[was@modular sharifi]$ [was@modular sharifi]$ Magma V2.8-10     Mon Apr  8 2002 15:45:32 on modular  [Seed = 2417844109]
Type ? for help.  Type <Ctrl>-D to quit.

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

Loading "/home/was/magma/local/init.m"
> Attach("unitcomp.m");
> f, L, K, del, tr_alpha := FindDegree37FieldMod(59);
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: 0.860

Finished computing trace of random element.
Computing minimal polynomial of trace(alpha), as an element of K[X]
Time: 1.880
> tr_alpha;
(34*z^35 + 58*z^34 + 27*z^33 + 52*z^32 + 52*z^30 + 9*z^29 + 57*z^28 + 24*z^27 + 9*z^26 + 34*z^25 + 27*z^24 + 24*z^23 + 28*z^22 + 28*z^21 + 57*z^20 + 58*z^19 + 58*z^18 + 57*z^17 + 28*z^16 + 28*z^15 + 24*z^14 + 27*z^13 + 34*z^12 + 9*z^11 + 24*z^10 + 57*z^9 + 9*z^8 + 52*z^7 + 52*z^5 + 27*z^4 + 58*z^3 + 34*z^2 + 10)*w^34 + (58*z^35 + 9*z^34 + 51*z^33 + 51*z^32 + 51*z^30 + 5*z^29 + 11*z^28 + 25*z^27 + 5*z^26 + 58*z^25 + 51*z^24 + 25*z^23 + 49*z^22 + 49*z^21 + 11*z^20 + 9*z^19 + 9*z^18 + 11*z^17 + 49*z^16 + 49*z^15 + 25*z^14 + 51*z^13 + 58*z^12 + 5*z^11 + 25*z^10 + 11*z^9 + 5*z^8 + 51*z^7 + 51*z^5 + 51*z^4 + 9*z^3 + 58*z^2 + 38)*w^33 + (4*z^35 + 9*z^34 + 58*z^33 + 29*z^32 + 29*z^30 + 37*z^29 + 46*z^28 + 53*z^27 + 37*z^26 + 4*z^25 + 58*z^24 + 53*z^23 + 42*z^22 + 42*z^21 + 46*z^20 + 9*z^19 + 9*z^18 + 46*z^17 + 42*z^16 + 42*z^15 + 53*z^14 + 58*z^13 + 4*z^12 + 37*z^11 + 53*z^10 + 46*z^9 + 37*z^8 + 29*z^7 + 29*z^5 + 58*z^4 + 9*z^3 + 4*z^2 + 48)*w^26 + (26*z^35 + 28*z^34 + z^33 + 16*z^32 + 16*z^30 + 51*z^29 + 49*z^28 + 52*z^27 + 51*z^26 + 26*z^25 + z^24 + 52*z^23 + 6*z^22 + 6*z^21 + 49*z^20 + 28*z^19 + 28*z^18 + 49*z^17 + 6*z^16 + 6*z^15 + 52*z^14 + z^13 + 26*z^12 + 51*z^11 + 52*z^10 + 49*z^9 + 51*z^8 + 16*z^7 + 16*z^5 + z^4 + 28*z^3 + 26*z^2 + 53)*w^16 + (27*z^35 + 41*z^34 + 15*z^33 + 5*z^32 + 5*z^30 + 6*z^29 + 13*z^28 + 19*z^27 + 6*z^26 + 27*z^25 + 15*z^24 + 19*z^23 + 36*z^22 + 36*z^21 + 13*z^20 + 41*z^19 + 41*z^18 + 13*z^17 + 36*z^16 + 36*z^15 + 19*z^14 + 15*z^13 + 27*z^12 + 6*z^11 + 19*z^10 + 13*z^9 + 6*z^8 + 5*z^7 + 5*z^5 + 15*z^4 + 41*z^3 + 27*z^2 + 14)*w^12 + (9*z^35 + 31*z^34 + 32*z^33 + 30*z^32 + 30*z^30 + 20*z^29 + 11*z^28 + 31*z^27 + 20*z^26 + 9*z^25 + 32*z^24 + 31*z^23 + 58*z^22 + 58*z^21 + 11*z^20 + 31*z^19 + 31*z^18 + 11*z^17 + 58*z^16 + 58*z^15 + 31*z^14 + 32*z^13 + 9*z^12 + 20*z^11 + 31*z^10 + 11*z^9 + 20*z^8 + 30*z^7 + 30*z^5 + 32*z^4 + 31*z^3 + 9*z^2 + 33)*w^10 + (58*z^35 + 28*z^34 + 17*z^33 + 13*z^32 + 13*z^30 + 48*z^29 + 31*z^28 + 55*z^27 + 48*z^26 + 58*z^25 + 17*z^24 + 55*z^23 + 19*z^22 + 19*z^21 + 31*z^20 + 28*z^19 + 28*z^18 + 31*z^17 + 19*z^16 + 19*z^15 + 55*z^14 + 17*z^13 + 58*z^12 + 48*z^11 + 55*z^10 + 31*z^9 + 48*z^8 + 13*z^7 + 13*z^5 + 17*z^4 + 28*z^3 + 58*z^2 + 48)*w^9 + (18*z^35 + 27*z^34 + 39*z^33 + 42*z^32 + 42*z^30 + 31*z^29 + 11*z^28 + 3*z^27 + 31*z^26 + 18*z^25 + 39*z^24 + 3*z^23 + 33*z^22 + 33*z^21 + 11*z^20 + 27*z^19 + 27*z^18 + 11*z^17 + 33*z^16 + 33*z^15 + 3*z^14 + 39*z^13 + 18*z^12 + 31*z^11 + 3*z^10 + 11*z^9 + 31*z^8 + 42*z^7 + 42*z^5 + 39*z^4 + 27*z^3 + 18*z^2 + 22)*w^7 + 4*w
> f;
X^37 + (14*z^35 + 36*z^34 + 9*z^33 + 23*z^32 + 23*z^30 + 33*z^29 + 44*z^28 + 10*z^27 + 33*z^26 + 14*z^25 + 9*z^24 + 10*z^23 + 54*z^22 + 54*z^21 + 44*z^20 + 36*z^19 + 36*z^18 + 44*z^17 + 54*z^16 + 54*z^15 + 10*z^14 + 9*z^13 + 14*z^12 + 33*z^11 + 10*z^10 + 44*z^9 + 33*z^8 + 23*z^7 + 23*z^5 + 9*z^4 + 36*z^3 + 14*z^2 + 15)*X^34 + (37*z^35 + 2*z^34 + 17*z^33 + 44*z^32 + 44*z^30 + 37*z^29 + 53*z^28 + 6*z^27 + 37*z^26 + 37*z^25 + 17*z^24 + 6*z^23 + 23*z^22 + 23*z^21 + 53*z^20 + 2*z^19 + 2*z^18 + 53*z^17 + 23*z^16 + 23*z^15 + 6*z^14 + 17*z^13 + 37*z^12 + 37*z^11 + 6*z^10 + 53*z^9 + 37*z^8 + 44*z^7 + 44*z^5 + 17*z^4 + 2*z^3 + 37*z^2 + 30)*X^33 + (46*z^35 + 55*z^34 + 8*z^33 + 50*z^32 + 50*z^30 + 57*z^29 + 19*z^28 + 48*z^27 + 57*z^26 + 46*z^25 + 8*z^24 + 48*z^23 + 35*z^22 + 35*z^21 + 19*z^20 + 55*z^19 + 55*z^18 + 19*z^17 + 35*z^16 + 35*z^15 + 48*z^14 + 8*z^13 + 46*z^12 + 57*z^11 + 48*z^10 + 19*z^9 + 57*z^8 + 50*z^7 + 50*z^5 + 8*z^4 + 55*z^3 + 46*z^2 + 56)*X^32 + (46*z^35 + 21*z^34 + 39*z^33 + 41*z^32 + 41*z^30 + 26*z^29 + 43*z^28 + 41*z^27 + 26*z^26 + 46*z^25 + 39*z^24 + 41*z^23 + 16*z^22 + 16*z^21 + 43*z^20 + 21*z^19 + 21*z^18 + 43*z^17 + 16*z^16 + 16*z^15 + 41*z^14 + 39*z^13 + 46*z^12 + 26*z^11 + 41*z^10 + 43*z^9 + 26*z^8 + 41*z^7 + 41*z^5 + 39*z^4 + 21*z^3 + 46*z^2 + 6)*X^31 + (9*z^35 + z^34 + 30*z^33 + 7*z^32 + 7*z^30 + 13*z^29 + 21*z^28 + 20*z^27 + 13*z^26 + 9*z^25 + 30*z^24 + 20*z^23 + 10*z^22 + 10*z^21 + 21*z^20 + z^19 + z^18 + 21*z^17 + 10*z^16 + 10*z^15 + 20*z^14 + 30*z^13 + 9*z^12 + 13*z^11 + 20*z^10 + 21*z^9 + 13*z^8 + 7*z^7 + 7*z^5 + 30*z^4 + z^3 + 9*z^2 + 51)*X^30 + (41*z^35 + 15*z^34 + 49*z^33 + 4*z^32 + 4*z^30 + 29*z^29 + 34*z^28 + 57*z^27 + 29*z^26 + 41*z^25 + 49*z^24 + 57*z^23 + 42*z^22 + 42*z^21 + 34*z^20 + 15*z^19 + 15*z^18 + 34*z^17 + 42*z^16 + 42*z^15 + 57*z^14 + 49*z^13 + 41*z^12 + 29*z^11 + 57*z^10 + 34*z^9 + 29*z^8 + 4*z^7 + 4*z^5 + 49*z^4 + 15*z^3 + 41*z^2 + 57)*X^29 + (27*z^35 + 13*z^34 + 45*z^33 + 47*z^32 + 47*z^30 + 43*z^29 + 26*z^28 + 4*z^27 + 43*z^26 + 27*z^25 + 45*z^24 + 4*z^23 + 14*z^22 + 14*z^21 + 26*z^20 + 13*z^19 + 13*z^18 + 26*z^17 + 14*z^16 + 14*z^15 + 4*z^14 + 45*z^13 + 27*z^12 + 43*z^11 + 4*z^10 + 26*z^9 + 43*z^8 + 47*z^7 + 47*z^5 + 45*z^4 + 13*z^3 + 27*z^2 + 38)*X^28 + (17*z^35 + 38*z^34 + 26*z^33 + 17*z^32 + 17*z^30 + 47*z^29 + 21*z^28 + 46*z^27 + 47*z^26 + 17*z^25 + 26*z^24 + 46*z^23 + 13*z^22 + 13*z^21 + 21*z^20 + 38*z^19 + 38*z^18 + 21*z^17 + 13*z^16 + 13*z^15 + 46*z^14 + 26*z^13 + 17*z^12 + 47*z^11 + 46*z^10 + 21*z^9 + 47*z^8 + 17*z^7 + 17*z^5 + 26*z^4 + 38*z^3 + 17*z^2 + 55)*X^27 + (53*z^35 + 2*z^34 + 55*z^33 + 2*z^32 + 2*z^30 + 52*z^29 + 35*z^28 + 36*z^27 + 52*z^26 + 53*z^25 + 55*z^24 + 36*z^23 + 22*z^22 + 22*z^21 + 35*z^20 + 2*z^19 + 2*z^18 + 35*z^17 + 22*z^16 + 22*z^15 + 36*z^14 + 55*z^13 + 53*z^12 + 52*z^11 + 36*z^10 + 35*z^9 + 52*z^8 + 2*z^7 + 2*z^5 + 55*z^4 + 2*z^3 + 53*z^2 + 55)*X^26 + (13*z^35 + 40*z^34 + 20*z^33 + 14*z^32 + 14*z^30 + 41*z^29 + 42*z^28 + 6*z^27 + 41*z^26 + 13*z^25 + 20*z^24 + 6*z^23 + 25*z^22 + 25*z^21 + 42*z^20 + 40*z^19 + 40*z^18 + 42*z^17 + 25*z^16 + 25*z^15 + 6*z^14 + 20*z^13 + 13*z^12 + 41*z^11 + 6*z^10 + 42*z^9 + 41*z^8 + 14*z^7 + 14*z^5 + 20*z^4 + 40*z^3 + 13*z^2 + 57)*X^25 + (45*z^35 + 9*z^34 + 11*z^33 + 15*z^32 + 15*z^30 + 18*z^29 + 50*z^28 + 6*z^27 + 18*z^26 + 45*z^25 + 11*z^24 + 6*z^23 + 38*z^22 + 38*z^21 + 50*z^20 + 9*z^19 + 9*z^18 + 50*z^17 + 38*z^16 + 38*z^15 + 6*z^14 + 11*z^13 + 45*z^12 + 18*z^11 + 6*z^10 + 50*z^9 + 18*z^8 + 15*z^7 + 15*z^5 + 11*z^4 + 9*z^3 + 45*z^2 + 39)*X^24 + (39*z^35 + 24*z^34 + 29*z^33 + 30*z^32 + 30*z^30 + 20*z^29 + 42*z^28 + 48*z^27 + 20*z^26 + 39*z^25 + 29*z^24 + 48*z^23 + 47*z^22 + 47*z^21 + 42*z^20 + 24*z^19 + 24*z^18 + 42*z^17 + 47*z^16 + 47*z^15 + 48*z^14 + 29*z^13 + 39*z^12 + 20*z^11 + 48*z^10 + 42*z^9 + 20*z^8 + 30*z^7 + 30*z^5 + 29*z^4 + 24*z^3 + 39*z^2 + 57)*X^23 + (16*z^35 + 56*z^34 + 37*z^33 + 57*z^32 + 57*z^30 + 17*z^29 + 6*z^28 + 38*z^27 + 17*z^26 + 16*z^25 + 37*z^24 + 38*z^23 + 12*z^22 + 12*z^21 + 6*z^20 + 56*z^19 + 56*z^18 + 6*z^17 + 12*z^16 + 12*z^15 + 38*z^14 + 37*z^13 + 16*z^12 + 17*z^11 + 38*z^10 + 6*z^9 + 17*z^8 + 57*z^7 + 57*z^5 + 37*z^4 + 56*z^3 + 16*z^2 + 32)*X^22 + (38*z^35 + 31*z^34 + 40*z^33 + 32*z^32 + 32*z^30 + 6*z^28 + 52*z^27 + 38*z^25 + 40*z^24 + 52*z^23 + 14*z^22 + 14*z^21 + 6*z^20 + 31*z^19 + 31*z^18 + 6*z^17 + 14*z^16 + 14*z^15 + 52*z^14 + 40*z^13 + 38*z^12 + 52*z^10 + 6*z^9 + 32*z^7 + 32*z^5 + 40*z^4 + 31*z^3 + 38*z^2 + 1)*X^21 + (12*z^35 + 6*z^34 + 17*z^33 + 26*z^32 + 26*z^30 + 39*z^29 + 