 + z^8 + z^7 + z^6 + z^5 + z^4 + z^3 + z^2 + z + 1
with modulus w^37 + 343*z^35 + 331*z^34 + 307*z^33 + 412*z^32 + 412*z^30 + 409*z^29 + 366*z^28 + 197*z^27 + 409*z^26 + 343*z^25 + 307*z^24 + 197*z^23 + 364*z^22 + 364*z^21 + 366*z^20 + 331*z^19 + 331*z^18 + 366*z^17 + 364*z^16 + 364*z^15 + 197*z^14 + 307*z^13 + 343*z^12 + 409*z^11 + 197*z^10 + 366*z^9 + 409*z^8 + 412*z^7 + 412*z^5 + 307*z^4 + 331*z^3 + 343*z^2 + 346
Computing trace of random element (alpha = w
)
34 steps: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, Time: 0.100

Finished computing trace of random element.
Computing minimal polynomial of trace(alpha), as an element of K[X]
Time: 0.950
f =  X^37 + 7*X^34 + 342*X^33 + 355*X^32 + 131*X^31 + 214*X^30 + 9*X^29 + 395*X^28 + 141*X^27 + 388*X^26 + 436*X^25 + 146*X^24 + 187*X^23 + 254*X^22 + 181*X^21 + 256*X^20 + 272*X^19 + 362*X^18 + 102*X^17 + 17*X^16 + 68*X^15 + 292*X^14 + 121*X^13 + 180*X^12 + 239*X^11 + 175*X^10 + 115*X^9 + 425*X^8 + 197*X^7 + 171*X^6 + 230*X^5 + 34*X^4 + 421*X^3 + 192*X^2 + 299*X + 49
g =  T^37 + 7*T^34 + 342*T^33 + 355*T^32 + 131*T^31 + 214*T^30 + 9*T^29 + 395*T^28 + 141*T^27 + 388*T^26 + 436*T^25 + 146*T^24 + 187*T^23 + 254*T^22 + 181*T^21 + 256*T^20 + 272*T^19 + 362*T^18 + 102*T^17 + 17*T^16 + 68*T^15 + 292*T^14 + 121*T^13 + 180*T^12 + 239*T^11 + 175*T^10 + 115*T^9 + 425*T^8 + 197*T^7 + 171*T^6 + 230*T^5 + 34*T^4 + 421*T^3 + 192*T^2 + 299*T + 49
Forming extension L.
Time: 0.000
L =  Univariate Quotient Polynomial Algebra in w over Univariate Quotient Polynomial Algebra in z over Finite field of size 449
with modulus z^36 + z^35 + z^34 + z^33 + z^32 + z^31 + z^30 + z^29 + z^28 + z^27 + z^26 + z^25 + z^24 + z^23 + z^22 + z^21 + z^20 + z^19 + z^18 + z^17 + z^16 + z^15 + z^14 + z^13 + z^12 + z^11 + z^10 + z^9 + z^8 + z^7 + z^6 + z^5 + z^4 + z^3 + z^2 + z + 1
with modulus w^37 + 328*z^35 + 190*z^34 + 423*z^33 + 303*z^32 + 303*z^30 + 391*z^29 + 109*z^28 + 147*z^27 + 391*z^26 + 328*z^25 + 423*z^24 + 147*z^23 + 19*z^22 + 19*z^21 + 109*z^20 + 190*z^19 + 190*z^18 + 109*z^17 + 19*z^16 + 19*z^15 + 147*z^14 + 423*z^13 + 328*z^12 + 391*z^11 + 147*z^10 + 109*z^9 + 391*z^8 + 303*z^7 + 303*z^5 + 423*z^4 + 190*z^3 + 328*z^2 + 358
Computing trace of random element (alpha = w
)
34 steps: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, Time: 0.110

Finished computing trace of random element.
Computing minimal polynomial of trace(alpha), as an element of K[X]
Time: 0.950
f =  X^37 + 425*X^34 + 111*X^33 + 230*X^32 + 155*X^31 + 4*X^30 + 131*X^29 + 148*X^28 + 392*X^27 + 128*X^26 + 306*X^25 + 333*X^24 + 149*X^23 + 377*X^22 + 167*X^21 + 77*X^20 + 92*X^19 + 4*X^18 + 261*X^17 + 197*X^16 + 90*X^15 + 312*X^14 + 355*X^13 + 405*X^12 + 143*X^11 + 379*X^10 + 285*X^9 + 432*X^8 + 317*X^7 + 227*X^6 + 268*X^5 + 49*X^4 + 251*X^3 + 417*X^2 + 93*X + 380
g =  T^37 + 425*T^34 + 111*T^33 + 230*T^32 + 155*T^31 + 4*T^30 + 131*T^29 + 148*T^28 + 392*T^27 + 128*T^26 + 306*T^25 + 333*T^24 + 149*T^23 + 377*T^22 + 167*T^21 + 77*T^20 + 92*T^19 + 4*T^18 + 261*T^17 + 197*T^16 + 90*T^15 + 312*T^14 + 355*T^13 + 405*T^12 + 143*T^11 + 379*T^10 + 285*T^9 + 432*T^8 + 317*T^7 + 227*T^6 + 268*T^5 + 49*T^4 + 251*T^3 + 417*T^2 + 93*T + 380
Forming extension L.
Time: 0.000
L =  Univariate Quotient Polynomial Algebra in w over Univariate Quotient Polynomial Algebra in z over Finite field of size 457
with modulus z^36 + z^35 + z^34 + z^33 + z^32 + z^31 + z^30 + z^29 + z^28 + z^27 + z^26 + z^25 + z^24 + z^23 + z^22 + z^21 + z^20 + z^19 + z^18 + z^17 + z^16 + z^15 + z^14 + z^13 + z^12 + z^11 + z^10 + z^9 + z^8 + z^7 + z^6 + z^5 + z^4 + z^3 + z^2 + z + 1
with modulus w^37 + 44*z^35 + 195*z^34 + 443*z^33 + 249*z^32 + 249*z^30 + 19*z^29 + 349*z^28 + 186*z^27 + 19*z^26 + 44*z^25 + 443*z^24 + 186*z^23 + 24*z^22 + 24*z^21 + 349*z^20 + 195*z^19 + 195*z^18 + 349*z^17 + 24*z^16 + 24*z^15 + 186*z^14 + 443*z^13 + 44*z^12 + 19*z^11 + 186*z^10 + 349*z^9 + 19*z^8 + 249*z^7 + 249*z^5 + 443*z^4 + 195*z^3 + 44*z^2 + 413
Computing trace of random element (alpha = w
)
34 steps: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, Time: 0.120

Finished computing trace of random element.
Computing minimal polynomial of trace(alpha), as an element of K[X]
Time: 0.950
f =  X^37 + 332*X^34 + 16*X^33 + 292*X^32 + 260*X^31 + 419*X^30 + 212*X^29 + 262*X^28 + 241*X^27 + 382*X^26 + 203*X^25 + 335*X^24 + 290*X^23 + 417*X^22 + 400*X^21 + 188*X^20 + 289*X^19 + 342*X^18 + 404*X^17 + 422*X^16 + 263*X^15 + 45*X^14 + 152*X^13 + 160*X^12 + 276*X^11 + 148*X^10 + 257*X^9 + 426*X^8 + 205*X^7 + 83*X^6 + 155*X^5 + 109*X^4 + 450*X^3 + 434*X^2 + 432*X + 178
g =  T^37 + 332*T^34 + 16*T^33 + 292*T^32 + 260*T^31 + 419*T^30 + 212*T^29 + 262*T^28 + 241*T^27 + 382*T^26 + 203*T^25 + 335*T^24 + 290*T^23 + 417*T^22 + 400*T^21 + 188*T^20 + 289*T^19 + 342*T^18 + 404*T^17 + 422*T^16 + 263*T^15 + 45*T^14 + 152*T^13 + 160*T^12 + 276*T^11 + 148*T^10 + 257*T^9 + 426*T^8 + 205*T^7 + 83*T^6 + 155*T^5 + 109*T^4 + 450*T^3 + 434*T^2 + 432*T + 178
CRT step --  5.479
So far:   [ 2259598051409281005747948056388365513730358395848379223709784339674, -836834887780310355517560262129551213184364928369675075963116105286, 3551129353861745945070288904713258925029366767970566195782842180619, -4468601038293327908035566879424466869989210536003550751588362938612, 1822787285952361758740333278685050704493939370557686521237783160715, 408065110546456160549928090214398446497229913779414595311243302716, -4436161209859644132973149596883285559637457275546690235521840008584, -3690947513734218516296434641192621640127806663361263646521290807830, 3761863199366604529195237751951458787900824220940714299342202351040, 2114502381510252882382725210179499746554660442389052485554646725084, -1802016669934724868076431151975978828741239601206199480692677425847, 2885743906442520632702880221908555824574593101234244300020385915183, -4254207989382863240384953602785033142175999958636875683757241271572, 2854705449484624416795330612386811215415869973011706932441160613888, 31183544125608715763774641955998078374374445370791241228146966528, -20651404785477501467881895153357983415526349942938256921329664, 37244222236334875481641252538596552828631758622687299108864, 1772659418875854490177280483057352783210247369401565184, -872057565672136492561824204817812097995282872168087552, -80268638062435074559599184759300711777564488630272, -331493134727514939719441018060252656606965137408, -1396232608839552259966984463923520026947092480, 476259323830076662111107898811789814530048, -3171787436319383501703813676940597919744, -13099755496539209311468832290825568256, -2249002615426863992005848511545344, -4805711697609190244214712041472, -33628014249666292632903483392, -2221784070205669762924544, -19612786666813992009728, -25584896141781024768, -7894900273815552, -123335506765824, -118234637824, -6483584, 0, 0, 1 ]
Forming extension L.
Time: 0.000
L =  Univariate Quotient Polynomial Algebra in w over Univariate Quotient Polynomial Algebra in z over Finite field of size 461
with modulus z^36 + z^35 + z^34 + z^33 + z^32 + z^31 + z^30 + z^29 + z^28 + z^27 + z^26 + z^25 + z^24 + z^23 + z^22 + z^21 + z^20 + z^19 + z^18 + z^17 + z^16 + z^15 + z^14 + z^13 + z^12 + z^11 + z^10 + z^9 + z^8 + z^7 + z^6 + z^5 + z^4 + z^3 + z^2 + z + 1
with modulus w^37 + 342*z^35 + 203*z^34 + 328*z^33 + 85*z^32 + 85*z^30 + 136*z^29 + 257*z^28 + 452*z^27 + 136*z^26 + 342*z^25 + 328*z^24 + 452*z^23 + 349*z^22 + 349*z^21 + 257*z^20 + 203*z^19 + 203*z^18 + 257*z^17 + 349*z^16 + 349*z^15 + 452*z^14 + 328*z^13 + 342*z^12 + 136*z^11 + 452*z^10 + 257*z^9 + 136*z^8 + 85*z^7 + 85*z^5 + 328*z^4 + 203*z^3 + 342*z^2 + 369
Computing trace of random element (alpha = w
)
34 steps: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, Time: 0.110