38*z^28 + 11*z^27 + 39*z^26 + 12*z^25 + 17*z^24 + 11*z^23 + 17*z^22 + 17*z^21 + 38*z^20 + 6*z^19 + 6*z^18 + 38*z^17 + 17*z^16 + 17*z^15 + 11*z^14 + 17*z^13 + 12*z^12 + 39*z^11 + 11*z^10 + 38*z^9 + 39*z^8 + 26*z^7 + 26*z^5 + 17*z^4 + 6*z^3 + 12*z^2 + 50)*X^20 + (15*z^35 + 39*z^34 + 39*z^33 + 58*z^32 + 58*z^30 + 5*z^29 + 56*z^28 + 20*z^27 + 5*z^26 + 15*z^25 + 39*z^24 + 20*z^23 + 12*z^22 + 12*z^21 + 56*z^20 + 39*z^19 + 39*z^18 + 56*z^17 + 12*z^16 + 12*z^15 + 20*z^14 + 39*z^13 + 15*z^12 + 5*z^11 + 20*z^10 + 56*z^9 + 5*z^8 + 58*z^7 + 58*z^5 + 39*z^4 + 39*z^3 + 15*z^2 + 20)*X^19 + (52*z^35 + 32*z^34 + 31*z^33 + 57*z^32 + 57*z^30 + 57*z^29 + 57*z^28 + 29*z^27 + 57*z^26 + 52*z^25 + 31*z^24 + 29*z^23 + 46*z^22 + 46*z^21 + 57*z^20 + 32*z^19 + 32*z^18 + 57*z^17 + 46*z^16 + 46*z^15 + 29*z^14 + 31*z^13 + 52*z^12 + 57*z^11 + 29*z^10 + 57*z^9 + 57*z^8 + 57*z^7 + 57*z^5 + 31*z^4 + 32*z^3 + 52*z^2 + 32)*X^18 + (36*z^35 + 30*z^34 + z^33 + 28*z^32 + 28*z^30 + 13*z^29 + 12*z^27 + 13*z^26 + 36*z^25 + z^24 + 12*z^23 + 32*z^22 + 32*z^21 + 30*z^19 + 30*z^18 + 32*z^16 + 32*z^15 + 12*z^14 + z^13 + 36*z^12 + 13*z^11 + 12*z^10 + 13*z^8 + 28*z^7 + 28*z^5 + z^4 + 30*z^3 + 36*z^2 + 40)*X^17 + (45*z^35 + 39*z^34 + 5*z^33 + 5*z^32 + 5*z^30 + 57*z^28 + 39*z^27 + 45*z^25 + 5*z^24 + 39*z^23 + 20*z^22 + 20*z^21 + 57*z^20 + 39*z^19 + 39*z^18 + 57*z^17 + 20*z^16 + 20*z^15 + 39*z^14 + 5*z^13 + 45*z^12 + 39*z^10 + 57*z^9 + 5*z^7 + 5*z^5 + 5*z^4 + 39*z^3 + 45*z^2 + 11)*X^16 + (7*z^35 + 8*z^34 + 38*z^33 + 6*z^32 + 6*z^30 + 37*z^29 + 19*z^28 + 2*z^27 + 37*z^26 + 7*z^25 + 38*z^24 + 2*z^23 + 38*z^22 + 38*z^21 + 19*z^20 + 8*z^19 + 8*z^18 + 19*z^17 + 38*z^16 + 38*z^15 + 2*z^14 + 38*z^13 + 7*z^12 + 37*z^11 + 2*z^10 + 19*z^9 + 37*z^8 + 6*z^7 + 6*z^5 + 38*z^4 + 8*z^3 + 7*z^2 + 24)*X^15 + (3*z^35 + 42*z^34 + 27*z^33 + 26*z^32 + 26*z^30 + 56*z^29 + 11*z^28 + 55*z^27 + 56*z^26 + 3*z^25 + 27*z^24 + 55*z^23 + 5*z^22 + 5*z^21 + 11*z^20 + 42*z^19 + 42*z^18 + 11*z^17 + 5*z^16 + 5*z^15 + 55*z^14 + 27*z^13 + 3*z^12 + 56*z^11 + 55*z^10 + 11*z^9 + 56*z^8 + 26*z^7 + 26*z^5 + 27*z^4 + 42*z^3 + 3*z^2 + 1)*X^14 + (23*z^35 + 29*z^34 + 21*z^33 + 3*z^32 + 3*z^30 + 48*z^29 + 11*z^28 + 37*z^27 + 48*z^26 + 23*z^25 + 21*z^24 + 37*z^23 + 51*z^22 + 51*z^21 + 11*z^20 + 29*z^19 + 29*z^18 + 11*z^17 + 51*z^16 + 51*z^15 + 37*z^14 + 21*z^13 + 23*z^12 + 48*z^11 + 37*z^10 + 11*z^9 + 48*z^8 + 3*z^7 + 3*z^5 + 21*z^4 + 29*z^3 + 23*z^2 + 31)*X^13 + (32*z^35 + 35*z^34 + 48*z^33 + 32*z^32 + 32*z^30 + 38*z^29 + 57*z^28 + 41*z^27 + 38*z^26 + 32*z^25 + 48*z^24 + 41*z^23 + 14*z^22 + 14*z^21 + 57*z^20 + 35*z^19 + 35*z^18 + 57*z^17 + 14*z^16 + 14*z^15 + 41*z^14 + 48*z^13 + 32*z^12 + 38*z^11 + 41*z^10 + 57*z^9 + 38*z^8 + 32*z^7 + 32*z^5 + 48*z^4 + 35*z^3 + 32*z^2 + 23)*X^12 + (9*z^35 + 26*z^34 + 28*z^33 + 36*z^32 + 36*z^30 + 30*z^29 + 49*z^28 + 56*z^27 + 30*z^26 + 9*z^25 + 28*z^24 + 56*z^23 + 3*z^22 + 3*z^21 + 49*z^20 + 26*z^19 + 26*z^18 + 49*z^17 + 3*z^16 + 3*z^15 + 56*z^14 + 28*z^13 + 9*z^12 + 30*z^11 + 56*z^10 + 49*z^9 + 30*z^8 + 36*z^7 + 36*z^5 + 28*z^4 + 26*z^3 + 9*z^2 + 2)*X^11 + (7*z^35 + 58*z^34 + 31*z^33 + 46*z^32 + 46*z^30 + 26*z^29 + 24*z^28 + 44*z^27 + 26*z^26 + 7*z^25 + 31*z^24 + 44*z^23 + 32*z^22 + 32*z^21 + 24*z^20 + 58*z^19 + 58*z^18 + 24*z^17 + 32*z^16 + 32*z^15 + 44*z^14 + 31*z^13 + 7*z^12 + 26*z^11 + 44*z^10 + 24*z^9 + 26*z^8 + 46*z^7 + 46*z^5 + 31*z^4 + 58*z^3 + 7*z^2 + 55)*X^10 + (22*z^35 + 58*z^34 + 49*z^33 + 20*z^32 + 20*z^30 + 38*z^29 + 37*z^28 + 11*z^27 + 38*z^26 + 22*z^25 + 49*z^24 + 11*z^23 + 41*z^22 + 41*z^21 + 37*z^20 + 58*z^19 + 58*z^18 + 37*z^17 + 41*z^16 + 41*z^15 + 11*z^14 + 49*z^13 + 22*z^12 + 38*z^11 + 11*z^10 + 37*z^9 + 38*z^8 + 20*z^7 + 20*z^5 + 49*z^4 + 58*z^3 + 22*z^2 + 39)*X^9 + (11*z^35 + 28*z^34 + 8*z^33 + 57*z^32 + 57*z^30 + 56*z^29 + 19*z^28 + 57*z^27 + 56*z^26 + 11*z^25 + 8*z^24 + 57*z^23 + 18*z^22 + 18*z^21 + 19*z^20 + 28*z^19 + 28*z^18 + 19*z^17 + 18*z^16 + 18*z^15 + 57*z^14 + 8*z^13 + 11*z^12 + 56*z^11 + 57*z^10 + 19*z^9 + 56*z^8 + 57*z^7 + 57*z^5 + 8*z^4 + 28*z^3 + 11*z^2 + 34)*X^8 + (23*z^35 + 58*z^34 + 14*z^33 + 19*z^32 + 19*z^30 + 34*z^29 + 29*z^28 + 20*z^27 + 34*z^26 + 23*z^25 + 14*z^24 + 20*z^23 + 43*z^22 + 43*z^21 + 29*z^20 + 58*z^19 + 58*z^18 + 29*z^17 + 43*z^16 + 43*z^15 + 20*z^14 + 14*z^13 + 23*z^12 + 34*z^11 + 20*z^10 + 29*z^9 + 34*z^8 + 19*z^7 + 19*z^5 + 14*z^4 + 58*z^3 + 23*z^2 + 7)*X^7 + (9*z^35 + 28*z^34 + 9*z^33 + 24*z^32 + 24*z^30 + 20*z^29 + 51*z^28 + 37*z^27 + 20*z^26 + 9*z^25 + 9*z^24 + 37*z^23 + 44*z^22 + 44*z^21 + 51*z^20 + 28*z^19 + 28*z^18 + 51*z^17 + 44*z^16 + 44*z^15 + 37*z^14 + 9*z^13 + 9*z^12 + 20*z^11 + 37*z^10 + 51*z^9 + 20*z^8 + 24*z^7 + 24*z^5 + 9*z^4 + 28*z^3 + 9*z^2 + 46)*X^6 + (40*z^35 + 24*z^34 + 39*z^33 + 5*z^32 + 5*z^30 + 34*z^29 + 7*z^28 + 30*z^27 + 34*z^26 + 40*z^25 + 39*z^24 + 30*z^23 + 43*z^22 + 43*z^21 + 7*z^20 + 24*z^19 + 24*z^18 + 7*z^17 + 43*z^16 + 43*z^15 + 30*z^14 + 39*z^13 + 40*z^12 + 34*z^11 + 30*z^10 + 7*z^9 + 34*z^8 + 5*z^7 + 5*z^5 + 39*z^4 + 24*z^3 + 40*z^2 + 50)*X^5 + (9*z^35 + 21*z^34 + 44*z^33 + 14*z^32 + 14*z^30 + 22*z^29 + 18*z^28 + 32*z^27 + 22*z^26 + 9*z^25 + 44*z^24 + 32*z^23 + 13*z^22 + 13*z^21 + 18*z^20 + 21*z^19 + 21*z^18 + 18*z^17 + 13*z^16 + 13*z^15 + 32*z^14 + 44*z^13 + 9*z^12 + 22*z^11 + 32*z^10 + 18*z^9 + 22*z^8 + 14*z^7 + 14*z^5 + 44*z^4 + 21*z^3 + 9*z^2 + 18)*X^4 + (24*z^35 + 37*z^34 + 54*z^33 + 31*z^32 + 31*z^30 + 28*z^29 + 37*z^27 + 28*z^26 + 24*z^25 + 54*z^24 + 37*z^23 + 50*z^22 + 50*z^21 + 37*z^19 + 37*z^18 + 50*z^16 + 50*z^15 + 37*z^14 + 54*z^13 + 24*z^12 + 28*z^11 + 37*z^10 + 28*z^8 + 31*z^7 + 31*z^5 + 54*z^4 + 37*z^3 + 24*z^2 + 24)*X^3 + (24*z^35 + 54*z^34 + 54*z^33 + 23*z^32 + 23*z^30 + 19*z^29 + 21*z^28 + 48*z^27 + 19*z^26 + 24*z^25 + 54*z^24 + 48*z^23 + 44*z^22 + 44*z^21 + 21*z^20 + 54*z^19 + 54*z^18 + 21*z^17 + 44*z^16 + 44*z^15 + 48*z^14 + 54*z^13 + 24*z^12 + 19*z^11 + 48*z^10 + 21*z^9 + 19*z^8 + 23*z^7 + 23*z^5 + 54*z^4 + 54*z^3 + 24*z^2 + 2)*X^2 + (53*z^35 + 51*z^34 + 9*z^33 + 42*z^32 + 42*z^30 + 58*z^29 + 18*z^28 + 14*z^27 + 58*z^26 + 53*z^25 + 9*z^24 + 14*z^23 + 2*z^22 + 2*z^21 + 18*z^20 + 51*z^19 + 51*z^18 + 18*z^17 + 2*z^16 + 2*z^15 + 14*z^14 + 9*z^13 + 53*z^12 + 58*z^11 + 14*z^10 + 18*z^9 + 58*z^8 + 42*z^7 + 42*z^5 + 9*z^4 + 51*z^3 + 53*z^2 + 21)*X + 51*z^35 + 6*z^34 + 14*z^33 + 30*z^32 + 30*z^30 + 24*z^29 + 56*z^28 + 6*z^27 + 24*z^26 + 51*z^25 + 14*z^24 + 6*z^23 + 2*z^22 + 2*z^21 + 56*z^20 + 6*z^19 + 6*z^18 + 56*z^17 + 2*z^16 + 2*z^15 + 6*z^14 + 14*z^13 + 51*z^12 + 24*z^11 + 6*z^10 + 56*z^9 + 24*z^8 + 30*z^7 + 30*z^5 + 14*z^4 + 6*z^3 + 51*z^2 + 43
> Evaluate(f,tr_alpha);
0
> f, L, K, del, tr_alpha := FindDegree37FieldMod(11);
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 11
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 + 8*z^35 + 2*z^34 + 7*z^33 + 10*z^32 + 10*z^30 + 3*z^29 + 5*z^28 + 9*z^27 + 3*z^26 + 8*z^25 + 7*z^24 + 9*z^23 + 7*z^22 + 7*z^21 + 5*z^20 + 2*z^19 + 2*z^18 + 5*z^17 + 7*z^16 + 7*z^15 + 9*z^14 + 7*z^13 + 8*z^12 + 3*z^11 + 9*z^10 + 5*z^9 + 3*z^8 + 10*z^7 + 10*z^5 + 7*z^4 + 2*z^3 + 8*z^2 + 6
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: 0.760

Finished computing trace of random element.
Computing minimal polynomial of trace(alpha), as an element of K[X]

FindDegree37FieldMod(
ell: 11
)
In file "/home/was/people/sharifi/unitcomp.m", line 242, column 31:
>>    time f := MinimalPolynomial(tr_alpha);
                                 ^
Runtime error in 'MinimalPolynomial': Coefficient ring does not allow minimal polynomials
> f, L, K, del, tr_alpha := FindDegree37FieldMod(13);
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: 0.780

Finished computing trace of random element.
Computing minimal polynomial of trace(alpha), as an element of K[X]
Time: 1.720
> f;
X^37 + (2*z^35 + 10*z^34 + 7*z^33 + 2*z^32 + 2*z^30 + 10*z^29 + 11*z^28 + 5*z^27 + 10*z^26 + 2*z^25 + 7*z^24 + 5*z^23 + z^22 + z^21 + 11*z^20 + 10*z^19 + 10*z^18 + 11*z^17 + z^16 + z^15 + 5*z^14 + 7*z^13 + 2*z^12 + 10*z^11 + 5*z^10 + 11*z^9 + 10*z^8 + 2*z^7 + 2*z^5 + 7*z^4 + 10*z^3 + 2*z^2 + 3)*X^34 + (12*z^35 + 12*z^34 + 4*z^33 + 11*z^32 + 11*z^30 + 11*z^29 + 5*z^28 + 11*z^27 + 11*z^26 + 12*z^25 + 4*z^24 + 11*z^23 + 4*z^22 + 4*z^21 + 5*z^20 + 12*z^19 + 12*z^18 + 5*z^17 + 4*z^16 + 4*z^15 + 11*z^14 + 4*z^13 + 12*z^12 + 11*z^11 + 11*z^10 + 5*z^9 + 11*z^8 + 11*z^7 + 11*z^5 + 4*z^4 + 12*z^3 + 12*z^2 + 3)*X^33 + (6*z^35 + 10*z^34 + 9*z^33 + 11*z^32 + 11*z^30 + 12*z^29 + 8*z^28 + 6*z^27 + 12*z^26 + 6*z^25 + 9*z^24 + 6*z^23 + 3*z^22 + 3*z^21 + 8*z^20 + 10*z^19 + 10*z^18 + 8*z^17 + 3*z^16 + 3*z^15 + 6*z^14 + 9*z^13 + 6*z^12 + 12*z^11 + 6*z^10 + 8*z^9 + 12*z^8 + 11*z^7 + 11*z^5 + 9*z^4 + 10*z^3 + 6*z^2 + 10)*X^32 + (12*z^35 + 10*z^34 + 2*z^33 + 6*z^32 + 6*z^30 + 4*z^29 + 5*z^28 + 2*z^27 + 4*z^26 + 12*z^25 + 2*z^24 + 2*z^23 + 3*z^22 + 3*z^21 + 5*z^20 + 10*z^19 + 10*z^18 + 5*z^17 + 3*z^16 + 3*z^15 + 2*z^14 + 2*z^13 + 12*z^12 + 4*z^11 + 2*z^10 + 5*z^9 + 4*z^8 + 6*z^7 + 6*z^5 + 2*z^4 + 10*z^3 + 12*z^2 + 2)*X^31 + (6*z^35 + 2*z^34 + 7*z^33 + z^32 + z^30 + 6*z^29 + z^28 + 2*z^27 + 6*z^26 + 6*z^25 + 7*z^24 + 2*z^23 + 2*z^22 + 2*z^21 + z^20 + 2*z^19 + 2*z^18 + z^17 + 2*z^16 + 2*z^15 + 2*z^14 + 7*z^13 + 6*z^12 + 6*z^11 + 2*z^10 + z^9 + 6*z^8 + z^7 + z^5 + 7*z^4 + 2*z^3 + 6*z^2 + 8)*X^30 + (7*z^35 + 7*z^34 + 8*z^32 + 8*z^30 + 5*z^29 + 10*z^28 + 5*z^26 + 7*z^25 + 4*z^22 + 4*z^21 + 10*z^20 + 7*z^19 + 7*z^18 + 10*z^17 + 4*z^16 + 4*z^15 + 7*z^12 + 5*z^11 + 10*z^9 + 5*z^8 + 8*z^7 + 8*z^5 + 7*z^3 + 7*z^2 + 6)*X^29 + (z^35 + 5*z^34 + 2*z^33 + 8*z^32 + 8*z^30 + 8*z^29 + 2*z^28 + 11*z^27 + 8*z^26 + z^25 + 2*z^24 + 11*z^23 + 4*z^22 + 4*z^21 + 2*z^20 + 5*z^19 + 5*z^18 + 2*z^17 + 4*z^16 + 4*z^15 + 11*z^14 + 2*z^13 + z^12 + 8*z^11 + 11*z^10 + 2*z^9 + 8*z^8 + 8*z^7 + 8*z^5 + 2*z^4 + 5*z^3 + z^2 + 8)*X^28 + (2*z^35 + 4*z^34 + 2*z^33 + 5*z^32 + 5*z^30 + 4*z^29 + 2*z^28 + 11*z^27 + 4*z^26 + 2*z^25 + 2*z^24 + 11*z^23 + 2*z^20 + 4*z^19 + 4*z^18 + 2*z^17 + 11*z^14 + 2*z^13 + 2*z^12 + 4*z^11 + 11*z^10 + 2*z^9 + 4*z^8 + 5*z^7 + 5*z^5 + 2*z^4 + 4*z^3 + 2*z^2 + 5)*X^27 + (z^35 + 10*z^32 + 10*z^30 + 12*z^29 + 3*z^28 + 12*z^26 + z^25 + 10*z^22 + 10*z^21 + 3*z^20 + 3*z^17 + 10*z^16 + 10*z^15 + z^12 + 12*z^11 + 3*z^9 + 12*z^8 + 10*z^7 + 10*z^5 + z^2 + 11)*X^26 + (6*z^35 + 7*z^34 + 11*z^33 + 3*z^32 + 3*z^30 + z^29 + 7*z^28 + 6*z^27 + z^26 + 6*z^25 + 11*z^24 + 6*z^23 + 10*z^22 + 10*z^21 + 7*z^20 + 7*z^19 + 7*z^18 + 7*z^17 + 10*z^16 + 10*z^15 + 6*z^14 + 11*z^13 + 6*z^12 + z^11 + 6*z^10 + 7*z^9 + z^8 + 3*z^7 + 3*z^5 + 11*z^4 + 7*z^3 + 6*z^2 + 5)*X^25 + (12*z^35 + 9*z^34 + z^33 + 8*z^32 + 8*z^30 + 9*z^29 + 3*z^28 + 7*z^27 + 9*z^26 + 12*z^25 + z^24 + 7*z^23 + 7*z^22 + 7*z^21 + 3*z^20 + 9*z^19 + 9*z^18 + 3*z^17 + 7*z^16 + 7*z^15 + 7*z^14 + z^13 + 12*z^12 + 9*z^11 + 7*z^10 + 3*z^9 + 9*z^8 + 8*z^7 + 8*z^5 + z^4 + 9*z^3 + 12*z^2 + 3)*X^24 + (10*z^35 + 2*z^34 + 9*z^33 + 10*z^32 + 10*z^30 + 11*z^28 + 3*z^27 + 10*z^25 + 9*z^24 + 3*z^23 + 11*z^22 + 11*z^21 + 11*z^20 + 2*z^19 + 2*z^18 + 11*z^17 + 11*z^16 + 11*z^15 + 3*z^14 + 9*z^13 + 10*z^12 + 3*z^10 + 11*z^9 + 10*z^7 + 10*z^5 + 9*z^4 + 2*z^3 + 10*z^2 + 10)*X^23 + (6*z^35 + 9*z^34 + 12*z^33 + 5*z^32 + 5*z^30 + 4*z^29 + 12*z^28 + 7*z^27 + 4*z^26 + 6*z^25 + 12*z^24 + 7*z^23 + 6*z^22 + 6*z^21 + 12*z^20 + 9*z^19 + 9*z^18 + 12*z^17 + 6*z^16 + 6*z^15 + 7*z^14 + 12*z^13 + 6*z^12 + 4*z^11 + 7*z^10 + 12*z^9 + 4*z^8 + 5*z^7 + 5*z^5 + 12*z^4 + 9*z^3 + 6*z^2 + 5)*X^22 + (2*z^35 + z^34 + 7*z^33 + 3*z^29 + 6*z^28 + 3*z^27 + 3*z^26 + 2*z^25 + 7*z^24 + 3*z^23 + 10*z^22 + 10*z^21 + 6*z^20 + z^19 + z^18 + 6*z^17 + 10*z^16 + 10*z^15 + 3*z^14 + 7*z^13 + 2*z^12 + 3*z^11 + 3*z^10 + 6*z^9 + 3*z^8 + 7*z^4 + z^3 + 2*z^2 + 1)*X^21 + (6*z^35 + 6*z^33 + 8*z^32 + 8*z^30 + 6*z^25 + 6*z^24 + 6*z^22 + 6*z^21 + 6*z^16 + 6*z^15 + 6*z^13 + 6*z^12 + 8*z^7 + 8*z^5 + 6*z^4 + 6*z^2 + 7)*X^20 + (5*z^35 + 6*z^34 + 7*z^33 + 12*z^32 + 12*z^30 + 6*z^29 + 5*z^28 + 6*z^27 + 6*z^26 + 5*z^25 + 7*z^24 + 6*z^23 + 5*z^20 + 6*z^19 + 6*z^18 + 5*z^17 + 6*z^14 + 7*z^13 + 5*z^12 + 6*z^11 + 6*z^10 + 5*z^9 + 6*z^8 + 12*z^7 + 12*z^5 + 7*z^4 + 6*z^3 + 5*z^2 + 2)*X^19 + (7*z^35 + 4*z^34 + 8*z^33 + 10*z^29 + 6*z^28 + 11*z^27 + 10*z^26 + 7*z^25 + 8*z^24 + 11*z^23 + z^22 + z^21 + 6*z^20 + 4*z^19 + 4*z^18 + 6*z^17 + z^16 + z^15 + 11*z^14 + 8*z^13 + 7*z^12 + 10*z^11 + 11*z^10 + 6*z^9 + 10*z^8 + 8*z^4 + 4*z^3 + 7*z^2 + 6)*X^18 + (z^35 + 12*z^34 + 10*z^33 + 5*z^32 + 5*z^30 + 11*z^29 + 7*z^28 + 11*z^26 + z^25 + 10*z^24 + 4*z^22 + 4*z^21 + 7*z^20 + 12*z^19 + 12*z^18 + 7*z^17 + 4*z^16 + 4*z^15 + 10*z^13 + z^12 + 11*z^11 + 7*z^9 + 11*z^8 + 5*z^7 + 5*z^5 + 10*z^4 + 12*z^3 + z^2)*X^17 + (9*z^35 + 8*z^33 + 2*z^32 + 2*z^30 + 6*z^29 + z^27 + 6*z^26 + 9*z^25 + 8*z^24 + z^23 + z^22 + z^21 + z^16 + z^15 + z^14 + 8*z^13 + 9*z^12 + 6*z^11 + z^10 + 6*z^8 + 2*z^7 + 2*z^5 + 8*z^4 + 9*z^2 + 4)*X^16 + (2*z^35 + 7*z^34 + 4*z^33 + 3*z^32 + 3*z^30 + 12*z^29 + 6*z^28 + 6*z^27 + 12*z^26 + 2*z^25 + 4*z^24 + 6*z^23 + 5*z^22 + 5*z^21 + 6*z^20 + 7*z^19 + 7*z^18 + 6*z^17 + 5*z^16 + 5*z^15 + 6*z^14 + 4*z^13 + 2*z^12 + 12*z^11 + 6*z^10 + 6*z^9 + 12*z^8 + 3*z^7 + 3*z^5 + 4*z^4 + 7*z^3 + 2*z^2 + 3)*X^15 + (7*z^34 + 2*z^33 + 3*z^32 + 3*z^30 + 6*z^29 + 2*z^28 + 11*z^27 + 6*z^26 + 2*z^24 + 11*z^23 + 12*z^22 + 12*z^21 + 2*z^20 + 7*z^19 + 7*z^18 + 2*z^17 + 12*z^16 + 12*z^15 + 11*z^14 + 2*z^13 + 6*z^11 + 11*z^10 + 2*z^9 + 6*z^8 + 3*z^7 + 3*z^5 + 2*z^4 + 7*z^3 + 8)*X^14 + (12*z^35 + 5*z^34 + 9*z^33 + 10*z^32 + 10*z^30 + 8*z^29 + 6*z^28 + 6*z^27 + 8*z^26 + 12*z^25 + 9*z^24 + 6*z^23 + 3*z^22 + 3*z^21 + 6*z^20 + 5*z^19 + 5*z^18 + 6*z^17 + 3*z^16 + 3*z^15 + 6*z^14 + 9*z^13 + 12*z^12 + 8*z^11 + 6*z^10 + 6*z^9 + 8*z^8 + 10*z^7 + 10*z^5 + 9*z^4 + 5*z^3 + 12*z^2 + 12)*X^13 + (2*z^35 + z^34 + 6*z^33 + 4*z^32 + 4*z^30 + 5*z^28 + 2*z^27 + 2*z^25 + 6*z^24 + 2*z^23 + 9*z^22 + 9*z^21 + 5*z^20 + z^19 + z^18 + 5*z^17 + 9*z^16 + 9*z^15 + 2*z^14 + 6*z^13 + 2*z^12 + 2*z^10 + 5*z^9 + 4*z^7 + 4*z^5 + 6*z^4 + z^3 + 2*z^2 + 3)*X^12 + (7*z^35 + 5*z^34 + 2*z^33 + z^32 + z^30 + 10*z^29 + 7*z^28 + 7*z^27 + 10*z^26 + 7*z^25 + 2*z^24 + 7*z^23 + 6*z^22 + 6*z^21 + 7*z^20 + 5*z^19 + 5*z^18 + 7*z^17 + 6*z^16 + 6*z^15 + 7*z^14 + 2*z^13 + 7*z^12 + 10*z^11 + 7*z^10 + 7*z^9 + 10*z^8 + z^7 + z^5 + 2*z^4 + 5*z^3 + 7*z^2 + 11)*X^11 + (8*z^35 + 8*z^34 + 3*z^33 + 11*z^29 + 4*z^28 + 7*z^27 + 11*z^26 + 8*z^25 + 3*z^24 + 7*z^23 + 8*z^22 + 8*z^21 + 4*z^20 + 8*z^19 + 8*z^18 + 4*z^17 + 8*z^16 + 8*z^15 + 7*z^14 + 3*z^13 + 8*z^12 + 11*z^11 + 7*z^10 + 4*z^9 + 11*z^8 + 3*z^4 + 8*z^3 + 8*z^2 + 3)*X^10 + (9*z^35 + 5*z^33 + 11*z^29 + 6*z^28 + 10*z^27 + 11*z^26 + 9*z^25 + 5*z^24 + 10*z^23 + 8*z^22 + 8*z^21 + 6*z^20 + 6*z^17 + 8*z^16 + 8*z^15 + 10*z^14 + 5*z^13 + 9*z^12 + 11*z^11 + 10*z^10 + 6*z^9 + 11*z^8 + 5*z^4 + 9*z^2 + 10)*X^9 + (8*z^35 + 9*z^34 + 9*z^33 + 4*z^32 + 4*z^30 + z^29 + 4*z^28 + 8*z^27 + z^26 + 8*z^25 + 9*z^24 + 8*z^23 + 3*z^22 + 3*z^21 + 4*z^20 + 9*z^19 + 9*z^18 + 4*z^17 + 3*z^16 + 3*z^15 + 8*z^14 + 9*z^13 + 8*z^12 + z^11 + 8*z^10 + 4*z^9 + z^8 + 4*z^7 + 4*z^5 + 9*z^4 + 9*z^3 + 8*z^2 + 12)*X^8 + (11*z^35 + z^34 + 5*z^33 + 9*z^32 + 9*z^30 + 8*z^29 + 4*z^28 + 5*z^27 + 8*z^26 + 11*z^25 + 5*z^24 + 5*z^23 + 10*z^22 + 10*z^21 + 4*z^20 + z^19 + z^18 + 4*z^17 + 10*z^16 + 10*z^15 + 5*z^14 + 5*z^13 + 11*z^12 + 8*z^11 + 5*z^10 + 4*z^9 + 8*z^8 + 9*z^7 + 9*z^5 + 5*z^4 + z^3 + 11*z^2 + 7)*X^7 + (8*z^35 + 12*z^34 + z^33 + 4*z^32 + 4*z^30 + 9*z^29 + 11*z^28 + 9*z^27 + 9*z^26 + 8*z^25 + z^24 + 9*z^23 + 7*z^22 + 7*z^21 + 