Finished computing trace of random element.
Computing minimal polynomial of trace(alpha), as an element of K[X]
Time: 0.960
f =  X^37 + 381*X^34 + 185*X^33 + 206*X^32 + 393*X^31 + 397*X^30 + 305*X^29 + 205*X^28 + 207*X^27 + 217*X^26 + 105*X^25 + 417*X^24 + 303*X^23 + 279*X^22 + 368*X^21 + 300*X^20 + 383*X^19 + 108*X^18 + 113*X^17 + 300*X^16 + 84*X^15 + 179*X^14 + 359*X^13 + 245*X^12 + 148*X^11 + 85*X^10 + 51*X^9 + 246*X^8 + 4*X^7 + 280*X^6 + 415*X^5 + 410*X^3 + 343*X^2 + 114*X + 442
g =  T^37 + 381*T^34 + 185*T^33 + 206*T^32 + 393*T^31 + 397*T^30 + 305*T^29 + 205*T^28 + 207*T^27 + 217*T^26 + 105*T^25 + 417*T^24 + 303*T^23 + 279*T^22 + 368*T^21 + 300*T^20 + 383*T^19 + 108*T^18 + 113*T^17 + 300*T^16 + 84*T^15 + 179*T^14 + 359*T^13 + 245*T^12 + 148*T^11 + 85*T^10 + 51*T^9 + 246*T^8 + 4*T^7 + 280*T^6 + 415*T^5 + 410*T^3 + 343*T^2 + 114*T + 442
Forming extension L.
Time: 0.010
L =  Univariate Quotient Polynomial Algebra in w over Univariate Quotient Polynomial Algebra in z over Finite field of size 463
with modulus z^36 + z^35 + z^34 + z^33 + z^32 + z^31 + z^30 + z^29 + z^28 + z^27 + z^26 + z^25 + z^24 + z^23 + z^22 + z^21 + z^20 + z^19 + z^18 + z^17 + z^16 + z^15 + z^14 + z^13 + z^12 + z^11 + z^10 + z^9 + z^8 + z^7 + z^6 + z^5 + z^4 + z^3 + z^2 + z + 1
with modulus w^37 + 407*z^35 + 116*z^34 + 256*z^33 + 258*z^32 + 258*z^30 + 452*z^29 + 142*z^28 + 401*z^27 + 452*z^26 + 407*z^25 + 256*z^24 + 401*z^23 + 114*z^22 + 114*z^21 + 142*z^20 + 116*z^19 + 116*z^18 + 142*z^17 + 114*z^16 + 114*z^15 + 401*z^14 + 256*z^13 + 407*z^12 + 452*z^11 + 401*z^10 + 142*z^9 + 452*z^8 + 258*z^7 + 258*z^5 + 256*z^4 + 116*z^3 + 407*z^2 + 349
Computing trace of random element (alpha = w
)
34 steps: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, Time: 0.090

Finished computing trace of random element.
Computing minimal polynomial of trace(alpha), as an element of K[X]
Time: 0.970
f =  X^37 + 268*X^34 + 283*X^33 + 248*X^32 + 163*X^31 + 270*X^30 + 336*X^29 + 116*X^28 + 437*X^27 + 438*X^26 + 150*X^25 + 118*X^24 + 77*X^23 + 384*X^22 + 395*X^21 + 265*X^20 + 333*X^19 + 245*X^18 + 404*X^17 + 356*X^16 + 304*X^15 + 85*X^14 + 236*X^13 + 134*X^12 + 187*X^11 + 68*X^10 + 261*X^9 + 335*X^8 + 370*X^7 + 282*X^6 + 165*X^5 + 393*X^4 + 209*X^3 + 416*X^2 + 21*X + 164
g =  T^37 + 268*T^34 + 283*T^33 + 248*T^32 + 163*T^31 + 270*T^30 + 336*T^29 + 116*T^28 + 437*T^27 + 438*T^26 + 150*T^25 + 118*T^24 + 77*T^23 + 384*T^22 + 395*T^21 + 265*T^20 + 333*T^19 + 245*T^18 + 404*T^17 + 356*T^16 + 304*T^15 + 85*T^14 + 236*T^13 + 134*T^12 + 187*T^11 + 68*T^10 + 261*T^9 + 335*T^8 + 370*T^7 + 282*T^6 + 165*T^5 + 393*T^4 + 209*T^3 + 416*T^2 + 21*T + 164
Forming extension L.
Time: 0.000
L =  Univariate Quotient Polynomial Algebra in w over Univariate Quotient Polynomial Algebra in z over Finite field of size 479
with modulus z^36 + z^35 + z^34 + z^33 + z^32 + z^31 + z^30 + z^29 + z^28 + z^27 + z^26 + z^25 + z^24 + z^23 + z^22 + z^21 + z^20 + z^19 + z^18 + z^17 + z^16 + z^15 + z^14 + z^13 + z^12 + z^11 + z^10 + z^9 + z^8 + z^7 + z^6 + z^5 + z^4 + z^3 + z^2 + z + 1
with modulus w^37 + 120*z^35 + 384*z^34 + 29*z^33 + 345*z^32 + 345*z^30 + 319*z^29 + 431*z^28 + 198*z^27 + 319*z^26 + 120*z^25 + 29*z^24 + 198*z^23 + 71*z^22 + 71*z^21 + 431*z^20 + 384*z^19 + 384*z^18 + 431*z^17 + 71*z^16 + 71*z^15 + 198*z^14 + 29*z^13 + 120*z^12 + 319*z^11 + 198*z^10 + 431*z^9 + 319*z^8 + 345*z^7 + 345*z^5 + 29*z^4 + 384*z^3 + 120*z^2 + 303
Computing trace of random element (alpha = w
)
34 steps: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, Time: 0.130

Finished computing trace of random element.
Computing minimal polynomial of trace(alpha), as an element of K[X]
Time: 0.950
f =  X^37 + 160*X^34 + 171*X^33 + 389*X^32 + 109*X^31 + 99*X^30 + 359*X^29 + 464*X^28 + 472*X^27 + 301*X^26 + 249*X^25 + 157*X^24 + 152*X^23 + 399*X^22 + 437*X^21 + 35*X^20 + 74*X^19 + 189*X^18 + 277*X^17 + 252*X^16 + 235*X^15 + 152*X^14 + 243*X^13 + 471*X^12 + 453*X^11 + 300*X^10 + 132*X^9 + 387*X^8 + 46*X^7 + 398*X^6 + 162*X^5 + 158*X^4 + 50*X^3 + 419*X^2 + 50*X + 233
g =  T^37 + 160*T^34 + 171*T^33 + 389*T^32 + 109*T^31 + 99*T^30 + 359*T^29 + 464*T^28 + 472*T^27 + 301*T^26 + 249*T^25 + 157*T^24 + 152*T^23 + 399*T^22 + 437*T^21 + 35*T^20 + 74*T^19 + 189*T^18 + 277*T^17 + 252*T^16 + 235*T^15 + 152*T^14 + 243*T^13 + 471*T^12 + 453*T^11 + 300*T^10 + 132*T^9 + 387*T^8 + 46*T^7 + 398*T^6 + 162*T^5 + 158*T^4 + 50*T^3 + 419*T^2 + 50*T + 233
Forming extension L.
Time: 0.010
L =  Univariate Quotient Polynomial Algebra in w over Univariate Quotient Polynomial Algebra in z over Finite field of size 499
with modulus z^36 + z^35 + z^34 + z^33 + z^32 + z^31 + z^30 + z^29 + z^28 + z^27 + z^26 + z^25 + z^24 + z^23 + z^22 + z^21 + z^20 + z^19 + z^18 + z^17 + z^16 + z^15 + z^14 + z^13 + z^12 + z^11 + z^10 + z^9 + z^8 + z^7 + z^6 + z^5 + z^4 + z^3 + z^2 + z + 1
with modulus w^37 + 436*z^35 + 414*z^34 + 393*z^33 + 269*z^32 + 269*z^30 + 57*z^29 + 279*z^28 + 328*z^27 + 57*z^26 + 436*z^25 + 393*z^24 + 328*z^23 + 411*z^22 + 411*z^21 + 279*z^20 + 414*z^19 + 414*z^18 + 279*z^17 + 411*z^16 + 411*z^15 + 328*z^14 + 393*z^13 + 436*z^12 + 57*z^11 + 328*z^10 + 279*z^9 + 57*z^8 + 269*z^7 + 269*z^5 + 393*z^4 + 414*z^3 + 436*z^2 + 310
Computing trace of random element (alpha = w
)
34 steps: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, Time: 0.110