11*z^20 + 12*z^19 + 12*z^18 + 11*z^17 + 7*z^16 + 7*z^15 + 9*z^14 + z^13 + 8*z^12 + 9*z^11 + 9*z^10 + 11*z^9 + 9*z^8 + 4*z^7 + 4*z^5 + z^4 + 12*z^3 + 8*z^2 + 7)*X^6 + (5*z^34 + 9*z^33 + 2*z^32 + 2*z^30 + z^29 + 12*z^28 + z^27 + z^26 + 9*z^24 + z^23 + 4*z^22 + 4*z^21 + 12*z^20 + 5*z^19 + 5*z^18 + 12*z^17 + 4*z^16 + 4*z^15 + z^14 + 9*z^13 + z^11 + z^10 + 12*z^9 + z^8 + 2*z^7 + 2*z^5 + 9*z^4 + 5*z^3 + 2)*X^5 + (9*z^35 + 11*z^34 + z^33 + 4*z^32 + 4*z^30 + 4*z^29 + 10*z^28 + 2*z^27 + 4*z^26 + 9*z^25 + z^24 + 2*z^23 + 2*z^22 + 2*z^21 + 10*z^20 + 11*z^19 + 11*z^18 + 10*z^17 + 2*z^16 + 2*z^15 + 2*z^14 + z^13 + 9*z^12 + 4*z^11 + 2*z^10 + 10*z^9 + 4*z^8 + 4*z^7 + 4*z^5 + z^4 + 11*z^3 + 9*z^2 + 9)*X^4 + (11*z^35 + 8*z^33 + z^32 + z^30 + 6*z^29 + 5*z^28 + z^27 + 6*z^26 + 11*z^25 + 8*z^24 + z^23 + 9*z^22 + 9*z^21 + 5*z^20 + 5*z^17 + 9*z^16 + 9*z^15 + z^14 + 8*z^13 + 11*z^12 + 6*z^11 + z^10 + 5*z^9 + 6*z^8 + z^7 + z^5 + 8*z^4 + 11*z^2 + 5)*X^3 + (7*z^35 + 9*z^33 + 6*z^32 + 6*z^30 + 2*z^29 + 12*z^28 + 5*z^27 + 2*z^26 + 7*z^25 + 9*z^24 + 5*z^23 + 8*z^22 + 8*z^21 + 12*z^20 + 12*z^17 + 8*z^16 + 8*z^15 + 5*z^14 + 9*z^13 + 7*z^12 + 2*z^11 + 5*z^10 + 12*z^9 + 2*z^8 + 6*z^7 + 6*z^5 + 9*z^4 + 7*z^2 + 9)*X^2 + (9*z^35 + 7*z^34 + 5*z^33 + 9*z^32 + 9*z^30 + 5*z^29 + 11*z^28 + 4*z^27 + 5*z^26 + 9*z^25 + 5*z^24 + 4*z^23 + 3*z^22 + 3*z^21 + 11*z^20 + 7*z^19 + 7*z^18 + 11*z^17 + 3*z^16 + 3*z^15 + 4*z^14 + 5*z^13 + 9*z^12 + 5*z^11 + 4*z^10 + 11*z^9 + 5*z^8 + 9*z^7 + 9*z^5 + 5*z^4 + 7*z^3 + 9*z^2 + 8)*X + 8*z^35 + 6*z^34 + 10*z^32 + 10*z^30 + 8*z^29 + 8*z^28 + 5*z^27 + 8*z^26 + 8*z^25 + 5*z^23 + 7*z^22 + 7*z^21 + 8*z^20 + 6*z^19 + 6*z^18 + 8*z^17 + 7*z^16 + 7*z^15 + 5*z^14 + 8*z^12 + 8*z^11 + 5*z^10 + 8*z^9 + 8*z^8 + 10*z^7 + 10*z^5 + 6*z^3 + 8*z^2 + 6
> g := CyclotomicPolynomial(37);
> Factorization(PolynomialRing(GF(11))!g);
[
<$.1^6 + $.1^5 + 3*$.1^4 + 5*$.1^3 + 3*$.1^2 + $.1 + 1, 1>,
<$.1^6 + 4*$.1^5 + 3*$.1^4 + 7*$.1^3 + 3*$.1^2 + 4*$.1 + 1, 1>,
<$.1^6 + 5*$.1^5 + 5*$.1^4 + 4*$.1^3 + 5*$.1^2 + 5*$.1 + 1, 1>,
<$.1^6 + 7*$.1^5 + 2*$.1^4 + 2*$.1^2 + 7*$.1 + 1, 1>,
<$.1^6 + 7*$.1^5 + 6*$.1^4 + 8*$.1^3 + 6*$.1^2 + 7*$.1 + 1, 1>,
<$.1^6 + 10*$.1^5 + 8*$.1^4 + 8*$.1^2 + 10*$.1 + 1, 1>
]
> Factorization(PolynomialRing(GF(13))!g);
> [
<$.1^36 + $.1^35 + $.1^34 + $.1^33 + $.1^32 + $.1^31 + $.1^30 + $.1^29 + $.1^28 + $.1^27 + $.1^26 + $.1^25 + $.1^24 + $.1^23 + $.1^22 + $.1^21 + $.1^20 + $.1^19 + $.1^18 + $.1^17 + $.1^16 + $.1^15 + $.1^14 + $.1^13 + $.1^12 + $.1^11 + $.1^10 + $.1^9 + $.1^8 + $.1^7 + $.1^6 + $.1^5 + $.1^4 + $.1^3 + $.1^2 + $.1 + 1, 1>
]
> a := Coefficient(f,0);
> a;
8*z^35 + 6*z^34 + 10*z^32 + 10*z^30 + 8*z^29 + 8*z^28 + 5*z^27 + 8*z^26 + 8*z^25 + 5*z^23 + 7*z^22 + 7*z^21 + 8*z^20 + 6*z^19 + 6*z^18 + 8*z^17 + 7*z^16 + 7*z^15 + 5*z^14 + 8*z^12 + 8*z^11 + 5*z^10 + 8*z^9 + 8*z^8 + 10*z^7 + 10*z^5 + 6*z^3 + 8*z^2 + 6
> del(a);
7*z^35 + 2*z^34 + 2*z^33 + z^32 + z^30 + 7*z^29 + 12*z^28 + 4*z^27 + 7*z^26 + 7*z^25 + 2*z^24 + 4*z^23 + 2*z^22 + 2*z^21 + 12*z^20 + 2*z^19 + 2*z^18 + 12*z^17 + 2*z^16 + 2*z^15 + 4*z^14 + 2*z^13 + 7*z^12 + 7*z^11 + 4*z^10 + 12*z^9 + 7*z^8 + z^7 + z^5 + 2*z^4 + 2*z^3 + 7*z^2
> a-del(a);
z^35 + 4*z^34 + 11*z^33 + 9*z^32 + 9*z^30 + z^29 + 9*z^28 + z^27 + z^26 + z^25 + 11*z^24 + z^23 + 5*z^22 + 5*z^21 + 9*z^20 + 4*z^19 + 4*z^18 + 9*z^17 + 5*z^16 + 5*z^15 + z^14 + 11*z^13 + z^12 + z^11 + z^10 + 9*z^9 + z^8 + 9*z^7 + 9*z^5 + 11*z^4 + 4*z^3 + z^2 + 6
> R<X> := Parent(f);
> E := Eltseq(f);
> EE := [del(e) : e in E];
> g := R!EE;

>> g := R!EE;
         ^
Runtime error in '!': Can't coerce sequence element 37 into the coefficient ring
> E;
[
8*z^35 + 6*z^34 + 10*z^32 + 10*z^30 + 8*z^29 + 8*z^28 + 5*z^27 + 8*z^26 + 8*z^25 + 5*z^23 + 7*z^22 + 7*z^21 + 8*z^20 + 6*z^19 + 6*z^18 + 8*z^17 + 7*z^16 + 7*z^15 + 5*z^14 + 8*z^12 + 8*z^11 + 5*z^10 + 8*z^9 + 8*z^8 + 10*z^7 + 10*z^5 + 6*z^3 + 8*z^2 + 6,
9*z^35 + 7*z^34 + 5*z^33 + 9*z^32 + 9*z^30 + 5*z^29 + 11*z^28 + 4*z^27 + 5*z^26 + 9*z^25 + 5*z^24 + 4*z^23 + 3*z^22 + 3*z^21 + 11*z^20 + 7*z^19 + 7*z^18 + 11*z^17 + 3*z^16 + 3*z^15 + 4*z^14 + 5*z^13 + 9*z^12 + 5*z^11 + 4*z^10 + 11*z^9 + 5*z^8 + 9*z^7 + 9*z^5 + 5*z^4 + 7*z^3 + 9*z^2 + 8,
7*z^35 + 9*z^33 + 6*z^32 + 6*z^30 + 2*z^29 + 12*z^28 + 5*z^27 + 2*z^26 + 7*z^25 + 9*z^24 + 5*z^23 + 8*z^22 + 8*z^21 + 12*z^20 + 12*z^17 + 8*z^16 + 8*z^15 + 5*z^14 + 9*z^13 + 7*z^12 + 2*z^11 + 5*z^10 + 12*z^9 + 2*z^8 + 6*z^7 + 6*z^5 + 9*z^4 + 7*z^2 + 9,
11*z^35 + 8*z^33 + z^32 + z^30 + 6*z^29 + 5*z^28 + z^27 + 6*z^26 + 11*z^25 + 8*z^24 + z^23 + 9*z^22 + 9*z^21 + 5*z^20 + 5*z^17 + 9*z^16 + 9*z^15 + z^14 + 8*z^13 + 11*z^12 + 6*z^11 + z^10 + 5*z^9 + 6*z^8 + z^7 + z^5 + 8*z^4 + 11*z^2 + 5,
9*z^35 + 11*z^34 + z^33 + 4*z^32 + 4*z^30 + 4*z^29 + 10*z^28 + 2*z^27 + 4*z^26 + 9*z^25 + z^24 + 2*z^23 + 2*z^22 + 2*z^21 + 10*z^20 + 11*z^19 + 11*z^18 + 10*z^17 + 2*z^16 + 2*z^15 + 2*z^14 + z^13 + 9*z^12 + 4*z^11 + 2*z^10 + 10*z^9 + 4*z^8 + 4*z^7 + 4*z^5 + z^4 + 11*z^3 + 9*z^2 + 9,
5*z^34 + 9*z^33 + 2*z^32 + 2*z^30 + z^29 + 12*z^28 + z^27 + z^26 + 9*z^24 + z^23 + 4*z^22 + 4*z^21 + 12*z^20 + 5*z^19 + 5*z^18 + 12*z^17 + 4*z^16 + 4*z^15 + z^14 + 9*z^13 + z^11 + z^10 + 12*z^9 + z^8 + 2*z^7 + 2*z^5 + 9*z^4 + 5*z^3 + 2,
8*z^35 + 12*z^34 + z^33 + 4*z^32 + 4*z^30 + 9*z^29 + 11*z^28 + 9*z^27 + 9*z^26 + 8*z^25 + z^24 + 9*z^23 + 7*z^22 + 7*z^21 + 11*z^20 + 12*z^19 + 12*z^18 + 11*z^17 + 7*z^16 + 7*z^15 + 9*z^14 + z^13 + 8*z^12 + 9*z^11 + 9*z^10 + 11*z^9 + 9*z^8 + 4*z^7 + 4*z^5 + z^4 + 12*z^3 + 8*z^2 + 7,
11*z^35 + z^34 + 5*z^33 + 9*z^32 + 9*z^30 + 8*z^29 + 4*z^28 + 5*z^27 + 8*z^26 + 11*z^25 + 5*z^24 + 5*z^23 + 10*z^22 + 10*z^21 + 4*z^20 + z^19 + z^18 + 4*z^17 + 10*z^16 + 10*z^15 + 5*z^14 + 5*z^13 + 11*z^12 + 8*z^11 + 5*z^10 + 4*z^9 + 8*z^8 + 9*z^7 + 9*z^5 + 5*z^4 + z^3 + 11*z^2 + 7,
8*z^35 + 9*z^34 + 9*z^33 + 4*z^32 + 4*z^30 + z^29 + 4*z^28 + 8*z^27 + z^26 + 8*z^25 + 9*z^24 + 8*z^23 + 3*z^22 + 3*z^21 + 4*z^20 + 9*z^19 + 9*z^18 + 4*z^17 + 3*z^16 + 3*z^15 + 8*z^14 + 9*z^13 + 8*z^12 + z^11 + 8*z^10 + 4*z^9 + z^8 + 4*z^7 + 4*z^5 + 9*z^4 + 9*z^3 + 8*z^2 + 12,
9*z^35 + 5*z^33 + 11*z^29 + 6*z^28 + 10*z^27 + 11*z^26 + 9*z^25 + 5*z^24 + 10*z^23 + 8*z^22 + 8*z^21 + 6*z^20 + 6*z^17 + 8*z^16 + 8*z^15 + 10*z^14 + 5*z^13 + 9*z^12 + 11*z^11 + 10*z^10 + 6*z^9 + 11*z^8 + 5*z^4 + 9*z^2 + 10,
8*z^35 + 8*z^34 + 3*z^33 + 11*z^29 + 4*z^28 + 7*z^27 + 11*z^26 + 8*z^25 + 3*z^24 + 7*z^23 + 8*z^22 + 8*z^21 + 4*z^20 + 8*z^19 + 8*z^18 + 4*z^17 + 8*z^16 + 8*z^15 + 7*z^14 + 3*z^13 + 8*z^12 + 11*z^11 + 7*z^10 + 4*z^9 + 11*z^8 + 3*z^4 + 8*z^3 + 8*z^2 + 3,
7*z^35 + 5*z^34 + 2*z^33 + z^32 + z^30 + 10*z^29 + 7*z^28 + 7*z^27 + 10*z^26 + 7*z^25 + 2*z^24 + 7*z^23 + 6*z^22 + 6*z^21 + 7*z^20 + 5*z^19 + 5*z^18 + 7*z^17 + 6*z^16 + 6*z^15 + 7*z^14 + 2*z^13 + 7*z^12 + 10*z^11 + 7*z^10 + 7*z^9 + 10*z^8 + z^7 + z^5 + 2*z^4 + 5*z^3 + 7*z^2 + 11,
2*z^35 + z^34 + 6*z^33 + 4*z^32 + 4*z^30 + 5*z^28 + 2*z^27 + 2*z^25 + 6*z^24 + 2*z^23 + 9*z^22 + 9*z^21 + 5*z^20 + z^19 + z^18 + 5*z^17 + 9*z^16 + 9*z^15 + 2*z^14 + 6*z^13 + 2*z^12 + 2*z^10 + 5*z^9 + 4*z^7 + 4*z^5 + 6*z^4 + z^3 + 2*z^2 + 3,
12*z^35 + 5*z^34 + 9*z^33 + 10*z^32 + 10*z^30 + 8*z^29 + 6*z^28 + 6*z^27 + 8*z^26 + 12*z^25 + 9*z^24 + 6*z^23 + 3*z^22 + 3*z^21 + 6*z^20 + 5*z^19 + 5*z^18 + 6*z^17 + 3*z^16 + 3*z^15 + 6*z^14 + 9*z^13 + 12*z^12 + 8*z^11 + 6*z^10 + 6*z^9 + 8*z^8 + 10*z^7 + 10*z^5 + 9*z^4 + 5*z^3 + 12*z^2 + 12,
7*z^34 + 2*z^33 + 3*z^32 + 3*z^30 + 6*z^29 + 2*z^28 + 11*z^27 + 6*z^26 + 2*z^24 + 11*z^23 + 12*z^22 + 12*z^21 + 2*z^20 + 7*z^19 + 7*z^18 + 2*z^17 + 12*z^16 + 12*z^15 + 11*z^14 + 2*z^13 + 6*z^11 + 11*z^10 + 2*z^9 + 6*z^8 + 3*z^7 + 3*z^5 + 2*z^4 + 7*z^3 + 8,
2*z^35 + 7*z^34 + 4*z^33 + 3*z^32 + 3*z^30 + 12*z^29 + 6*z^28 + 6*z^27 + 12*z^26 + 2*z^25 + 4*z^24 + 6*z^23 + 5*z^22 + 5*z^21 + 6*z^20 + 7*z^19 + 7*z^18 + 6*z^17 + 5*z^16 + 5*z^15 + 6*z^14 + 4*z^13 + 2*z^12 + 12*z^11 + 6*z^10 + 6*z^9 + 12*z^8 + 3*z^7 + 3*z^5 + 4*z^4 + 7*z^3 + 2*z^2 + 3,
9*z^35 + 8*z^33 + 2*z^32 + 2*z^30 + 6*z^29 + z^27 + 6*z^26 + 9*z^25 + 8*z^24 + z^23 + z^22 + z^21 + z^16 + z^15 + z^14 + 8*z^13 + 9*z^12 + 6*z^11 + z^10 + 6*z^8 + 2*z^7 + 2*z^5 + 8*z^4 + 9*z^2 + 4,
z^35 + 12*z^34 + 10*z^33 + 5*z^32 + 5*z^30 + 11*z^29 + 7*z^28 + 11*z^26 + z^25 + 10*z^24 + 4*z^22 + 4*z^21 + 7*z^20 + 12*z^19 + 12*z^18 + 7*z^17 + 4*z^16 + 4*z^15 + 10*z^13 + z^12 + 11*z^11 + 7*z^9 + 11*z^8 + 5*z^7 + 5*z^5 + 10*z^4 + 12*z^3 + z^2,
7*z^35 + 4*z^34 + 8*z^33 + 10*z^29 + 6*z^28 + 11*z^27 + 10*z^26 + 7*z^25 + 8*z^24 + 11*z^23 + z^22 + z^21 + 6*z^20 + 4*z^19 + 4*z^18 + 6*z^17 + z^16 + z^15 + 11*z^14 + 8*z^13 + 7*z^12 + 10*z^11 + 11*z^10 + 6*z^9 + 10*z^8 + 8*z^4 + 4*z^3 + 7*z^2 + 6,
5*z^35 + 6*z^34 + 7*z^33 + 12*z^32 + 12*z^30 + 6*z^29 + 5*z^28 + 6*z^27 + 6*z^26 + 5*z^25 + 7*z^24 + 6*z^23 + 5*z^20 + 6*z^19 + 6*z^18 + 5*z^17 + 6*z^14 + 7*z^13 + 5*z^12 + 6*z^11 + 6*z^10 + 5*z^9 + 6*z^8 + 12*z^7 + 12*z^5 + 7*z^4 + 6*z^3 + 5*z^2 + 2,
6*z^35 + 6*z^33 + 8*z^32 + 8*z^30 + 6*z^25 + 6*z^24 + 6*z^22 + 6*z^21 + 6*z^16 + 6*z^15 + 6*z^13 + 6*z^12 + 8*z^7 + 8*z^5 + 6*z^4 + 6*z^2 + 7,
2*z^35 + z^34 + 7*z^33 + 3*z^29 + 6*z^28 + 3*z^27 + 3*z^26 + 2*z^25 + 7*z^24 + 3*z^23 + 10*z^22 + 10*z^21 + 6*z^20 + z^19 + z^18 + 6*z^17 + 10*z^16 + 10*z^15 + 3*z^14 + 7*z^13 + 2*z^12 + 3*z^11 + 3*z^10 + 6*z^9 + 3*z^8 + 7*z^4 + z^3 + 2*z^2 + 1,
6*z^35 + 9*z^34 + 12*z^33 + 5*z^32 + 5*z^30 + 4*z^29 + 12*z^28 + 7*z^27 + 4*z^26 + 6*z^25 + 12*z^24 + 7*z^23 + 6*z^22 + 6*z^21 + 12*z^20 + 9*z^19 + 9*z^18 + 12*z^17 + 6*z^16 + 6*z^15 + 7*z^14 + 12*z^13 + 6*z^12 + 4*z^11 + 7*z^10 + 12*z^9 + 4*z^8 + 5*z^7 + 5*z^5 + 12*z^4 + 9*z^3 + 6*z^2 + 5,
10*z^35 + 2*z^34 + 9*z^33 + 10*z^32 + 10*z^30 + 11*z^28 + 3*z^27 + 10*z^25 + 9*z^24 + 3*z^23 + 11*z^22 + 11*z^21 + 11*z^20 + 2*z^19 + 2*z^18 + 11*z^17 + 11*z^16 + 11*z^15 + 3*z^14 + 9*z^13 + 10*z^12 + 3*z^10 + 11*z^9 + 10*z^7 + 10*z^5 + 9*z^4 + 2*z^3 + 10*z^2 + 10,
12*z^35 + 9*z^34 + z^33 + 8*z^32 + 8*z^30 + 9*z^29 + 3*z^28 + 7*z^27 + 9*z^26 + 12*z^25 + z^24 + 7*z^23 + 7*z^22 + 7*z^21 + 3*z^20 + 9*z^19 + 9*z^18 + 3*z^17 + 7*z^16 + 7*z^15 + 7*z^14 + z^13 + 12*z^12 + 9*z^11 + 7*z^10 + 3*z^9 + 9*z^8 + 8*z^7 + 8*z^5 + z^4 + 9*z^3 + 12*z^2 + 3,
6*z^35 + 7*z^34 + 11*z^33 + 3*z^32 + 3*z^30 + z^29 + 7*z^28 + 6*z^27 + z^26 + 6*z^25 + 11*z^24 + 6*z^23 + 10*z^22 + 10*z^21 + 7*z^20 + 7*z^19 + 7*z^18 + 7*z^17 + 10*z^16 + 10*z^15 + 6*z^14 + 11*z^13 + 6*z^12 + z^11 + 6*z^10 + 7*z^9 + z^8 + 3*z^7 + 3*z^5 + 11*z^4 + 7*z^3 + 6*z^2 + 5,
z^35 + 10*z^32 + 10*z^30 + 12*z^29 + 3*z^28 + 12*z^26 + z^25 + 10*z^22 + 10*z^21 + 3*z^20 + 3*z^17 + 10*z^16 + 10*z^15 + z^12 + 12*z^11 + 3*z^9 + 12*z^8 + 10*z^7 + 10*z^5 + z^2 + 11,
2*z^35 + 4*z^34 + 2*z^33 + 5*z^32 + 5*z^30 + 4*z^29 + 2*z^28 + 11*z^27 + 4*z^26 + 2*z^25 + 2*z^24 + 11*z^23 + 2*z^20 + 4*z^19 + 4*z^18 + 2*z^17 + 11*z^14 + 2*z^13 + 2*z^12 + 4*z^11 + 11*z^10 + 2*z^9 + 4*z^8 + 5*z^7 + 5*z^5 + 2*z^4 + 4*z^3 + 2*z^2 + 5,
z^35 + 5*z^34 + 2*z^33 + 8*z^32 + 8*z^30 + 8*z^29 + 2*z^28 + 11*z^27 + 8*z^26 + z^25 + 2*z^24 + 11*z^23 + 4*z^22 + 4*z^21 + 2*z^20 + 5*z^19 + 5*z^18 + 2*z^17 + 4*z^16 + 4*z^15 + 11*z^14 + 2*z^13 + z^12 + 8*z^11 + 11*z^10 + 2*z^9 + 8*z^8 + 8*z^7 + 8*z^5 + 2*z^4 + 5*z^3 + z^2 + 8,
7*z^35 + 7*z^34 + 8*z^32 + 8*z^30 + 5*z^29 + 10*z^28 + 5*z^26 + 7*z^25 + 4*z^22 + 4*z^21 + 10*z^20 + 7*z^19 + 7*z^18 + 10*z^17 + 4*z^16 + 4*z^15 + 7*z^12 + 5*z^11 + 10*z^9 + 5*z^8 + 8*z^7 + 8*z^5 + 7*z^3 + 7*z^2 + 6,
6*z^35 + 2*z^34 + 7*z^33 + z^32 + z^30 + 6*z^29 + z^28 + 2*z^27 + 6*z^26 + 6*z^25 + 7*z^24 + 2*z^23 + 2*z^22 + 2*z^21 + z^20 + 2*z^19 + 2*z^18 + z^17 + 2*z^16 + 2*z^15 + 2*z^14 + 7*z^13 + 6*z^12 + 6*z^11 + 2*z^10 + z^9 + 6*z^8 + z^7 + z^5 + 7*z^4 + 2*z^3 + 6*z^2 + 8,
12*z^35 + 10*z^34 + 2*z^33 + 6*z^32 + 6*z^30 + 4*z^29 + 5*z^28 + 2*z^27 + 4*z^26 + 12*z^25 + 2*z^24 + 2*z^23 + 3*z^22 + 3*z^21 + 5*z^20 + 10*z^19 + 10*z^18 + 5*z^17 + 3*z^16 + 3*z^15 + 2*z^14 + 2*z^13 + 12*z^12 + 4*z^11 + 2*z^10 + 5*z^9 + 4*z^8 + 6*z^7 + 6*z^5 + 2*z^4 + 10*z^3 + 12*z^2 + 2,
6*z^35 + 10*z^34 + 9*z^33 + 11*z^32 + 11*z^30 + 12*z^29 + 8*z^28 + 6*z^27 + 12*z^26 + 6*z^25 + 9*z^24 + 6*z^23 + 3*z^22 + 3*z^21 + 8*z^20 + 10*z^19 + 10*z^18 + 8*z^17 + 3*z^16 + 3*z^15 + 6*z^14 + 9*z^13 + 6*z^12 + 12*z^11 + 6*z^10 + 8*z^9 + 12*z^8 + 11*z^7 + 11*z^5 + 9*z^4 + 10*z^3 + 6*z^2 + 10,
12*z^35 + 12*z^34 + 4*z^33 + 11*z^32 + 11*z^30 + 11*z^29 + 5*z^28 + 11*z^27 + 11*z^26 + 12*z^25 + 4*z^24 + 11*z^23 + 4*z^22 + 4*z^21 + 5*z^20 + 12*z^19 + 12*z^18 + 5*z^17 + 4*z^16 + 4*z^15 + 11*z^14 + 4*z^13 + 12*z^12 + 11*z^11 + 11*z^10 + 5*z^9 + 11*z^8 + 11*z^7 + 11*z^5 + 4*z^4 + 12*z^3 + 12*z^2 + 3,
2*z^35 + 10*z^34 + 7*z^33 + 2*z^32 + 2*z^30 + 10*z^29 + 11*z^28 + 5*z^27 + 10*z^26 + 2*z^25 + 7*z^24 + 5*z^23 + z^22 + z^21 + 11*z^20 + 10*z^19 + 10*z^18 + 11*z^17 + z^16 + z^15 + 5*z^14 + 7*z^13 + 2*z^12 + 10*z^11 + 5*z^10 + 11*z^9 + 10*z^8 + 2*z^7 + 2*z^5 + 7*z^4 + 10*z^3 + 2*z^2 + 3,
0,
0,
1
]
> EE;
[
7*z^35 + 2*z^34 + 2*z^33 + z^32 + z^30 + 7*z^29 + 12*z^28 + 4*z^27 + 7*z^26 + 7*z^25 + 2*z^24 + 4*z^23 + 2*z^22 + 2*z^21 + 12*z^20 + 2*z^19 + 2*z^18 + 12*z^17 + 2*z^16 + 2*z^15 + 4*z^14 + 2*z^13 + 7*z^12 + 7*z^11 + 4*z^10 + 12*z^9 + 7*z^8 + z^7 + z^5 + 2*z^4 + 2*z^3 + 7*z^2,
6*z^35 + 4*z^34 + 2*z^33 + 9*z^32 + 9*z^30 + 11*z^29 + 10*z^28 + 2*z^27 + 11*z^26 + 6*z^25 + 2*z^24 + 2*z^23 + 11*z^22 + 11*z^21 + 10*z^20 + 4*z^19 + 4*z^18 + 10*z^17 + 11*z^16 + 11*z^15 + 2*z^14 + 2*z^13 + 6*z^12 + 11*z^11 + 2*z^10 + 10*z^9 + 11*z^8 + 9*z^7 + 9*z^5 + 2*z^4 + 4*z^3 + 6*z^2 + 1,
12*z^34 + 7*z^33 + 8*z^32 + 8*z^30 + 9*z^29 + 5*z^28 + 6*z^27 + 9*z^26 + 7*z^24 + 6*z^23 + 2*z^22 + 2*z^21 + 5*z^20 + 12*z^19 + 12*z^18 + 5*z^17 + 2*z^16 + 2*z^15 + 6*z^14 + 7*z^13 + 9*z^11 + 6*z^10 + 5*z^9 + 9*z^8 + 8*z^7 + 8*z^5 + 7*z^4 + 12*z^3 + 9,
5*z^34 + 11*z^33 + 9*z^32 + 9*z^30 + 8*z^29 + z^28 + z^27 + 8*z^26 + 11*z^24 + z^23 + 6*z^22 + 6*z^21 + z^20 + 5*z^19 + 5*z^18 + z^17 + 6*z^16 + 6*z^15 + z^14 + 11*z^13 + 8*z^11 + z^10 + z^9 + 8*z^8 + 9*z^7 + 9*z^5 + 11*z^4 + 5*z^3 + 5,
2*z^35 + 12*z^34 + 11*z^33 + 4*z^32 + 4*z^30 + 3*z^29 + 4*z^28 + 6*z^27 + 3*z^26 + 2*z^25 + 11*z^24 + 6*z^23 + 6*z^22 + 6*z^21 + 4*z^20 + 12*z^19 + 12*z^18 + 4*z^17 + 6*z^16 + 6*z^15 + 6*z^14 + 11*z^13 + 2*z^12 + 3*z^11 + 6*z^10 + 4*z^9 + 3*z^8 + 4*z^7 + 4*z^5 + 11*z^4 + 12*z^3 + 2*z^2 + 11,
8*z^35 + 7*z^34 + 8*z^33 + 12*z^32 + 12*z^30 + 4*z^29 + 9*z^28 + 10*z^27 + 4*z^26 + 8*z^25 + 8*z^24 + 10*z^23 + 9*z^22 + 9*z^21 + 9*z^20 + 7*z^19 + 7*z^18 + 9*z^17 + 9*z^16 + 9*z^15 + 10*z^14 + 8*z^13 + 8*z^12 + 4*z^11 + 10*z^10 + 9*z^9 + 4*z^8 + 12*z^7 + 12*z^5 + 8*z^4 + 7*z^3 + 8*z^2 + 10,
z^35 + 12*z^34 + 9*z^33 + 8*z^32 + 8*z^30 + 2*z^29 + 10*z^28 + 5*z^27 + 2*z^26 + z^25 + 9*z^24 + 5*z^23 + 10*z^22 + 10*z^21 + 10*z^20 + 12*z^19 + 12*z^18 + 10*z^17 + 10*z^16 + 10*z^15 + 5*z^14 + 9*z^13 + z^12 + 2*z^11 + 5*z^10 + 10*z^9 + 2*z^8 + 8*z^7 + 8*z^5 + 9*z^4 + 12*z^3 + z^2 + 8,
12*z^35 + 3*z^34 + 10*z^33 + 9*z^32 + 9*z^30 + 4*z^29 + 4*z^28 + 8*z^27 + 4*z^26 + 12*z^25 + 10*z^24 + 8*z^23 + 7*z^22 + 7*z^21 + 4*z^20 + 3*z^19 + 3*z^18 + 4*z^17 + 7*z^16 + 7*z^15 + 8*z^14 + 10*z^13 + 12*z^12 + 4*z^11 + 8*z^10 + 4*z^9 + 4*z^8 + 9*z^7 + 9*z^5 + 10*z^4 + 3*z^3 + 12*z^2 + 6,
4*z^35 + 8*z^34 + 12*z^33 + 7*z^32 + 7*z^30 + 12*z^28 + 8*z^27 + 4*z^25 + 12*z^24 + 8*z^23 + 5*z^22 + 5*z^21 + 12*z^20 + 8*z^19 + 8*z^18 + 12*z^17 + 5*z^16 + 5*z^15 + 8*z^14 + 12*z^13 + 4*z^12 + 8*z^10 + 12*z^9 + 7*z^7 + 7*z^5 + 12*z^4 + 8*z^3 + 4*z^2 + 3,
6*z^34 + 9*z^33 + 8*z^32 + 8*z^30 + 5*z^29 + 10*z^28 + 5*z^26 + 9*z^24 + 11*z^22 + 11*z^21 + 10*z^20 + 6*z^19 + 6*z^18 + 10*z^17 + 11*z^16 + 11*z^15 + 9*z^13 + 5*z^11 + 10*z^9 + 5*z^8 + 8*z^7 + 8*z^5 + 9*z^4 + 6*z^3 + 10,