Finished computing trace of random element.
Computing minimal polynomial of trace(alpha), as an element of K[X]
Time: 0.950
f =  X^37 + 422*X^34 + 14*X^33 + 455*X^32 + 447*X^31 + 228*X^30 + 196*X^29 + 21*X^28 + 134*X^27 + 451*X^26 + 476*X^25 + 475*X^24 + 31*X^23 + 42*X^22 + 130*X^21 + 474*X^20 + 226*X^19 + 274*X^18 + 423*X^17 + 88*X^16 + 132*X^15 + 60*X^14 + 488*X^13 + 326*X^12 + 395*X^11 + 177*X^10 + 414*X^9 + 78*X^8 + 191*X^7 + 420*X^6 + 378*X^5 + 360*X^4 + 168*X^3 + 359*X^2 + 355*X + 23
g =  T^37 + 422*T^34 + 14*T^33 + 455*T^32 + 447*T^31 + 228*T^30 + 196*T^29 + 21*T^28 + 134*T^27 + 451*T^26 + 476*T^25 + 475*T^24 + 31*T^23 + 42*T^22 + 130*T^21 + 474*T^20 + 226*T^19 + 274*T^18 + 423*T^17 + 88*T^16 + 132*T^15 + 60*T^14 + 488*T^13 + 326*T^12 + 395*T^11 + 177*T^10 + 414*T^9 + 78*T^8 + 191*T^7 + 420*T^6 + 378*T^5 + 360*T^4 + 168*T^3 + 359*T^2 + 355*T + 23
Forming extension L.
Time: 0.000
L =  Univariate Quotient Polynomial Algebra in w over Univariate Quotient Polynomial Algebra in z over Finite field of size 503
with modulus z^36 + z^35 + z^34 + z^33 + z^32 + z^31 + z^30 + z^29 + z^28 + z^27 + z^26 + z^25 + z^24 + z^23 + z^22 + z^21 + z^20 + z^19 + z^18 + z^17 + z^16 + z^15 + z^14 + z^13 + z^12 + z^11 + z^10 + z^9 + z^8 + z^7 + z^6 + z^5 + z^4 + z^3 + z^2 + z + 1
with modulus w^37 + 288*z^35 + 416*z^34 + 76*z^33 + 18*z^32 + 18*z^30 + 485*z^29 + 237*z^28 + 125*z^27 + 485*z^26 + 288*z^25 + 76*z^24 + 125*z^23 + 279*z^22 + 279*z^21 + 237*z^20 + 416*z^19 + 416*z^18 + 237*z^17 + 279*z^16 + 279*z^15 + 125*z^14 + 76*z^13 + 288*z^12 + 485*z^11 + 125*z^10 + 237*z^9 + 485*z^8 + 18*z^7 + 18*z^5 + 76*z^4 + 416*z^3 + 288*z^2 + 188
Computing trace of random element (alpha = w
)
34 steps: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, Time: 0.110

Finished computing trace of random element.
Computing minimal polynomial of trace(alpha), as an element of K[X]
Time: 0.960
f =  X^37 + 86*X^34 + 445*X^33 + 108*X^32 + 178*X^31 + 72*X^30 + 277*X^29 + 359*X^28 + 489*X^27 + 357*X^26 + 74*X^25 + 141*X^24 + 374*X^23 + 277*X^22 + 96*X^21 + 367*X^20 + 350*X^19 + 297*X^18 + 299*X^17 + 278*X^16 + 330*X^15 + 490*X^14 + 262*X^13 + 85*X^12 + 266*X^11 + 415*X^10 + 29*X^9 + 338*X^8 + 263*X^7 + 168*X^6 + 87*X^5 + 51*X^4 + 361*X^3 + 70*X^2 + 423*X + 493
g =  T^37 + 86*T^34 + 445*T^33 + 108*T^32 + 178*T^31 + 72*T^30 + 277*T^29 + 359*T^28 + 489*T^27 + 357*T^26 + 74*T^25 + 141*T^24 + 374*T^23 + 277*T^22 + 96*T^21 + 367*T^20 + 350*T^19 + 297*T^18 + 299*T^17 + 278*T^16 + 330*T^15 + 490*T^14 + 262*T^13 + 85*T^12 + 266*T^11 + 415*T^10 + 29*T^9 + 338*T^8 + 263*T^7 + 168*T^6 + 87*T^5 + 51*T^4 + 361*T^3 + 70*T^2 + 423*T + 493
CRT step --  5.46
So far:   [ 50344668208296332090131692727805911025008626466205791850786813843155255029327678, -71802161540262382505702911175855040614265697094258305650671409274784365476813408, 107405155772728307118004192192714661338508988209609640386529802745768627353805835, 5478572780555099488736074110115696774417389935667809396900007197052733753414731, 1744775437812182505976835180919805561212223433509013104221907910744704328103364, 54748359467545679453520438898215516157127358795816866938942939762995870869342816, 94733140406859004596315142780782806789992474705387830504161462429319846136222669, 13876918502033294002714073432346497693081464801444771309794512068752118219457393, 7908137731001626381452380388843812733346825849958165739441475545650923800505294, -181630591887896963687470296480916555113983363630481468702049951552077809319936, -844861169134880185162881813189113039529594781451540816736263726469132320768, 3087405021478910646130093242279350919332930043815268747163999299543498752, -18557314583560485308211477301528775481854373440798991639264756844462080, 2854705449484624416795330612386811215415869973011706932441160613888, 31183544125608715763774641955998078374374445370791241228146966528, -20651404785477501467881895153357983415526349942938256921329664, 37244222236334875481641252538596552828631758622687299108864, 1772659418875854490177280483057352783210247369401565184, -872057565672136492561824204817812097995282872168087552, -80268638062435074559599184759300711777564488630272, -331493134727514939719441018060252656606965137408, -1396232608839552259966984463923520026947092480, 476259323830076662111107898811789814530048, -3171787436319383501703813676940597919744, -13099755496539209311468832290825568256, -2249002615426863992005848511545344, -4805711697609190244214712041472, -33628014249666292632903483392, -2221784070205669762924544, -19612786666813992009728, -25584896141781024768, -7894900273815552, -123335506765824, -118234637824, -6483584, 0, 0, 1 ]
Forming extension L.
Time: 0.000
L =  Univariate Quotient Polynomial Algebra in w over Univariate Quotient Polynomial Algebra in z over Finite field of size 523
with modulus z^36 + z^35 + z^34 + z^33 + z^32 + z^31 + z^30 + z^29 + z^28 + z^27 + z^26 + z^25 + z^24 + z^23 + z^22 + z^21 + z^20 + z^19 + z^18 + z^17 + z^16 + z^15 + z^14 + z^13 + z^12 + z^11 + z^10 + z^9 + z^8 + z^7 + z^6 + z^5 + z^4 + z^3 + z^2 + z + 1
with modulus w^37 + 74*z^35 + 456*z^34 + 414*z^33 + 513*z^32 + 513*z^30 + 58*z^29 + 299*z^28 + 8*z^27 + 58*z^26 + 74*z^25 + 414*z^24 + 8*z^23 + 149*z^22 + 149*z^21 + 299*z^20 + 456*z^19 + 456*z^18 + 299*z^17 + 149*z^16 + 149*z^15 + 8*z^14 + 414*z^13 + 74*z^12 + 58*z^11 + 8*z^10 + 299*z^9 + 58*z^8 + 513*z^7 + 513*z^5 + 414*z^4 + 456*z^3 + 74*z^2 + 66
Computing trace of random element (alpha = w
)
34 steps: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, Time: 0.100