5*z^35 + 9*z^34 + 8*z^29 + 12*z^28 + 5*z^27 + 8*z^26 + 5*z^25 + 5*z^23 + 3*z^22 + 3*z^21 + 12*z^20 + 9*z^19 + 9*z^18 + 12*z^17 + 3*z^16 + 3*z^15 + 5*z^14 + 5*z^12 + 8*z^11 + 5*z^10 + 12*z^9 + 8*z^8 + 9*z^3 + 5*z^2 + 8,
8*z^35 + 2*z^34 + 2*z^33 + z^32 + z^30 + 10*z^29 + 2*z^28 + 9*z^27 + 10*z^26 + 8*z^25 + 2*z^24 + 9*z^23 + 5*z^22 + 5*z^21 + 2*z^20 + 2*z^19 + 2*z^18 + 2*z^17 + 5*z^16 + 5*z^15 + 9*z^14 + 2*z^13 + 8*z^12 + 10*z^11 + 9*z^10 + 2*z^9 + 10*z^8 + z^7 + z^5 + 2*z^4 + 2*z^3 + 8*z^2 + 6,
12*z^35 + 4*z^34 + z^33 + 8*z^32 + 8*z^30 + 5*z^29 + z^28 + 3*z^27 + 5*z^26 + 12*z^25 + z^24 + 3*z^23 + 12*z^22 + 12*z^21 + z^20 + 4*z^19 + 4*z^18 + z^17 + 12*z^16 + 12*z^15 + 3*z^14 + z^13 + 12*z^12 + 5*z^11 + 3*z^10 + z^9 + 5*z^8 + 8*z^7 + 8*z^5 + z^4 + 4*z^3 + 12*z^2 + 2,
8*z^35 + z^34 + 7*z^33 + 11*z^32 + 11*z^30 + 4*z^29 + z^28 + 5*z^27 + 4*z^26 + 8*z^25 + 7*z^24 + 5*z^23 + 3*z^22 + 3*z^21 + z^20 + z^19 + z^18 + z^17 + 3*z^16 + 3*z^15 + 5*z^14 + 7*z^13 + 8*z^12 + 4*z^11 + 5*z^10 + z^9 + 4*z^8 + 11*z^7 + 11*z^5 + 7*z^4 + z^3 + 8*z^2 + 7,
6*z^35 + 8*z^34 + 6*z^33 + 5*z^32 + 5*z^30 + 8*z^29 + 4*z^28 + 9*z^27 + 8*z^26 + 6*z^25 + 6*z^24 + 9*z^23 + 12*z^22 + 12*z^21 + 4*z^20 + 8*z^19 + 8*z^18 + 4*z^17 + 12*z^16 + 12*z^15 + 9*z^14 + 6*z^13 + 6*z^12 + 8*z^11 + 9*z^10 + 4*z^9 + 8*z^8 + 5*z^7 + 5*z^5 + 6*z^4 + 8*z^3 + 6*z^2 + 1,
6*z^35 + 12*z^34 + 8*z^33 + 11*z^32 + 11*z^30 + 10*z^29 + 12*z^28 + 9*z^27 + 10*z^26 + 6*z^25 + 8*z^24 + 9*z^23 + 5*z^22 + 5*z^21 + 12*z^20 + 12*z^19 + 12*z^18 + 12*z^17 + 5*z^16 + 5*z^15 + 9*z^14 + 8*z^13 + 6*z^12 + 10*z^11 + 9*z^10 + 12*z^9 + 10*z^8 + 11*z^7 + 11*z^5 + 8*z^4 + 12*z^3 + 6*z^2 + 9,
9*z^33 + z^32 + z^30 + 8*z^29 + z^28 + 2*z^27 + 8*z^26 + 9*z^24 + 2*z^23 + 6*z^22 + 6*z^21 + z^20 + z^17 + 6*z^16 + 6*z^15 + 2*z^14 + 9*z^13 + 8*z^11 + 2*z^10 + z^9 + 8*z^8 + z^7 + z^5 + 9*z^4 + 4,
z^35 + 8*z^34 + 2*z^33 + 5*z^32 + 5*z^30 + 11*z^29 + z^28 + 6*z^27 + 11*z^26 + z^25 + 2*z^24 + 6*z^23 + 12*z^22 + 12*z^21 + z^20 + 8*z^19 + 8*z^18 + z^17 + 12*z^16 + 12*z^15 + 6*z^14 + 2*z^13 + z^12 + 11*z^11 + 6*z^10 + z^9 + 11*z^8 + 5*z^7 + 5*z^5 + 2*z^4 + 8*z^3 + z^2 + 1,
9*z^35 + 2*z^34 + 3*z^33 + 10*z^32 + 10*z^30 + 4*z^29 + 7*z^28 + 9*z^27 + 4*z^26 + 9*z^25 + 3*z^24 + 9*z^23 + 6*z^22 + 6*z^21 + 7*z^20 + 2*z^19 + 2*z^18 + 7*z^17 + 6*z^16 + 6*z^15 + 9*z^14 + 3*z^13 + 9*z^12 + 4*z^11 + 9*z^10 + 7*z^9 + 4*z^8 + 10*z^7 + 10*z^5 + 3*z^4 + 2*z^3 + 9*z^2 + 2,
7*z^35 + 12*z^34 + 12*z^33 + 7*z^32 + 7*z^30 + z^29 + 6*z^27 + z^26 + 7*z^25 + 12*z^24 + 6*z^23 + 12*z^19 + 12*z^18 + 6*z^14 + 12*z^13 + 7*z^12 + z^11 + 6*z^10 + z^8 + 7*z^7 + 7*z^5 + 12*z^4 + 12*z^3 + 7*z^2 + 9,
6*z^33 + 6*z^32 + 6*z^30 + 6*z^29 + 8*z^27 + 6*z^26 + 6*z^24 + 8*z^23 + 8*z^14 + 6*z^13 + 6*z^11 + 8*z^10 + 6*z^8 + 6*z^7 + 6*z^5 + 6*z^4 + 7,
12*z^35 + 5*z^34 + z^33 + 9*z^32 + 9*z^30 + 6*z^29 + 2*z^28 + 12*z^27 + 6*z^26 + 12*z^25 + z^24 + 12*z^23 + 2*z^22 + 2*z^21 + 2*z^20 + 5*z^19 + 5*z^18 + 2*z^17 + 2*z^16 + 2*z^15 + 12*z^14 + z^13 + 12*z^12 + 6*z^11 + 12*z^10 + 2*z^9 + 6*z^8 + 9*z^7 + 9*z^5 + z^4 + 5*z^3 + 12*z^2,
4*z^35 + 3*z^34 + 10*z^33 + 10*z^32 + 10*z^30 + 3*z^29 + 11*z^28 + 9*z^27 + 3*z^26 + 4*z^25 + 10*z^24 + 9*z^23 + 8*z^22 + 8*z^21 + 11*z^20 + 3*z^19 + 3*z^18 + 11*z^17 + 8*z^16 + 8*z^15 + 9*z^14 + 10*z^13 + 4*z^12 + 3*z^11 + 9*z^10 + 11*z^9 + 3*z^8 + 10*z^7 + 10*z^5 + 10*z^4 + 3*z^3 + 4*z^2 + 9,
11*z^35 + 9*z^34 + 8*z^33 + 9*z^32 + 9*z^30 + 7*z^29 + z^28 + 8*z^27 + 7*z^26 + 11*z^25 + 8*z^24 + 8*z^23 + 11*z^22 + 11*z^21 + z^20 + 9*z^19 + 9*z^18 + z^17 + 11*z^16 + 11*z^15 + 8*z^14 + 8*z^13 + 11*z^12 + 7*z^11 + 8*z^10 + z^9 + 7*z^8 + 9*z^7 + 9*z^5 + 8*z^4 + 9*z^3 + 11*z^2 + 8,
4*z^35 + 7*z^34 + 3*z^33 + 11*z^32 + 11*z^30 + 5*z^29 + 11*z^28 + 12*z^27 + 5*z^26 + 4*z^25 + 3*z^24 + 12*z^23 + 11*z^20 + 7*z^19 + 7*z^18 + 11*z^17 + 12*z^14 + 3*z^13 + 4*z^12 + 5*z^11 + 12*z^10 + 11*z^9 + 5*z^8 + 11*z^7 + 11*z^5 + 3*z^4 + 7*z^3 + 4*z^2 + 7,
6*z^35 + 12*z^33 + 3*z^32 + 3*z^30 + 4*z^29 + 12*z^28 + 9*z^27 + 4*z^26 + 6*z^25 + 12*z^24 + 9*z^23 + 7*z^22 + 7*z^21 + 12*z^20 + 12*z^17 + 7*z^16 + 7*z^15 + 9*z^14 + 12*z^13 + 6*z^12 + 4*z^11 + 9*z^10 + 12*z^9 + 4*z^8 + 3*z^7 + 3*z^5 + 12*z^4 + 6*z^2 + 11,
3*z^34 + z^33 + 10*z^32 + 10*z^30 + 10*z^27 + z^24 + 10*z^23 + 12*z^22 + 12*z^21 + 3*z^19 + 3*z^18 + 12*z^16 + 12*z^15 + 10*z^14 + z^13 + 10*z^10 + 10*z^7 + 10*z^5 + z^4 + 3*z^3 + 11,
9*z^35 + 11*z^34 + 11*z^33 + 9*z^32 + 9*z^30 + 11*z^29 + 7*z^28 + z^27 + 11*z^26 + 9*z^25 + 11*z^24 + z^23 + 7*z^20 + 11*z^19 + 11*z^18 + 7*z^17 + z^14 + 11*z^13 + 9*z^12 + 11*z^11 + z^10 + 7*z^9 + 11*z^8 + 9*z^7 + 9*z^5 + 11*z^4 + 11*z^3 + 9*z^2 + 1,
8*z^35 + 10*z^34 + 9*z^33 + 12*z^32 + 12*z^30 + 10*z^29 + 6*z^28 + 3*z^27 + 10*z^26 + 8*z^25 + 9*z^24 + 3*z^23 + 3*z^22 + 3*z^21 + 6*z^20 + 10*z^19 + 10*z^18 + 6*z^17 + 3*z^16 + 3*z^15 + 3*z^14 + 9*z^13 + 8*z^12 + 10*z^11 + 3*z^10 + 6*z^9 + 10*z^8 + 12*z^7 + 12*z^5 + 9*z^4 + 10*z^3 + 8*z^2 + 3,
6*z^35 + 3*z^34 + 10*z^32 + 10*z^30 + 6*z^29 + 6*z^28 + z^27 + 6*z^26 + 6*z^25 + z^23 + 11*z^22 + 11*z^21 + 6*z^20 + 3*z^19 + 3*z^18 + 6*z^17 + 11*z^16 + 11*z^15 + z^14 + 6*z^12 + 6*z^11 + z^10 + 6*z^9 + 6*z^8 + 10*z^7 + 10*z^5 + 3*z^3 + 6*z^2 + 12,
11*z^35 + 12*z^34 + 4*z^33 + 5*z^29 + 12*z^27 + 5*z^26 + 11*z^25 + 4*z^24 + 12*z^23 + 4*z^22 + 4*z^21 + 12*z^19 + 12*z^18 + 4*z^16 + 4*z^15 + 12*z^14 + 4*z^13 + 11*z^12 + 5*z^11 + 12*z^10 + 5*z^8 + 4*z^4 + 12*z^3 + 11*z^2 + 6,
3*z^35 + 8*z^34 + 2*z^33 + 6*z^32 + 6*z^30 + 5*z^29 + 5*z^28 + 9*z^27 + 5*z^26 + 3*z^25 + 2*z^24 + 9*z^23 + 7*z^22 + 7*z^21 + 5*z^20 + 8*z^19 + 8*z^18 + 5*z^17 + 7*z^16 + 7*z^15 + 9*z^14 + 2*z^13 + 3*z^12 + 5*z^11 + 9*z^10 + 5*z^9 + 5*z^8 + 6*z^7 + 6*z^5 + 2*z^4 + 8*z^3 + 3*z^2 + 5,
3*z^35 + 11*z^34 + 9*z^33 + 6*z^32 + 6*z^30 + 12*z^29 + 9*z^28 + z^27 + 12*z^26 + 3*z^25 + 9*z^24 + z^23 + 2*z^22 + 2*z^21 + 9*z^20 + 11*z^19 + 11*z^18 + 9*z^17 + 2*z^16 + 2*z^15 + z^14 + 9*z^13 + 3*z^12 + 12*z^11 + z^10 + 9*z^9 + 12*z^8 + 6*z^7 + 6*z^5 + 9*z^4 + 11*z^3 + 3*z^2,
z^35 + 6*z^34 + 5*z^32 + 5*z^30 + 5*z^29 + 12*z^28 + 12*z^27 + 5*z^26 + z^25 + 12*z^23 + 12*z^22 + 12*z^21 + 12*z^20 + 6*z^19 + 6*z^18 + 12*z^17 + 12*z^16 + 12*z^15 + 12*z^14 + z^12 + 5*z^11 + 12*z^10 + 12*z^9 + 5*z^8 + 5*z^7 + 5*z^5 + 6*z^3 + z^2 + 4,
3*z^35 + z^34 + 5*z^33 + 4*z^32 + 4*z^30 + 10*z^29 + 8*z^28 + 5*z^27 + 10*z^26 + 3*z^25 + 5*z^24 + 5*z^23 + 8*z^20 + z^19 + z^18 + 8*z^17 + 5*z^14 + 5*z^13 + 3*z^12 + 10*z^11 + 5*z^10 + 8*z^9 + 10*z^8 + 4*z^7 + 4*z^5 + 5*z^4 + z^3 + 3*z^2 + 6,
0,
0,
1
]
> EE[37];
0
> #EE;
38
> R!E;
X^37 + (2*z^35 + 10*z^34 + 7*z^33 + 2*z^32 + 2*z^30 + 10*z^29 + 11*z^28 + 5*z^27 + 10*z^26 + 2*z^25 + 7*z^24 + 5*z^23 + z^22 + z^21 + 11*z^20 + 10*z^19 + 10*z^18 + 11*z^17 + z^16 + z^15 + 5*z^14 + 7*z^13 + 2*z^12 + 10*z^11 + 5*z^10 + 11*z^9 + 10*z^8 + 2*z^7 + 2*z^5 + 7*z^4 + 10*z^3 + 2*z^2 + 3)*X^34 + (12*z^35 + 12*z^34 + 4*z^33 + 11*z^32 + 11*z^30 + 11*z^29 + 5*z^28 + 11*z^27 + 11*z^26 + 12*z^25 + 4*z^24 + 11*z^23 + 4*z^22 + 4*z^21 + 5*z^20 + 12*z^19 + 12*z^18 + 5*z^17 + 4*z^16 + 4*z^15 + 11*z^14 + 4*z^13 + 12*z^12 + 11*z^11 + 11*z^10 + 5*z^9 + 11*z^8 + 11*z^7 + 11*z^5 + 4*z^4 + 12*z^3 + 12*z^2 + 3)*X^33 + (6*z^35 + 10*z^34 + 9*z^33 + 11*z^32 + 11*z^30 + 12*z^29 + 8*z^28 + 6*z^27 + 12*z^26 + 6*z^25 + 9*z^24 + 6*z^23 + 3*z^22 + 3*z^21 + 8*z^20 + 10*z^19 + 10*z^18 + 8*z^17 + 3*z^16 + 3*z^15 + 6*z^14 + 9*z^13 + 6*z^12 + 12*z^11 + 6*z^10 + 8*z^9 + 12*z^8 + 11*z^7 + 11*z^5 + 9*z^4 + 10*z^3 + 6*z^2 + 10)*X^32 + (12*z^35 + 10*z^34 + 2*z^33 + 6*z^32 + 6*z^30 + 4*z^29 + 5*z^28 + 2*z^27 + 4*z^26 + 12*z^25 + 2*z^24 + 2*z^23 + 3*z^22 + 3*z^21 + 5*z^20 + 10*z^19 + 10*z^18 + 5*z^17 + 3*z^16 + 3*z^15 + 2*z^14 + 2*z^13 + 12*z^12 + 4*z^11 + 2*z^10 + 5*z^9 + 4*z^8 + 6*z^7 + 6*z^5 + 2*z^4 + 10*z^3 + 12*z^2 + 2)*X^31 + (6*z^35 + 2*z^34 + 7*z^33 + z^32 + z^30 + 6*z^29 + z^28 + 2*z^27 + 6*z^26 + 6*z^25 + 7*z^24 + 2*z^23 + 2*z^22 + 2*z^21 + z^20 + 2*z^19 + 2*z^18 + z^17 + 2*z^16 + 2*z^15 + 2*z^14 + 7*z^13 + 6*z^12 + 6*z^11 + 2*z^10 + z^9 + 6*z^8 + z^7 + z^5 + 7*z^4 + 2*z^3 + 6*z^2 + 8)*X^30 + (7*z^35 + 7*z^34 + 8*z^32 + 8*z^30 + 5*z^29 + 10*z^28 + 5*z^26 + 7*z^25 + 4*z^22 + 4*z^21 + 10*z^20 + 7*z^19 + 7*z^18 + 10*z^17 + 4*z^16 + 4*z^15 + 7*z^12 + 5*z^11 + 10*z^9 + 5*z^8 + 8*z^7 + 8*z^5 + 7*z^3 + 7*z^2 + 6)*X^29 + (z^35 + 5*z^34 + 2*z^33 + 8*z^32 + 8*z^30 + 8*z^29 + 2*z^28 + 11*z^27 + 8*z^26 + z^25 + 2*z^24 + 11*z^23 + 4*z^22 + 4*z^21 + 2*z^20 + 5*z^19 + 5*z^18 + 2*z^17 + 4*z^16 + 4*z^15 + 11*z^14 + 2*z^13 + z^12 + 8*z^11 + 11*z^10 + 2*z^9 + 8*z^8 + 8*z^7 + 8*z^5 + 2*z^4 + 5*z^3 + z^2 + 8)*X^28 + (2*z^35 + 4*z^34 + 2*z^33 + 5*z^32 + 5*z^30 + 4*z^29 + 2*z^28 + 11*z^27 + 4*z^26 + 2*z^25 + 2*z^24 + 11*z^23 + 2*z^20 + 4*z^19 + 4*z^18 + 2*z^17 + 11*z^14 + 2*z^13 + 2*z^12 + 4*z^11 + 11*z^10 + 2*z^9 + 4*z^8 + 5*z^7 + 5*z^5 + 2*z^4 + 4*z^3 + 2*z^2 + 5)*X^27 + (z^35 + 10*z^32 + 10*z^30 + 12*z^29 + 3*z^28 + 12*z^26 + z^25 + 10*z^22 + 10*z^21 + 3*z^20 + 3*z^17 + 10*z^16 + 10*z^15 + z^12 + 12*z^11 + 3*z^9 + 12*z^8 + 10*z^7 + 10*z^5 + z^2 + 11)*X^26 + (6*z^35 + 7*z^34 + 11*z^33 + 3*z^32 + 3*z^30 + z^29 + 7*z^28 + 6*z^27 + z^26 + 6*z^25 + 11*z^24 + 6*z^23 + 10*z^22 + 10*z^21 + 7*z^20 + 7*z^19 + 7*z^18 + 7*z^17 + 10*z^16 + 10*z^15 + 6*z^14 + 11*z^13 + 6*z^12 + z^11 + 6*z^10 + 7*z^9 + z^8 + 3*z^7 + 3*z^5 + 11*z^4 + 7*z^3 + 6*z^2 + 5)*X^25 + (12*z^35 + 9*z^34 + z^33 + 8*z^32 + 8*z^30 + 9*z^29 + 3*z^28 + 7*z^27 + 9*z^26 + 12*z^25 + z^24 + 7*z^23 + 7*z^22 + 7*z^21 + 3*z^20 + 9*z^19 + 9*z^18 + 3*z^17 + 7*z^16 + 7*z^15 + 7*z^14 + z^13 + 12*z^12 + 9*z^11 + 7*z^10 + 3*z^9 + 9*z^8 + 8*z^7 + 8*z^5 + z^4 + 9*z^3 + 12*z^2 + 3)*X^24 + (10*z^35 + 2*z^34 + 9*z^33 + 10*z^32 + 10*z^30 + 11*z^28 + 3*z^27 + 10*z^25 + 9*z^24 + 3*z^23 + 11*z^22 + 11*z^21 + 11*z^20 + 2*z^19 + 2*z^18 + 11*z^17 + 11*z^16 + 11*z^15 + 3*z^14 + 9*z^13 + 10*z^12 + 3*z^10 + 11*z^9 + 10*z^7 + 10*z^5 + 9*z^4 + 2*z^3 + 10*z^2 + 10)*X^23 + (6*z^35 + 9*z^34 + 12*z^33 + 5*z^32 + 5*z^30 + 4*z^29 + 12*z^28 + 7*z^27 + 4*z^26 + 6*z^25 + 12*z^24 + 7*z^23 + 6*z^22 + 6*z^21 + 12*z^20 + 9*z^19 + 9*z^18 + 12*z^17 + 6*z^16 + 6*z^15 + 7*z^14 + 12*z^13 + 6*z^12 + 4*z^11 + 7*z^10 + 12*z^9 + 4*z^8 + 5*z^7 + 5*z^5 + 12*z^4 + 9*z^3 + 6*z^2 + 5)*X^22 + (2*z^35 + z^34 + 7*z^33 + 3*z^29 + 6*z^28 + 3*z^27 + 3*z^26 + 2*z^25 + 7*z^24 + 3*z^23 + 10*z^22 + 10*z^21 + 6*z^20 + z^19 + z^18 + 6*z^17 + 10*z^16 + 10*z^15 + 3*z^14 + 7*z^13 + 2*z^12 + 3*z^11 + 3*z^10 + 6*z^9 + 3*z^8 + 7*z^4 + z^3 + 2*z^2 + 1)*X^21 + (6*z^35 + 6*z^33 + 8*z^32 + 8*z^30 + 6*z^25 + 6*z^24 + 6*z^22 + 6*z^21 + 6*z^16 + 6*z^15 + 6*z^13 + 6*z^12 + 8*z^7 + 8*z^5 + 6*z^4 + 6*z^2 + 7)*X^20 + (5*z^35 + 6*z^34 + 7*z^33 + 12*z^32 + 12*z^30 + 6*z^29 + 5*z^28 + 6*z^27 + 6*z^26 + 5*z^25 + 7*z^24 + 6*z^23 + 5*z^20 + 6*z^19 + 6*z^18 + 5*z^17 + 6*z^14 + 7*z^13 + 5*z^12 + 6*z^11 + 6*z^10 + 5*z^9 + 6*z^8 + 12*z^7 + 12*z^5 + 7*z^4 + 6*z^3 + 5*z^2 + 2)*X^19 + (7*z^35 + 4*z^34 + 8*z^33 + 10*z^29 + 6*z^28 + 11*z^27 + 10*z^26 + 7*z^25 + 8*z^24 + 11*z^23 + z^22 + z^21 + 6*z^20 + 4*z^19 + 4*z^18 + 6*z^17 + z^16 + z^15 + 11*z^14 + 8*z^13 + 7*z^12 + 10*z^11 + 11*z^10 + 6*z^9 + 10*z^8 + 8*z^4 + 4*z^3 + 7*z^2 + 6)*X^18 + (z^35 + 12*z^34 + 10*z^33 + 5*z^32 + 5*z^30 + 11*z^29 + 7*z^28 + 11*z^26 + z^25 + 10*z^24 + 4*z^22 + 4*z^21 + 7*z^20 + 12*z^19 + 12*z^18 + 7*z^17 + 4*z^16 + 4*z^15 + 10*z^13 + z^12 + 11*z^11 + 7*z^9 + 11*z^8 + 5*z^7 + 5*z^5 + 10*z^4 + 12*z^3 + z^2)*X^17 + (9*z^35 + 8*z^33 + 2*z^32 + 2*z^30 + 6*z^29 + z^27 + 6*z^26 + 9*z^25 + 8*z^24 + z^23 + z^22 + z^21 + z^16 + z^15 + z^14 + 8*z^13 + 9*z^12 + 6*z^11 + z^10 + 6*z^8 + 2*z^7 + 2*z^5 + 8*z^4 + 9*z^2 + 4)*X^16 + (2*z^35 + 7*z^34 + 4*z^33 + 3*z^32 + 3*z^30 + 12*z^29 + 6*z^28 + 6*z^27 + 12*z^26 + 2*z^25 + 4*z^24 + 6*z^23 + 5*z^22 + 5*z^21 + 6*z^20 + 7*z^19 + 7*z^18 + 6*z^17 + 5*z^16 + 5*z^15 + 6*z^14 + 4*z^13 + 2*z^12 + 12*z^11 + 6*z^10 + 6*z^9 + 12*z^8 + 3*z^7 + 3*z^5 + 4*z^4 + 7*z^3 + 2*z^2 + 3)*X^15 + (7*z^34 + 2*z^33 + 3*z^32 + 3*z^30 + 6*z^29 + 2*z^28 + 11*z^27 + 6*z^26 + 2*z^24 + 11*z^23 + 12*z^22 + 12*z^21 + 2*z^20 + 7*z^19 + 7*z^18 + 2*z^17 + 12*z^16 + 12*z^15 + 11*z^14 + 2*z^13 + 6*z^11 + 11*z^10 + 2*z^9 + 6*z^8 + 3*z^7 + 3*z^5 + 2*z^4 + 7*z^3 + 8)*X^14 + (12*z^35 + 5*z^34 + 9*z^33 + 10*z^32 + 10*z^30 + 8*z^29 + 6*z^28 + 6*z^27 + 8*z^26 + 12*z^25 + 9*z^24 + 6*z^23 + 3*z^22 + 3*z^21 + 6*z^20 + 5*z^19 + 5*z^18 + 6*z^17 + 3*z^16 + 3*z^15 + 6*z^14 + 9*z^13 + 12*z^12 + 8*z^11 + 6*z^10 + 6*z^9 + 8*z^8 + 10*z^7 + 10*z^5 + 9*z^4 + 5*z^3 + 12*z^2 + 12)*X^13 + (2*z^35 + z^34 + 6*z^33 + 4*z^32 + 4*z^30 + 5*z^28 + 2*z^27 + 2*z^25 + 6*z^24 + 2*z^23 + 9*z^22 + 9*z^21 + 5*z^20 + z^19 + z^18 + 5*z^17 + 9*z^16 + 9*z^15 + 2*z^14 + 6*z^13 + 2*z^12 + 2*z^10 + 5*z^9 + 4*z^7 + 4*z^5 + 6*z^4 + z^3 + 2*z^2 + 3)*X^12 + (7*z^35 + 5*z^34 + 2*z^33 + z^32 + z^30 + 10*z^29 + 7*z^28 + 7*z^27 + 10*z^26 + 7*z^25 + 2*z^24 + 7*z^23 + 6*z^22 + 6*z^21 + 7*z^20 + 5*z^19 + 5*z^18 + 7*z^17 + 6*z^16 + 6*z^15 + 7*z^14 + 2*z^13 + 7*z^12 + 10*z^11 + 7*z^10 + 7*z^9 + 10*z^8 + z^7 + z^5 + 2*z^4 + 5*z^3 + 7*z^2 + 11)*X^11 + (8*z^35 + 8*z^34 + 3*z^33 + 11*z^29 + 4*z^28 + 7*z^27 + 11*z^26 + 8*z^25 + 3*z^24 + 7*z^23 + 8*z^22 + 8*z^21 + 4*z^20 + 8*z^19 + 8*z^18 + 4*z^17 + 8*z^16 + 8*z^15 + 7*z^14 + 3*z^13 + 8*z^12 + 11*z^11 + 7*z^10 + 4*z^9 + 11*z^8 + 3*z^4 + 8*z^3 + 8*z^2 + 3)*X^10 + (9*z^35 + 5*z^33 + 11*z^29 + 6*z^28 + 10*z^27 + 11*z^26 + 9*z^25 + 5*z^24 + 10*z^23 + 8*z^22 + 8*z^21 + 6*z^20 + 6*z^17 + 8*z^16 + 8*z^15 + 10*z^14 + 5*z^13 + 9*z^12 + 11*z^11 + 10*z^10 + 6*z^9 + 11*z^8 + 5*z^4 + 9*z^2 + 10)*X^9 + (8*z^35 + 9*z^34 + 9*z^33 + 4*z^32 + 4*z^30 + z^29 + 4*z^28 + 8*z^27 + z^26 + 8*z^25 + 9*z^24 + 8*z^23 + 3*z^22 + 3*z^21 + 4*z^20 + 9*z^19 + 9*z^18 + 4*z^17 + 3*z^16 + 3*z^15 + 8*z^14 + 9*z^13 + 8*z^12 + z^11 + 8*z^10 + 4*z^9 + z^8 + 4*z^7 + 4*z^5 + 9*z^4 + 9*z^3 + 8*z^2 + 12)*X^8 + (11*z^35 + z^34 + 5*z^33 + 9*z^32 + 9*z^30 + 8*z^29 + 4*z^28 + 5*z^27 + 8*z^26 + 11*z^25 + 5*z^24 + 5*z^23 + 10*z^22 + 10*z^21 + 4*z^20 + z^19 + z^18 + 4*z^17 + 10*z^16 + 10*z^15 + 5*z^14 + 5*z^13 + 11*z^12 + 8*z^11 + 5*z^10 + 4*z^9 + 8*z^8 + 9*z^7 + 9*z^5 + 5*z^4 + z^3 + 11*z^2 + 7)*X^7 + (8*z^35 + 12*z^34 + z^33 + 4*z^32 + 4*z^30 + 9*z^29 + 11*z^28 + 9*z^27 + 9*z^26 + 8*z^25 + z^24 + 9*z^23 + 7*z^22 + 7*z^21 + 11*z^20 + 12*z^19 + 12*z^18 + 11*z^17 + 7*z^16 + 7*z^15 + 9*z^14 + z^13 + 8*z^12 + 9*z^11 + 9*z^10 + 11*z^9 + 9*z^8 + 4*z^7 + 4*z^5 + z^4 + 12*z^3 + 8*z^2 + 7)*X^6 + (5*z^34 + 9*z^33 + 2*z^32 + 2*z^30 + z^29 + 12*z^28 + z^27 + z^26 + 9*z^24 + z^23 + 4*z^22 + 4*z^21 + 12*z^20 + 5*z^19 + 5*z^18 + 12*z^17 + 4*z^16 + 4*z^15 + z^14 + 9*z^13 + z^11 + z^10 + 12*z^9 + z^8 + 2*z^7 + 2*z^5 + 9*z^4 + 5*z^3 + 2)*X^5 + (9*z^35 + 11*z^34 + z^33 + 4*z^32 + 4*z^30 + 4*z^29 + 10*z^28 + 2*z^27 + 4*z^26 + 9*z^25 + z^24 + 2*z^23 + 2*z^22 + 2*z^21 + 10*z^20 + 11*z^19 + 11*z^18 + 10*z^17 + 2*z^16 + 2*z^15 + 2*z^14 + z^13 + 9*z^12 + 4*z^11 + 2*z^10 + 10*z^9 + 4*z^8 + 4*z^7 + 4*z^5 + z^4 + 11*z^3 + 9*z^2 + 9)*X^4 + (11*z^35 + 8*z^33 + z^32 + z^30 + 6*z^29 + 5*z^28 + z^27 + 6*z^26 + 11*z^25 + 8*z^24 + z^23 + 9*z^22 + 9*z^21 + 5*z^20 + 5*z^17 + 9*z^16 + 9*z^15 + z^14 + 8*z^13 + 11*z^12 + 6*z^11 + z^10 + 5*z^9 + 6*z^8 + z^7 + z^5 + 8*z^4 + 11*z^2 + 5)*X^3 + (7*z^35 + 9*z^33 + 6*z^32 + 6*z^30 + 2*z^29 + 12*z^28 + 5*z^27 + 2*z^26 + 7*z^25 + 9*z^24 + 5*z^23 + 8*z^22 + 8*z^21 + 12*z^20 + 12*z^17 + 8*z^16 + 8*z^15 + 5*z^14 + 9*z^13 + 7*z^12 + 2*z^11 + 5*z^10 + 12*z^9 + 2*z^8 + 6*z^7 + 6*z^5 + 9*z^4 + 7*z^2 + 9)*X^2 + (9*z^35 + 7*z^34 + 5*z^33 + 9*z^32 + 9*z^30 + 5*z^29 + 11*z^28 + 4*z^27 + 5*z^26 + 9*z^25 + 5*z^24 + 4*z^23 + 3*z^22 + 3*z^21 + 11*z^20 + 7*z^19 + 7*z^18 + 11*z^17 + 3*z^16 + 3*z^15 + 4*z^14 + 5*z^13 + 9*z^12 + 5*z^11 + 4*z^10 + 11*z^9 + 5*z^8 + 9*z^7 + 9*z^5 + 5*z^4 + 7*z^3 + 9*z^2 + 8)*X + 8*z^35 + 6*z^34 + 10*z^32 + 10*z^30 + 8*z^29 + 8*z^28 + 5*z^27 + 8*z^26 + 8*z^25 + 5*z^23 + 7*z^22 + 7*z^21 + 8*z^20 + 6*z^19 + 6*z^18 + 8*z^17 + 7*z^16 + 7*z^15 + 5*z^14 + 8*z^12 + 8*z^11 + 5*z^10 + 8*z^9 + 8*z^8 + 10*z^7 + 10*z^5 + 6*z^3 + 8*z^2 + 6