Finished computing trace of random element.
Computing minimal polynomial of trace(alpha), as an element of K[X]
Time: 1.010
f =  X^37 + 47*X^34 + 418*X^33 + 92*X^32 + 493*X^31 + 101*X^30 + 395*X^29 + 219*X^28 + 114*X^27 + 380*X^26 + 469*X^25 + 227*X^24 + 57*X^23 + 508*X^22 + 47*X^21 + 310*X^20 + 400*X^19 + 112*X^18 + 142*X^17 + 78*X^16 + 422*X^15 + 85*X^14 + 35*X^13 + 27*X^12 + 373*X^11 + 38*X^10 + 85*X^9 + 360*X^8 + 243*X^7 + 181*X^6 + 441*X^5 + 443*X^4 + 491*X^3 + 216*X^2 + 418*X + 321
g =  T^37 + 47*T^34 + 418*T^33 + 92*T^32 + 493*T^31 + 101*T^30 + 395*T^29 + 219*T^28 + 114*T^27 + 380*T^26 + 469*T^25 + 227*T^24 + 57*T^23 + 508*T^22 + 47*T^21 + 310*T^20 + 400*T^19 + 112*T^18 + 142*T^17 + 78*T^16 + 422*T^15 + 85*T^14 + 35*T^13 + 27*T^12 + 373*T^11 + 38*T^10 + 85*T^9 + 360*T^8 + 243*T^7 + 181*T^6 + 441*T^5 + 443*T^4 + 491*T^3 + 216*T^2 + 418*T + 321
Forming extension L.
Time: 0.000
L =  Univariate Quotient Polynomial Algebra in w over Univariate Quotient Polynomial Algebra in z over Finite field of size 557
with modulus z^36 + z^35 + z^34 + z^33 + z^32 + z^31 + z^30 + z^29 + z^28 + z^27 + z^26 + z^25 + z^24 + z^23 + z^22 + z^21 + z^20 + z^19 + z^18 + z^17 + z^16 + z^15 + z^14 + z^13 + z^12 + z^11 + z^10 + z^9 + z^8 + z^7 + z^6 + z^5 + z^4 + z^3 + z^2 + z + 1
with modulus w^37 + 528*z^35 + 65*z^34 + 339*z^33 + 263*z^32 + 263*z^30 + 504*z^29 + 285*z^28 + 236*z^27 + 504*z^26 + 528*z^25 + 339*z^24 + 236*z^23 + 224*z^22 + 224*z^21 + 285*z^20 + 65*z^19 + 65*z^18 + 285*z^17 + 224*z^16 + 224*z^15 + 236*z^14 + 339*z^13 + 528*z^12 + 504*z^11 + 236*z^10 + 285*z^9 + 504*z^8 + 263*z^7 + 263*z^5 + 339*z^4 + 65*z^3 + 528*z^2 + 551
Computing trace of random element (alpha = w
)
34 steps: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, Time: 0.110

Finished computing trace of random element.
Computing minimal polynomial of trace(alpha), as an element of K[X]
Time: 1.040
f =  X^37 + 453*X^34 + 41*X^33 + 310*X^32 + 332*X^31 + 94*X^30 + 457*X^29 + 246*X^28 + 200*X^27 + 152*X^26 + 448*X^25 + 200*X^24 + 238*X^23 + 71*X^22 + 193*X^21 + 40*X^20 + 9*X^19 + 91*X^18 + 172*X^17 + 299*X^16 + 473*X^15 + 427*X^14 + 241*X^13 + 125*X^12 + 337*X^11 + 135*X^10 + 432*X^9 + 108*X^8 + 95*X^7 + 384*X^6 + 234*X^5 + 55*X^4 + 81*X^3 + 173*X^2 + 230*X + 243
g =  T^37 + 453*T^34 + 41*T^33 + 310*T^32 + 332*T^31 + 94*T^30 + 457*T^29 + 246*T^28 + 200*T^27 + 152*T^26 + 448*T^25 + 200*T^24 + 238*T^23 + 71*T^22 + 193*T^21 + 40*T^20 + 9*T^19 + 91*T^18 + 172*T^17 + 299*T^16 + 473*T^15 + 427*T^14 + 241*T^13 + 125*T^12 + 337*T^11 + 135*T^10 + 432*T^9 + 108*T^8 + 95*T^7 + 384*T^6 + 234*T^5 + 55*T^4 + 81*T^3 + 173*T^2 + 230*T + 243
Forming extension L.
Time: 0.000
L =  Univariate Quotient Polynomial Algebra in w over Univariate Quotient Polynomial Algebra in z over Finite field of size 577
with modulus z^36 + z^35 + z^34 + z^33 + z^32 + z^31 + z^30 + z^29 + z^28 + z^27 + z^26 + z^25 + z^24 + z^23 + z^22 + z^21 + z^20 + z^19 + z^18 + z^17 + z^16 + z^15 + z^14 + z^13 + z^12 + z^11 + z^10 + z^9 + z^8 + z^7 + z^6 + z^5 + z^4 + z^3 + z^2 + z + 1
with modulus w^37 + 569*z^35 + 507*z^34 + 68*z^33 + 179*z^32 + 179*z^30 + 482*z^29 + 247*z^28 + 83*z^27 + 482*z^26 + 569*z^25 + 68*z^24 + 83*z^23 + 61*z^22 + 61*z^21 + 247*z^20 + 507*z^19 + 507*z^18 + 247*z^17 + 61*z^16 + 61*z^15 + 83*z^14 + 68*z^13 + 569*z^12 + 482*z^11 + 83*z^10 + 247*z^9 + 482*z^8 + 179*z^7 + 179*z^5 + 68*z^4 + 507*z^3 + 569*z^2 + 416
Computing trace of random element (alpha = w
)
34 steps: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, Time: 0.110

Finished computing trace of random element.
Computing minimal polynomial of trace(alpha), as an element of K[X]
Time: 1.030
f =  X^37 + 165*X^34 + 462*X^33 + 111*X^32 + 565*X^31 + 554*X^30 + 327*X^29 + 462*X^28 + 155*X^27 + 509*X^26 + 280*X^25 + 248*X^24 + 471*X^23 + 355*X^22 + 249*X^21 + 498*X^20 + 331*X^19 + 214*X^18 + 326*X^17 + 371*X^16 + 471*X^15 + 311*X^14 + 312*X^13 + 388*X^12 + 448*X^11 + 141*X^10 + 212*X^9 + 536*X^8 + 133*X^7 + 176*X^6 + 40*X^5 + 526*X^4 + 515*X^3 + 65*X^2 + 47*X + 368
g =  T^37 + 165*T^34 + 462*T^33 + 111*T^32 + 565*T^31 + 554*T^30 + 327*T^29 + 462*T^28 + 155*T^27 + 509*T^26 + 280*T^25 + 248*T^24 + 471*T^23 + 355*T^22 + 249*T^21 + 498*T^20 + 331*T^19 + 214*T^18 + 326*T^17 + 371*T^16 + 471*T^15 + 311*T^14 + 312*T^13 + 388*T^12 + 448*T^11 + 141*T^10 + 212*T^9 + 536*T^8 + 133*T^7 + 176*T^6 + 40*T^5 + 526*T^4 + 515*T^3 + 65*T^2 + 47*T + 368
Forming extension L.
Time: 0.000
L =  Univariate Quotient Polynomial Algebra in w over Univariate Quotient Polynomial Algebra in z over Finite field of size 587
with modulus z^36 + z^35 + z^34 + z^33 + z^32 + z^31 + z^30 + z^29 + z^28 + z^27 + z^26 + z^25 + z^24 + z^23 + z^22 + z^21 + z^20 + z^19 + z^18 + z^17 + z^16 + z^15 + z^14 + z^13 + z^12 + z^11 + z^10 + z^9 + z^8 + z^7 + z^6 + z^5 + z^4 + z^3 + z^2 + z + 1
with modulus w^37 + 426*z^35 + 112*z^34 + 502*z^33 + 498*z^32 + 498*z^30 + 538*z^29 + 203*z^28 + 418*z^27 + 538*z^26 + 426*z^25 + 502*z^24 + 418*z^23 + 208*z^22 + 208*z^21 + 203*z^20 + 112*z^19 + 112*z^18 + 203*z^17 + 208*z^16 + 208*z^15 + 418*z^14 + 502*z^13 + 426*z^12 + 538*z^11 + 418*z^10 + 203*z^9 + 538*z^8 + 498*z^7 + 498*z^5 + 502*z^4 + 112*z^3 + 426*z^2 + 191
Computing trace of random element (alpha = w
)
34 steps: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, Time: 0.120

Finished computing trace of random element.
Computing minimal polynomial of trace(alpha), as an element of K[X]
Time: 1.010
f =  X^37 + 418*X^34 + 453*X^33 + 474*X^32 + 104*X^31 + 161*X^30 + 291*X^29 + 126*X^28 + 9*X^27 + 38*X^26 + 133*X^25 + 418*X^24 + 44*X^23 + 270*X^22 + 78*X^21 + 130*X^20 + 198*X^19 + 372*X^18 + 490*X^17 + 362*X^16 + 164*X^15 + 488*X^14 + 11*X^13 + 439*X^12 + 222*X^11 + 524*X^10 + 561*X^9 + 180*X^8 + 247*X^7 + 458*X^6 + 36*X^5 + 113*X^4 + 313*X^3 + 178*X^2 + 228*X + 530
g =  T^37 + 418*T^34 + 453*T^33 + 474*T^32 + 104*T^31 + 161*T^30 + 291*T^29 + 126*T^28 + 9*T^27 + 38*T^26 + 133*T^25 + 418*T^24 + 44*T^23 + 270*T^22 + 78*T^21 + 130*T^20 + 198*T^19 + 372*T^18 + 490*T^17 + 362*T^16 + 164*T^15 + 488*T^14 + 11*T^13 + 439*T^12 + 222*T^11 + 524*T^10 + 561*T^9 + 180*T^8 + 247*T^7 + 458*T^6 + 36*T^5 + 113*T^4 + 313*T^3 + 178*T^2 + 228*T + 530
Forming extension L.
Time: 0.000
L =  Univariate Quotient Polynomial Algebra in w over Univariate Quotient Polynomial Algebra in z over Finite field of size 607
with modulus z^36 + z^35 + z^34 + z^33 + z^32 + z^31 + z^30 + z^29 + z^28 + z^27 + z^26 + z^25 + z^24 + z^23 + z^22 + z^21 + z^20 + z^19 + z^18 + z^17 + z^16 + z^15 + z^14 + z^13 + z^12 + z^11 + z^10 + z^9 + z^8 + z^7 + z^6 + z^5 + z^4 + z^3 + z^2 + z + 1
with modulus w^37 + 396*z^35 + 413*z^34 + 370*z^33 + 55*z^32 + 55*z^30 + 345*z^29 + 446*z^28 + 230*z^27 + 345*z^26 + 396*z^25 + 370*z^24 + 230*z^23 + 446*z^20 + 413*z^19 + 413*z^18 + 446*z^17 + 230*z^14 + 370*z^13 + 396*z^12 + 345*z^11 + 230*z^10 + 446*z^9 + 345*z^8 + 55*z^7 + 55*z^5 + 370*z^4 + 413*z^3 + 396*z^2 + 510
Computing trace of random element (alpha = w
)
34 steps: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, Time: 0.120

Finished computing trace of random element.
Computing minimal polynomial of trace(alpha), as an element of K[X]
Time: 1.130
f =  X^37 + 390*X^34 + 428*X^33 + 138*X^32 + 229*X^31 + 251*X^30 + 174*X^29 + 325*X^28 + 113*X^27 + 307*X^26 + 593*X^25 + 120*X^24 + 336*X^23 + 134*X^22 + 603*X^21 + 463*X^20 + 383*X^19 + 83*X^18 + 32*X^17 + 405*X^16 + 210*X^15 + 281*X^14 + 14*X^13 + 211*X^12 + 24*X^11 + 239*X^10 + 417*X^9 + 579*X^8 + 445*X^7 + 436*X^6 + 432*X^5 + 213*X^4 + 166*X^3 + 318*X^2 + 284*X + 134
g =  T^37 + 390*T^34 + 428*T^33 + 138*T^32 + 229*T^31 + 251*T^30 + 174*T^29 + 325*T^28 + 113*T^27 + 307*T^26 + 593*T^25 + 120*T^24 + 336*T^23 + 134*T^22 + 603*T^21 + 463*T^20 + 383*T^19 + 83*T^18 + 32*T^17 + 405*T^16 + 210*T^15 + 281*T^14 + 14*T^13 + 211*T^12 + 24*T^11 + 239*T^10 + 417*T^9 + 579*T^8 + 445*T^7 + 436*T^6 + 432*T^5 + 213*T^4 + 166*T^3 + 318*T^2 + 284*T + 134
CRT step --  5.94
So far:   [ 52870834189336794147471693635374969172305780557431265626685775053566967817728176961955310813, 7084557491228508392035621130980296518530570497350795436764633484485375261653829659930451583593, 6439446034097420131545898289561682246512413481448468906280654968929462602105939218621769526425, -660677952891702989779583125409354140514319272374345508868647000437128182296246506433818918912, 1982469259694895457314935195126430029297012127795195501396552566165464092269185291272585216, 122531389798606603051301724324273450024230408425919996998908148191119982817601008959488, -106850589825632789894896612887329721094911179135082410100519870323032421196184294522880, 55114049776782199582622334540957461483624433957263207123073326516074293876028866560, 484965911395764970871665544609840479278207020589886844109688505883361242049937408, -181630591887896963687470296480916555113983363630481468702049951552077809319936, -844861169134880185162881813189113039529594781451540816736263726469132320768, 3087405021478910646130093242279350919332930043815268747163999299543498752, -18557314583560485308211477301528775481854373440798991639264756844462080, 2854705449484624416795330612386811215415869973011706932441160613888, 31183544125608715763774641955998078374374445370791241228146966528, -20651404785477501467881895153357983415526349942938256921329664, 37244222236334875481641252538596552828631758622687299108864, 1772659418875854490177280483057352783210247369401565184, -872057565672136492561824204817812097995282872168087552, -80268638062435074559599184759300711777564488630272, -331493134727514939719441018060252656606965137408, -1396232608839552259966984463923520026947092480, 476259323830076662111107898811789814530048, -3171787436319383501703813676940597919744, -13099755496539209311468832290825568256, -2249002615426863992005848511545344, -4805711697609190244214712041472, -33628014249666292632903483392, -2221784070205669762924544, -19612786666813992009728, -25584896141781024768, -7894900273815552, -123335506765824, -118234637824, -6483584, 0, 0, 1 ]
Forming extension L.
Time: 0.000
L =  Univariate Quotient Polynomial Algebra in w over Univariate Quotient Polynomial Algebra in z over Finite field of size 631
with modulus z^36 + z^35 + z^34 + z^33 + z^32 + z^31 + z^30 + z^29 + z^28 + z^27 + z^26 + z^25 + z^24 + z^23 + z^22 + z^21 + z^20 + z^19 + z^18 + z^17 + z^16 + z^15 + z^14 + z^13 + z^12 + z^11 + z^10 + z^9 + z^8 + z^7 + z^6 + z^5 + z^4 + z^3 + z^2 + z + 1
with modulus w^37 + 552*z^35 + 468*z^34 + 594*z^33 + 85*z^32 + 85*z^30 + 605*z^29 + 393*z^28 + 230*z^27 + 605*z^26 + 552*z^25 + 594*z^24 + 230*z^23 + 121*z^22 + 121*z^21 + 393*z^20 + 468*z^19 + 468*z^18 + 393*z^17 + 121*z^16 + 121*z^15 + 230*z^14 + 594*z^13 + 552*z^12 + 605*z^11 + 230*z^10 + 393*z^9 + 605*z^8 + 85*z^7 + 85*z^5 + 594*z^4 + 468*z^3 + 552*z^2 + 263
Computing trace of random element (alpha = w
)
34 steps: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, Time: 0.120

Finished computing trace of random element.
Computing minimal polynomial of trace(alpha), as an element of K[X]
Time: 1.010
f =  X^37 + 572*X^34 + 562*X^33 + 608*X^32 + 126*X^31 + 400*X^30 + 113*X^29 + 348*X^28 + 47*X^27 + 47*X^26 + 209*X^25 + 48*X^24 + 71*X^23 + 262*X^22 + X^21 + 256*X^20 + 477*X^19 + 294*X^18 + 405*X^17 + 278*X^16 + 138*X^15 + 170*X^14 + 14*X^13 + 207*X^12 + 111*X^11 + 42*X^10 + 533*X^9 + 81*X^8 + 248*X^7 + 9*X^6 + 26*X^5 + 479*X^4 + 546*X^3 + 417*X^2 + 593*X + 331
g =  T^37 + 572*T^34 + 562*T^33 + 608*T^32 + 126*T^31 + 400*T^30 + 113*T^29 + 348*T^28 + 47*T^27 + 47*T^26 + 209*T^25 + 48*T^24 + 71*T^23 + 262*T^22 + T^21 + 256*T^20 + 477*T^19 + 294*T^18 + 405*T^17 + 278*T^16 + 138*T^15 + 170*T^14 + 14*T^13 + 207*T^12 + 111*T^11 + 42*T^10 + 533*T^9 + 81*T^8 + 248*T^7 + 9*T^6 + 26*T^5 + 479*T^4 + 546*T^3 + 417*T^2 + 593*T + 331
Forming extension L.
Time: 0.000
L =  Univariate Quotient Polynomial Algebra in w over Univariate Quotient Polynomial Algebra in z over Finite field of size 647
with modulus z^36 + z^35 + z^34 + z^33 + z^32 + z^31 + z^30 + z^29 + z^28 + z^27 + z^26 + z^25 + z^24 + z^23 + z^22 + z^21 + z^20 + z^19 + z^18 + z^17 + z^16 + z^15 + z^14 + z^13 + z^12 + z^11 + z^10 + z^9 + z^8 + z^7 + z^6 + z^5 + z^4 + z^3 + z^2 + z + 1
with modulus w^37 + 580*z^35 + 244*z^34 + 11*z^33 + 347*z^32 + 347*z^30 + 465*z^29 + 519*z^28 + 527*z^27 + 465*z^26 + 580*z^25 + 11*z^24 + 527*z^23 + 607*z^22 + 607*z^21 + 519*z^20 + 244*z^19 + 244*z^18 + 519*z^17 + 607*z^16 + 607*z^15 + 527*z^14 + 11*z^13 + 580*z^12 + 465*z^11 + 527*z^10 + 519*z^9 + 465*z^8 + 347*z^7 + 347*z^5 + 11*z^4 + 244*z^3 + 580*z^2 + 57
Computing trace of random element (alpha = w
)
34 steps: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, Time: 0.110

Finished computing trace of random element.
Computing minimal polynomial of trace(alpha), as an element of K[X]
Time: 1.000
f =  X^37 + 3*X^34 + 360*X^33 + 220*X^32 + 578*X^31 + 164*X^30 + 307*X^29 + 251*X^28 + 205*X^27 + 236*X^26 + 499*X^25 + 362*X^24 + 484*X^23 + 598*X^22 + 468*X^21 + 124*X^20 + 306*X^19 + 265*X^18 + 250*X^17 + 20*X^16 + 217*X^15 + 353*X^14 + 339*X^13 + 439*X^12 + 145*X^11 + 597*X^10 + 568*X^9 + 352*X^8 + 603*X^7 + 390*X^6 + 438*X^5 + 323*X^4 + 330*X^3 + 93*X^2 + 284*X + 642
g =  T^37 + 3*T^34 + 360*T^33 + 220*T^32 + 578*T^31 + 164*T^30 + 307*T^29 + 251*T^28 + 205*T^27 + 236*T^26 + 499*T^25 + 362*T^24 + 484*T^23 + 598*T^22 + 468*T^21 + 124*T^20 + 306*T^19 + 265*T^18 + 250*T^17 + 20*T^16 + 217*T^15 + 353*T^14 + 339*T^13 + 439*T^12 + 145*T^11 + 597*T^10 + 568*T^9 + 352*T^8 + 603*T^7 + 390*T^6 + 438*T^5 + 323*T^4 + 330*T^3 + 93*T^2 + 284*T + 642
Forming extension L.
Time: 0.000
L =  Univariate Quotient Polynomial Algebra in w over Univariate Quotient Polynomial Algebra in z over Finite field of size 653
with modulus z^36 + z^35 + z^34 + z^33 + z^32 + z^31 + z^30 + z^29 + z^28 + z^27 + z^26 + z^25 + z^24 + z^23 + z^22 + z^21 + z^20 + z^19 + z^18 + z^17 + z^16 + z^15 + z^14 + z^13 + z^12 + z^11 + z^10 + z^9 + z^8 + z^7 + z^6 + z^5 + z^4 + z^3 + z^2 + z + 1
with modulus w^37 + 425*z^35 + 418*z^34 + 648*z^33 + 448*z^32 + 448*z^30 + 472*z^29 + 289*z^28 + 470*z^27 + 472*z^26 + 425*z^25 + 648*z^24 + 470*z^23 + 452*z^22 + 452*z^21 + 289*z^20 + 418*z^19 + 418*z^18 + 289*z^17 + 452*z^16 + 452*z^15 + 470*z^14 + 648*z^13 + 425*z^12 + 472*z^11 + 470*z^10 + 289*z^9 + 472*z^8 + 448*z^7 + 448*z^5 + 648*z^4 + 418*z^3 + 425*z^2 + 140
Computing trace of random element (alpha = w
)
34 steps: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, Time: 0.120

Finished computing trace of random element.
Computing minimal polynomial of trace(alpha), as an element of K[X]
Time: 1.000
f =  X^37 + 53*X^34 + 68*X^33 + 434*X^32 + 500*X^31 + 162*X^30 + 535*X^29 + 340*X^28 + 585*X^27 + 386*X^26 + 632*X^25 + 135*X^24 + 326*X^23 + 249*X^22 + 373*X^21 + 66*X^20 + 57*X^19 + 388*X^18 + 323*X^17 + 593*X^16 + 380*X^15 + 438*X^14 + 447*X^13 + 325*X^12 + 586*X^11 + 344*X^10 + 266*X^9 + 284*X^8 + 459*X^7 + 635*X^6 + 605*X^5 + 301*X^4 + 638*X^3 + 284*X^2 + 393*X + 508
g =  T^37 + 53*T^34 + 68*T^33 + 434*T^32 + 500*T^31 + 162*T^30 + 535*T^29 + 340*T^28 + 585*T^27 + 386*T^26 + 632*T^25 + 135*T^24 + 326*T^23 + 249*T^22 + 373*T^21 + 66*T^20 + 57*T^19 + 388*T^18 + 323*T^17 + 593*T^16 + 380*T^15 + 438*T^14 + 447*T^13 + 325*T^12 + 586*T^11 + 344*T^10 + 266*T^9 + 284*T^8 + 459*T^7 + 635*T^6 + 605*T^5 + 301*T^4 + 638*T^3 + 284*T^2 + 393*T + 508
Forming extension L.
Time: 0.000
L =  Univariate Quotient Polynomial Algebra in w over Univariate Quotient Polynomial Algebra in z over Finite field of size 661
with modulus z^36 + z^35 + z^34 + z^33 + z^32 + z^31 + z^30 + z^29 + z^28 + z^27 + z^26 + z^25 + z^24 + z^23 + z^22 + z^21 + z^20 + z^19 + z^18 + z^17 + z^16 + z^15 + z^14 + z^13 + z^12 + z^11 + z^10 + z^9 + z^8 + z^7 + z^6 + z^5 + z^4 + z^3 + z^2 + z + 1
with modulus w^37 + 553*z^35 + 433*z^34 + 659*z^33 + 262*z^32 + 262*z^30 + 263*z^29 + 422*z^28 + 290*z^27 + 263*z^26 + 553*z^25 + 659*z^24 + 290*z^23 + 202*z^22 + 202*z^21 + 422*z^20 + 433*z^19 + 433*z^18 + 422*z^17 + 202*z^16 + 202*z^15 + 290*z^14 + 659*z^13 + 553*z^12 + 263*z^11 + 290*z^10 + 422*z^9 + 263*z^8 + 262*z^7 + 262*z^5 + 659*z^4 + 433*z^3 + 553*z^2 + 604
Computing trace of random element (alpha = w
)
34 steps: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, Time: 0.130

Finished computing trace of random element.
Computing minimal polynomial of trace(alpha), as an element of K[X]
Time: 1.000
f =  X^37 + 165*X^34 + 68*X^33 + 211*X^32 + 91*X^31 + 34*X^30 + 382*X^29 + 376*X^28 + 307*X^27 + 490*X^26 + 177*X^25 + 297*X^24 + 496*X^23 + 16*X^22 + 139*X^21 + 362*X^20 + 372*X^19 + 560*X^18 + 247*X^17 + 35*X^16 + 142*X^15 + 538*X^14 + 52*X^13 + 157*X^12 + 249*X^11 + 92*X^10 + 464*X^9 + 347*X^8 + 659*X^7 + 637*X^6 + 116*X^5 + 439*X^4 + 510*X^3 + 561*X^2 + 183*X + 38
g =  T^37 + 165*T^34 + 68*T^33 + 211*T^32 + 91*T^31 + 34*T^30 + 382*T^29 + 376*T^28 + 307*T^27 + 490*T^26 + 177*T^25 + 297*T^24 + 496*T^23 + 16*T^22 + 139*T^21 + 362*T^20 + 372*T^19 + 560*T^18 + 247*T^17 + 35*T^16 + 142*T^15 + 538*T^14 + 52*T^13 + 157*T^12 + 249*T^11 + 92*T^10 + 464*T^9 + 347*T^8 + 659*T^7 + 637*T^6 + 116*T^5 + 439*T^4 + 510*T^3 + 561*T^2 + 183*T + 38
Forming extension L.
Time: 0.000
L =  Univariate Quotient Polynomial Algebra in w over Univariate Quotient Polynomial Algebra in z over Finite field of size 683
with modulus z^36 + z^35 + z^34 + z^33 + z^32 + z^31 + z^30 + z^29 + z^28 + z^27 + z^26 + z^25 + z^24 + z^23 + z^22 + z^21 + z^20 + z^19 + z^18 + z^17 + z^16 + z^15 + z^14 + z^13 + z^12 + z^11 + z^10 + z^9 + z^8 + z^7 + z^6 + z^5 + z^4 + z^3 + z^2 + z + 1
with modulus w^37 + 611*z^35 + 491*z^34 + 254*z^33 + 258*z^32 + 258*z^30 + 517*z^29 + 477*z^28 + 486*z^27 + 517*z^26 + 611*z^25 + 254*z^24 + 486*z^23 + 575*z^22 + 575*z^21 + 477*z^20 + 491*z^19 + 491*z^18 + 477*z^17 + 575*z^16 + 575*z^15 + 486*z^14 + 254*z^13 + 611*z^12 + 517*z^11 + 486*z^10 + 477*z^9 + 517*z^8 + 258*z^7 + 258*z^5 + 254*z^4 + 491*z^3 + 611*z^2 + 461
Computing trace of random element (alpha = w
)
34 steps: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, Time: 0.100

Finished computing trace of random element.
Computing minimal polynomial of trace(alpha), as an element of K[X]
Time: 1.010
f =  X^37 + 135*X^34 + 328*X^33 + 288*X^32 + 607*X^31 + 172*X^30 + 540*X^29 + 83*X^28 + 675*X^27 + 242*X^26 + 680*X^25 + 635*X^24 + 481*X^23 + 84*X^22 + 579*X^21 + 680*X^20 + 168*X^19 + 142*X^18 + 217*X^17 + 338*X^16 + 262*X^15 + 172*X^14 + 543*X^13 + 201*X^12 + 42*X^11 + 604*X^10 + 590*X^9 + 646*X^8 + 556*X^7 + 73*X^6 + 352*X^5 + 251*X^4 + 459*X^3 + 125*X^2 + 17*X + 474
g =  T^37 + 135*T^34 + 328*T^33 + 288*T^32 + 607*T^31 + 172*T^30 + 540*T^29 + 83*T^28 + 675*T^27 + 242*T^26 + 680*T^25 + 635*T^24 + 481*T^23 + 84*T^22 + 579*T^21 + 680*T^20 + 168*T^19 + 142*T^18 + 217*T^17 + 338*T^16 + 262*T^15 + 172*T^14 + 543*T^13 + 201*T^12 + 42*T^11 + 604*T^10 + 590*T^9 + 646*T^8 + 556*T^7 + 73*T^6 + 352*T^5 + 251*T^4 + 459*T^3 + 125*T^2 + 17*T + 474
CRT step --  5.71
So far:   [ -262293029201456827937357306747978653209062535979993123331515899375253384527718903616471614294706880512, 672876206080541961605226903062733805192789531352250137517709918865110475053588494379165834704584704, -264988194757774598059997009109229291894782867188883433765067934878438826901051317961493560950784, -660677952891702989779583125409354140514319272374345508868647000437128182296246506433818918912, 1982469259694895457314935195126430029297012127795195501396552566165464092269185291272585216, 122531389798606603051301724324273450024230408425919996998908148191119982817601008959488, -106850589825632789894896612887329721094911179135082410100519870323032421196184294522880, 55114049776782199582622334540957461483624433957263207123073326516074293876028866560, 484965911395764970871665544609840479278207020589886844109688505883361242049937408, -181630591887896963687470296480916555113983363630481468702049951552077809319936, -844861169134880185162881813189113039529594781451540816736263726469132320768, 3087405021478910646130093242279350919332930043815268747163999299543498752, -18557314583560485308211477301528775481854373440798991639264756844462080, 2854705449484624416795330612386811215415869973011706932441160613888, 31183544125608715763774641955998078374374445370791241228146966528, -20651404785477501467881895153357983415526349942938256921329664, 37244222236334875481641252538596552828631758622687299108864, 1772659418875854490177280483057352783210247369401565184, -872057565672136492561824204817812097995282872168087552, -80268638062435074559599184759300711777564488630272, -331493134727514939719441018060252656606965137408, -1396232608839552259966984463923520026947092480, 476259323830076662111107898811789814530048, -3171787436319383501703813676940597919744, -13099755496539209311468832290825568256, -2249002615426863992005848511545344, -4805711697609190244214712041472, -33628014249666292632903483392, -2221784070205669762924544, -19612786666813992009728, -25584896141781024768, -7894900273815552, -123335506765824, -118234637824, -6483584, 0, 0, 1 ]
Forming extension L.
Time: 0.000
L =  Univariate Quotient Polynomial Algebra in w over Univariate Quotient Polynomial Algebra in z over Finite field of size 701
with modulus z^36 + z^35 + z^34 + z^33 + z^32 + z^31 + z^30 + z^29 + z^28 + z^27 + z^26 + z^25 + z^24 + z^23 + z^22 + z^21 + z^20 + z^19 + z^18 + z^17 + z^16 + z^15 + z^14 + z^13 + z^12 + z^11 + z^10 + z^9 + z^8 + z^7 + z^6 + z^5 + z^4 + z^3 + z^2 + z + 1
with modulus w^37 + 198*z^35 + 331*z^34 + 484*z^33 + 665*z^32 + 665*z^30 + 298*z^29 + 212*z^28 + 688*z^27 + 298*z^26 + 198*z^25 + 484*z^24 + 688*z^23 + 432*z^22 + 432*z^21 + 212*z^20 + 331*z^19 + 331*z^18 + 212*z^17 + 432*z^16 + 432*z^15 + 688*z^14 + 484*z^13 + 198*z^12 + 298*z^11 + 688*z^10 + 212*z^9 + 298*z^8 + 665*z^7 + 665*z^5 + 484*z^4 + 331*z^3 + 198*z^2 + 484
Computing trace of random element (alpha = w
)
34 steps: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, Time: 0.130

Finished computing trace of random element.
Computing minimal polynomial of trace(alpha), as an element of K[X]
Time: 1.010
f =  X^37 + 666*X^34 + 351*X^33 + 20*X^32 + 234*X^31 + 563*X^30 + X^29 + 181*X^28 + 138*X^27 + 493*X^26 + 98*X^25 + 147*X^24 + X^23 + 176*X^22 + 221*X^21 + 177*X^20 + 584*X^19 + 650*X^18 + 74*X^17 + 214*X^16 + 249*X^15 + 104*X^14 + 589*X^13 + 440*X^12 + 609*X^11 + 411*X^10 + 326*X^9 + 593*X^8 + 183*X^7 + 448*X^6 + 482*X^5 + 96*X^4 + 641*X^3 + 252*X^2 + 96*X + 312
g =  T^37 + 666*T^34 + 351*T^33 + 20*T^32 + 234*T^31 + 563*T^30 + T^29 + 181*T^28 + 138*T^27 + 493*T^26 + 98*T^25 + 147*T^24 + T^23 + 176*T^22 + 221*T^21 + 177*T^20 + 584*T^19 + 650*T^18 + 74*T^17 + 214*T^16 + 249*T^15 + 104*T^14 + 589*T^13 + 440*T^12 + 609*T^11 + 411*T^10 + 326*T^9 + 593*T^8 + 183*T^7 + 448*T^6 + 482*T^5 + 96*T^4 + 641*T^3 + 252*T^2 + 96*T + 312
Forming extension L.
Time: 0.000
L =  Univariate Quotient Polynomial Algebra in w over Univariate Quotient Polynomial Algebra in z over Finite field of size 727
with modulus z^36 + z^35 + z^34 + z^33 + z^32 + z^31 + z^30 + z^29 + z^28 + z^27 + z^26 + z^25 + z^24 + z^23 + z^22 + z^21 + z^20 + z^19 + z^18 + z^17 + z^16 + z^15 + z^14 + z^13 + z^12 + z^11 + z^10 + z^9 + z^8 + z^7 + z^6 + z^5 + z^4 + z^3 + z^2 + z + 1
with modulus w^37 + 369*z^35 + 585*z^34 + 697*z^33 + 348*z^32 + 348*z^30 + 725*z^29 + 254*z^28 + 566*z^27 + 725*z^26 + 369*z^25 + 697*z^24 + 566*z^23 + 480*z^22 + 480*z^21 + 254*z^20 + 585*z^19 + 585*z^18 + 254*z^17 + 480*z^16 + 480*z^15 + 566*z^14 + 697*z^13 + 369*z^12 + 725*z^11 + 566*z^10 + 254*z^9 + 725*z^8 + 348*z^7 + 348*z^5 + 697*z^4 + 585*z^3 + 369*z^2 + 48
Computing trace of random element (alpha = w
)
34 steps: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, Time: 0.110

Finished computing trace of random element.
Computing minimal polynomial of trace(alpha), as an element of K[X]
Time: 1.020
f =  X^37 + 529*X^34 + 281*X^33 + 213*X^32 + 200*X^31 + 670*X^30 + 379*X^29 + 500*X^28 + 416*X^27 + 83*X^26 + 607*X^25 + 132*X^24 + 232*X^23 + 190*X^22 + 305*X^21 + 358*X^20 + 358*X^19 + 92*X^18 + 415*X^17 + 442*X^16 + 316*X^15 + 438*X^14 + 553*X^13 + 638*X^12 + 139*X^11 + 517*X^10 + 388*X^9 + 329*X^8 + 87*X^7 + 397*X^6 + 440*X^5 + 387*X^4 + 604*X^3 + 266*X^2 + 120*X + 165
g =  T^37 + 529*T^34 + 281*T^33 + 213*T^32 + 200*T^31 + 670*T^30 + 379*T^29 + 500*T^28 + 416*T^27 + 83*T^26 + 607*T^25 + 132*T^24 + 232*T^23 + 190*T^22 + 305*T^21 + 358*T^20 + 358*T^19 + 92*T^18 + 415*T^17 + 442*T^16 + 316*T^15 + 438*T^14 + 553*T^13 + 638*T^12 + 139*T^11 + 517*T^10 + 388*T^9 + 329*T^8 + 87*T^7 + 397*T^6 + 440*T^5 + 387*T^4 + 604*T^3 + 266*T^2 + 120*T + 165
Forming extension L.
Time: 0.000
L =  Univariate Quotient Polynomial Algebra in w over Univariate Quotient Polynomial Algebra in z over Finite field of size 757
with modulus z^36 + z^35 + z^34 + z^33 + z^32 + z^31 + z^30 + z^29 + z^28 + z^27 + z^26 + z^25 + z^24 + z^23 + z^22 + z^21 + z^20 + z^19 + z^18 + z^17 + z^16 + z^15 + z^14 + z^13 + z^12 + z^11 + z^10 + z^9 + z^8 + z^7 + z^6 + z^5 + z^4 + z^3 + z^2 + z + 1
with modulus w^37 + 367*z^35 + 138*z^34 + 702*z^33 + 272*z^32 + 272*z^30 + 729*z^29 + 30*z^28 + 44*z^27 + 729*z^26 + 367*z^25 + 702*z^24 + 44*z^23 + 511*z^22 + 511*z^21 + 30*z^20 + 138*z^19 + 138*z^18 + 30*z^17 + 511*z^16 + 511*z^15 + 44*z^14 + 702*z^13 + 367*z^12 + 729*z^11 + 44*z^10 + 30*z^9 + 729*z^8 + 272*z^7 + 272*z^5 + 702*z^4 + 138*z^3 + 367*z^2 + 103
Computing trace of random element (alpha = w
)
34 steps: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, Time: 0.090

Finished computing trace of random element.
Computing minimal polynomial of trace(alpha), as an element of K[X]
Time: 1.020
f =  X^37 + 121*X^34 + 658*X^33 + 202*X^32 + 6*X^31 + 500*X^30 + 65*X^29 + 92*X^28 + 155*X^27 + 281*X^26 + 183*X^25 + 539*X^24 + 83*X^23 + 626*X^22 + 564*X^21 + 522*X^20 + 731*X^19 + 64*X^18 + 248*X^17 + 385*X^16 + 183*X^15 + 472*X^14 + 213*X^13 + 755*X^12 + 319*X^11 + 127*X^10 + 430*X^9 + 696*X^8 + 623*X^7 + 392*X^6 + 336*X^5 + 458*X^4 + 290*X^3 + 649*X^2 + 434*X + 694
g =  T^37 + 121*T^34 + 658*T^33 + 202*T^32 + 6*T^31 + 500*T^30 + 65*T^29 + 92*T^28 + 155*T^27 + 281*T^26 + 183*T^25 + 539*T^24 + 83*T^23 + 626*T^22 + 564*T^21 + 522*T^20 + 731*T^19 + 64*T^18 + 248*T^17 + 385*T^16 + 183*T^15 + 472*T^14 + 213*T^13 + 755*T^12 + 319*T^11 + 127*T^10 + 430*T^9 + 696*T^8 + 623*T^7 + 392*T^6 + 336*T^5 + 458*T^4 + 290*T^3 + 649*T^2 + 434*T + 694
Forming extension L.
Time: 0.000
L =  Univariate Quotient Polynomial Algebra in w over Univariate Quotient Polynomial Algebra in z over Finite field of size 797
with modulus z^36 + z^35 + z^34 + z^33 + z^32 + z^31 + z^30 + z^29 + z^28 + z^27 + z^26 + z^25 + z^24 + z^23 + z^22 + z^21 + z^20 + z^19 + z^18 + z^17 + z^16 + z^15 + z^14 + z^13 + z^12 + z^11 + z^10 + z^9 + z^8 + z^7 + z^6 + z^5 + z^4 + z^3 + z^2 + z + 1
with modulus w^37 + 409*z^35 + 36*z^34 + 412*z^33 + 169*z^32 + 169*z^30 + 403*z^29 + 45*z^28 + 717*z^27 + 403*z^26 + 409*z^25 + 412*z^24 + 717*z^23 + 645*z^22 + 645*z^21 + 45*z^20 + 36*z^19 + 36*z^18 + 45*z^17 + 645*z^16 + 645*z^15 + 717*z^14 + 412*z^13 + 409*z^12 + 403*z^11 + 717*z^10 + 45*z^9 + 403*z^8 + 169*z^7 + 169*z^5 + 412*z^4 + 36*z^3 + 409*z^2 + 621
Computing trace of random element (alpha = w
)
34 steps: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, Time: 0.120

Finished computing trace of random element.
Computing minimal polynomial of trace(alpha), as an element of K[X]
Time: 1.010
f =  X^37 + 11*X^34 + 549*X^33 + 137*X^32 + 382*X^31 + 570*X^30 + 702*X^29 + 470*X^28 + 793*X^27 + 668*X^26 + 11*X^25 + 508*X^24 + 750*X^23 + 767*X^22 + 300*X^21 + 59*X^20 + 380*X^19 + 71*X^18 + 294*X^17 + 443*X^16 + 754*X^15 + 765*X^14 + 149*X^13 + 268*X^12 + 452*X^11 + 636*X^10 + 701*X^9 + 471*X^8 + 587*X^7 + 317*X^6 + 391*X^5 + 81*X^4 + 698*X^3 + 722*X^2 + 134*X + 394
g =  T^37 + 11*T^34 + 549*T^33 + 137*T^32 + 382*T^31 + 570*T^30 + 702*T^29 + 470*T^28 + 793*T^27 + 668*T^26 + 11*T^25 + 508*T^24 + 750*T^23 + 767*T^22 + 300*T^21 + 59*T^20 + 380*T^19 + 71*T^18 + 294*T^17 + 443*T^16 + 754*T^15 + 765*T^14 + 149*T^13 + 268*T^12 + 452*T^11 + 636*T^10 + 701*T^9 + 471*T^8 + 587*T^7 + 317*T^6 + 391*T^5 + 81*T^4 + 698*T^3 + 722*T^2 + 134*T + 394
Forming extension L.
Time: 0.000
L =  Univariate Quotient Polynomial Algebra in w over Univariate Quotient Polynomial Algebra in z over Finite field of size 809
with modulus z^36 + z^35 + z^34 + z^33 + z^32 + z^31 + z^30 + z^29 + z^28 + z^27 + z^26 + z^25 + z^24 + z^23 + z^22 + z^21 + z^20 + z^19 + z^18 + z^17 + z^16 + z^15 + z^14 + z^13 + z^12 + z^11 + z^10 + z^9 + z^8 + z^7 + z^6 + z^5 + z^4 + z^3 + z^2 + z + 1
with modulus w^37 + 50*z^35 + 277*z^34 + 183*z^33 + 549*z^32 + 549*z^30 + 557*z^29 + 703*z^28 + 449*z^27 + 557*z^26 + 50*z^25 + 183*z^24 + 449*z^23 + 196*z^22 + 196*z^21 + 703*z^20 + 277*z^19 + 277*z^18 + 703*z^17 + 196*z^16 + 196*z^15 + 449*z^14 + 183*z^13 + 50*z^12 + 557*z^11 + 449*z^10 + 703*z^9 + 557*z^8 + 549*z^7 + 549*z^5 + 183*z^4 + 277*z^3 + 50*z^2 + 805
Computing trace of random element (alpha = w
)
34 steps: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, Time: 0.110

Finished computing trace of random element.
Computing minimal polynomial of trace(alpha), as an element of K[X]
Time: 1.010
f =  X^37 + 551*X^34 + 256*X^33 + 568*X^32 + 652*X^31 + 145*X^30 + 761*X^29 + 234*X^28 + 653*X^27 + 635*X^26 + 381*X^25 + 518*X^24 + 279*X^23 + 54*X^22 + 351*X^21 + 627*X^20 + 40*X^19 + 288*X^18 + 325*X^17 + 740*X^16 + 664*X^15 + 323*X^14 + 663*X^13 + 611*X^12 + 542*X^11 + 402*X^10 + 705*X^9 + 317*X^8 + 143*X^7 + 696*X^6 + 33*X^5 + 413*X^4 + 559*X^3 + 551*X^2 + 638*X + 26
g =  T^37 + 551*T^34 + 256*T^33 + 568*T^32 + 652*T^31 + 145*T^30 + 761*T^29 + 234*T^28 + 653*T^27 + 635*T^26 + 381*T^25 + 518*T^24 + 279*T^23 + 54*T^22 + 351*T^21 + 627*T^20 + 40*T^19 + 288*T^18 + 325*T^17 + 740*T^16 + 664*T^15 + 323*T^14 + 663*T^13 + 611*T^12 + 542*T^11 + 402*T^10 + 705*T^9 + 317*T^8 + 143*T^7 + 696*T^6 + 33*T^5 + 413*T^4 + 559*T^3 + 551*T^2 + 638*T + 26
Found it!!!
Time: 63.800
f :=  X^37 - 6483584*X^34 - 118234637824*X^33 - 123335506765824*X^32 - 7894900273815552*X^31 - 25584896141781024768*X^30 - 19612786666813992009728*X^29 - 2221784070205669762924544*X^28 - 33628014249666292632903483392*X^27 - 4805711697609190244214712041472*X^26 - 2249002615426863992005848511545344*X^25 - 13099755496539209311468832290825568256*X^24 - 3171787436319383501703813676940597919744*X^23 + 476259323830076662111107898811789814530048*X^22 - 1396232608839552259966984463923520026947092480*X^21 - 331493134727514939719441018060252656606965137408*X^20 - 80268638062435074559599184759300711777564488630272*X^19 - 872057565672136492561824204817812097995282872168087552*X^18 + 1772659418875854490177280483057352783210247369401565184*X^17 + 37244222236334875481641252538596552828631758622687299108864*X^16 - 20651404785477501467881895153357983415526349942938256921329664*X^15 + 31183544125608715763774641955998078374374445370791241228146966528*X^14 + 2854705449484624416795330612386811215415869973011706932441160613888*X^13 - 18557314583560485308211477301528775481854373440798991639264756844462080*X^12 + 3087405021478910646130093242279350919332930043815268747163999299543498752*X^11 - 844861169134880185162881813189113039529594781451540816736263726469132320768*X^10 - 181630591887896963687470296480916555113983363630481468702049951552077809319936*X^9 + 484965911395764970871665544609840479278207020589886844109688505883361242049937408*X^8 + 55114049776782199582622334540957461483624433957263207123073326516074293876028866560*X^7 - 106850589825632789894896612887329721094911179135082410100519870323032421196184294522880*X^6 + 122531389798606603051301724324273450024230408425919996998908148191119982817601008959488*X^5 + 1982469259694895457314935195126430029297012127795195501396552566165464092269185291272585216*X^4 - 660677952891702989779583125409354140514319272374345508868647000437128182296246506433818918912*X^3 - 264988194757774598059997009109229291894782867188883433765067934878438826901051317961493560950784*X^2 + 672876206080541961605226903062733805192789531352250137517709918865110475053588494379165834704584704*X - 262293029201456827937357306747978653209062535979993123331515899375253384527718903616471614294706880512

Total time: 65.849 seconds