> #E;
38
> 
R;
> Univariate Polynomial Ring in X over Univariate Quotient Polynomial Algebra in z over GF(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
> L := BaseRing(R);
> L;
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
> EEE := [L!e : e in EE];

>> EEE := [L!e : e in EE];
            ^
Runtime error in '!': Illegal coercion
> L!EE[1];

>> L!EE[1];
    ^
Runtime error in '!': Illegal coercion
> EE[1];
7*z^35 + 2*z^34 + 2*z^33 + z^32 + z^30 + 7*z^29 + 12*z^28 + 4*z^27 + 7*z^26 + 7*z^25 + 2*z^24 + 4*z^23 + 2*z^22 + 2*z^21 + 12*z^20 + 2*z^19 + 2*z^18 + 12*z^17 + 2*z^16 + 2*z^15 + 4*z^14 + 2*z^13 + 7*z^12 + 7*z^11 + 4*z^10 + 12*z^9 + 7*z^8 + z^7 + z^5 + 2*z^4 + 2*z^3 + 7*z^2
> L;
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
>  EEE := [L!Eltseq(e) : e in EE];

>>  EEE := [L!Eltseq(e) : e in EE];
             ^
Runtime error in '!': Can't coerce sequence element 0 into the coefficient ring
> EE;
[
7*z^35 + 2*z^34 + 2*z^33 + z^32 + z^30 + 7*z^29 + 12*z^28 + 4*z^27 + 7*z^26 + 7*z^25 + 2*z^24 + 4*z^23 + 2*z^22 + 2*z^21 + 12*z^20 + 2*z^19 + 2*z^18 + 12*z^17 + 2*z^16 + 2*z^15 + 4*z^14 + 2*z^13 + 7*z^12 + 7*z^11 + 4*z^10 + 12*z^9 + 7*z^8 + z^7 + z^5 + 2*z^4 + 2*z^3 + 7*z^2,
6*z^35 + 4*z^34 + 2*z^33 + 9*z^32 + 9*z^30 + 11*z^29 + 10*z^28 + 2*z^27 + 11*z^26 + 6*z^25 + 2*z^24 + 2*z^23 + 11*z^22 + 11*z^21 + 10*z^20 + 4*z^19 + 4*z^18 + 10*z^17 + 11*z^16 + 11*z^15 + 2*z^14 + 2*z^13 + 6*z^12 + 11*z^11 + 2*z^10 + 10*z^9 + 11*z^8 + 9*z^7 + 9*z^5 + 2*z^4 + 4*z^3 + 6*z^2 + 1,
12*z^34 + 7*z^33 + 8*z^32 + 8*z^30 + 9*z^29 + 5*z^28 + 6*z^27 + 9*z^26 + 7*z^24 + 6*z^23 + 2*z^22 + 2*z^21 + 5*z^20 + 12*z^19 + 12*z^18 + 5*z^17 + 2*z^16 + 2*z^15 + 6*z^14 + 7*z^13 + 9*z^11 + 6*z^10 + 5*z^9 + 9*z^8 + 8*z^7 + 8*z^5 + 7*z^4 + 12*z^3 + 9,
5*z^34 + 11*z^33 + 9*z^32 + 9*z^30 + 8*z^29 + z^28 + z^27 + 8*z^26 + 11*z^24 + z^23 + 6*z^22 + 6*z^21 + z^20 + 5*z^19 + 5*z^18 + z^17 + 6*z^16 + 6*z^15 + z^14 + 11*z^13 + 8*z^11 + z^10 + z^9 + 8*z^8 + 9*z^7 + 9*z^5 + 11*z^4 + 5*z^3 + 5,
2*z^35 + 12*z^34 + 11*z^33 + 4*z^32 + 4*z^30 + 3*z^29 + 4*z^28 + 6*z^27 + 3*z^26 + 2*z^25 + 11*z^24 + 6*z^23 + 6*z^22 + 6*z^21 + 4*z^20 + 12*z^19 + 12*z^18 + 4*z^17 + 6*z^16 + 6*z^15 + 6*z^14 + 11*z^13 + 2*z^12 + 3*z^11 + 6*z^10 + 4*z^9 + 3*z^8 + 4*z^7 + 4*z^5 + 11*z^4 + 12*z^3 + 2*z^2 + 11,
8*z^35 + 7*z^34 + 8*z^33 + 12*z^32 + 12*z^30 + 4*z^29 + 9*z^28 + 10*z^27 + 4*z^26 + 8*z^25 + 8*z^24 + 10*z^23 + 9*z^22 + 9*z^21 + 9*z^20 + 7*z^19 + 7*z^18 + 9*z^17 + 9*z^16 + 9*z^15 + 10*z^14 + 8*z^13 + 8*z^12 + 4*z^11 + 10*z^10 + 9*z^9 + 4*z^8 + 12*z^7 + 12*z^5 + 8*z^4 + 7*z^3 + 8*z^2 + 10,
z^35 + 12*z^34 + 9*z^33 + 8*z^32 + 8*z^30 + 2*z^29 + 10*z^28 + 5*z^27 + 2*z^26 + z^25 + 9*z^24 + 5*z^23 + 10*z^22 + 10*z^21 + 10*z^20 + 12*z^19 + 12*z^18 + 10*z^17 + 10*z^16 + 10*z^15 + 5*z^14 + 9*z^13 + z^12 + 2*z^11 + 5*z^10 + 10*z^9 + 2*z^8 + 8*z^7 + 8*z^5 + 9*z^4 + 12*z^3 + z^2 + 8,
12*z^35 + 3*z^34 + 10*z^33 + 9*z^32 + 9*z^30 + 4*z^29 + 4*z^28 + 8*z^27 + 4*z^26 + 12*z^25 + 10*z^24 + 8*z^23 + 7*z^22 + 7*z^21 + 4*z^20 + 3*z^19 + 3*z^18 + 4*z^17 + 7*z^16 + 7*z^15 + 8*z^14 + 10*z^13 + 12*z^12 + 4*z^11 + 8*z^10 + 4*z^9 + 4*z^8 + 9*z^7 + 9*z^5 + 10*z^4 + 3*z^3 + 12*z^2 + 6,
4*z^35 + 8*z^34 + 12*z^33 + 7*z^32 + 7*z^30 + 12*z^28 + 8*z^27 + 4*z^25 + 12*z^24 + 8*z^23 + 5*z^22 + 5*z^21 + 12*z^20 + 8*z^19 + 8*z^18 + 12*z^17 + 5*z^16 + 5*z^15 + 8*z^14 + 12*z^13 + 4*z^12 + 8*z^10 + 12*z^9 + 7*z^7 + 7*z^5 + 12*z^4 + 8*z^3 + 4*z^2 + 3,
6*z^34 + 9*z^33 + 8*z^32 + 8*z^30 + 5*z^29 + 10*z^28 + 5*z^26 + 9*z^24 + 11*z^22 + 11*z^21 + 10*z^20 + 6*z^19 + 6*z^18 + 10*z^17 + 11*z^16 + 11*z^15 + 9*z^13 + 5*z^11 + 10*z^9 + 5*z^8 + 8*z^7 + 8*z^5 + 9*z^4 + 6*z^3 + 10,
5*z^35 + 9*z^34 + 8*z^29 + 12*z^28 + 5*z^27 + 8*z^26 + 5*z^25 + 5*z^23 + 3*z^22 + 3*z^21 + 12*z^20 + 9*z^19 + 9*z^18 + 12*z^17 + 3*z^16 + 3*z^15 + 5*z^14 + 5*z^12 + 8*z^11 + 5*z^10 + 12*z^9 + 8*z^8 + 9*z^3 + 5*z^2 + 8,
8*z^35 + 2*z^34 + 2*z^33 + z^32 + z^30 + 10*z^29 + 2*z^28 + 9*z^27 + 10*z^26 + 8*z^25 + 2*z^24 + 9*z^23 + 5*z^22 + 5*z^21 + 2*z^20 + 2*z^19 + 2*z^18 + 2*z^17 + 5*z^16 + 5*z^15 + 9*z^14 + 2*z^13 + 8*z^12 + 10*z^11 + 9*z^10 + 2*z^9 + 10*z^8 + z^7 + z^5 + 2*z^4 + 2*z^3 + 8*z^2 + 6,
12*z^35 + 4*z^34 + z^33 + 8*z^32 + 8*z^30 + 5*z^29 + z^28 + 3*z^27 + 5*z^26 + 12*z^25 + z^24 + 3*z^23 + 12*z^22 + 12*z^21 + z^20 + 4*z^19 + 4*z^18 + z^17 + 12*z^16 + 12*z^15 + 3*z^14 + z^13 + 12*z^12 + 5*z^11 + 3*z^10 + z^9 + 5*z^8 + 8*z^7 + 8*z^5 + z^4 + 4*z^3 + 12*z^2 + 2,
8*z^35 + z^34 + 7*z^33 + 11*z^32 + 11*z^30 + 4*z^29 + z^28 + 5*z^27 + 4*z^26 + 8*z^25 + 7*z^24 + 5*z^23 + 3*z^22 + 3*z^21 + z^20 + z^19 + z^18 + z^17 + 3*z^16 + 3*z^15 + 5*z^14 + 7*z^13 + 8*z^12 + 4*z^11 + 5*z^10 + z^9 + 4*z^8 + 11*z^7 + 11*z^5 + 7*z^4 + z^3 + 8*z^2 + 7,
6*z^35 + 8*z^34 + 6*z^33 + 5*z^32 + 5*z^30 + 8*z^29 + 4*z^28 + 9*z^27 + 8*z^26 + 6*z^25 + 6*z^24 + 9*z^23 + 12*z^22 + 12*z^21 + 4*z^20 + 8*z^19 + 8*z^18 + 4*z^17 + 12*z^16 + 12*z^15 + 9*z^14 + 6*z^13 + 6*z^12 + 8*z^11 + 9*z^10 + 4*z^9 + 8*z^8 + 5*z^7 + 5*z^5 + 6*z^4 + 8*z^3 + 6*z^2 + 1,
6*z^35 + 12*z^34 + 8*z^33 + 11*z^32 + 11*z^30 + 10*z^29 + 12*z^28 + 9*z^27 + 10*z^26 + 6*z^25 + 8*z^24 + 9*z^23 + 5*z^22 + 5*z^21 + 12*z^20 + 12*z^19 + 12*z^18 + 12*z^17 + 5*z^16 + 5*z^15 + 9*z^14 + 8*z^13 + 6*z^12 + 10*z^11 + 9*z^10 + 12*z^9 + 10*z^8 + 11*z^7 + 11*z^5 + 8*z^4 + 12*z^3 + 6*z^2 + 9,
9*z^33 + z^32 + z^30 + 8*z^29 + z^28 + 2*z^27 + 8*z^26 + 9*z^24 + 2*z^23 + 6*z^22 + 6*z^21 + z^20 + z^17 + 6*z^16 + 6*z^15 + 2*z^14 + 9*z^13 + 8*z^11 + 2*z^10 + z^9 + 8*z^8 + z^7 + z^5 + 9*z^4 + 4,
z^35 + 8*z^34 + 2*z^33 + 5*z^32 + 5*z^30 + 11*z^29 + z^28 + 6*z^27 + 11*z^26 + z^25 + 2*z^24 + 6*z^23 + 12*z^22 + 12*z^21 + z^20 + 8*z^19 + 8*z^18 + z^17 + 12*z^16 + 12*z^15 + 6*z^14 + 2*z^13 + z^12 + 11*z^11 + 6*z^10 + z^9 + 11*z^8 + 5*z^7 + 5*z^5 + 2*z^4 + 8*z^3 + z^2 + 1,
9*z^35 + 2*z^34 + 3*z^33 + 10*z^32 + 10*z^30 + 4*z^29 + 7*z^28 + 9*z^27 + 4*z^26 + 9*z^25 + 3*z^24 + 9*z^23 + 6*z^22 + 6*z^21 + 7*z^20 + 2*z^19 + 2*z^18 + 7*z^17 + 6*z^16 + 6*z^15 + 9*z^14 + 3*z^13 + 9*z^12 + 4*z^11 + 9*z^10 + 7*z^9 + 4*z^8 + 10*z^7 + 10*z^5 + 3*z^4 + 2*z^3 + 9*z^2 + 2,
7*z^35 + 12*z^34 + 12*z^33 + 7*z^32 + 7*z^30 + z^29 + 6*z^27 + z^26 + 7*z^25 + 12*z^24 + 6*z^23 + 12*z^19 + 12*z^18 + 6*z^14 + 12*z^13 + 7*z^12 + z^11 + 6*z^10 + z^8 + 7*z^7 + 7*z^5 + 12*z^4 + 12*z^3 + 7*z^2 + 9,
6*z^33 + 6*z^32 + 6*z^30 + 6*z^29 + 8*z^27 + 6*z^26 + 6*z^24 + 8*z^23 + 8*z^14 + 6*z^13 + 6*z^11 + 8*z^10 + 6*z^8 + 6*z^7 + 6*z^5 + 6*z^4 + 7,
12*z^35 + 5*z^34 + z^33 + 9*z^32 + 9*z^30 + 6*z^29 + 2*z^28 + 12*z^27 + 6*z^26 + 12*z^25 + z^24 + 12*z^23 + 2*z^22 + 2*z^21 + 2*z^20 + 5*z^19 + 5*z^18 + 2*z^17 + 2*z^16 + 2*z^15 + 12*z^14 + z^13 + 12*z^12 + 6*z^11 + 12*z^10 + 2*z^9 + 6*z^8 + 9*z^7 + 9*z^5 + z^4 + 5*z^3 + 12*z^2,
4*z^35 + 3*z^34 + 10*z^33 + 10*z^32 + 10*z^30 + 3*z^29 + 11*z^28 + 9*z^27 + 3*z^26 + 4*z^25 + 10*z^24 + 9*z^23 + 8*z^22 + 8*z^21 + 11*z^20 + 3*z^19 + 3*z^18 + 11*z^17 + 8*z^16 + 8*z^15 + 9*z^14 + 10*z^13 + 4*z^12 + 3*z^11 + 9*z^10 + 11*z^9 + 3*z^8 + 10*z^7 + 10*z^5 + 10*z^4 + 3*z^3 + 4*z^2 + 9,
11*z^35 + 9*z^34 + 8*z^33 + 9*z^32 + 9*z^30 + 7*z^29 + z^28 + 8*z^27 + 7*z^26 + 11*z^25 + 8*z^24 + 8*z^23 + 11*z^22 + 11*z^21 + z^20 + 9*z^19 + 9*z^18 + z^17 + 11*z^16 + 11*z^15 + 8*z^14 + 8*z^13 + 11*z^12 + 7*z^11 + 8*z^10 + z^9 + 7*z^8 + 9*z^7 + 9*z^5 + 8*z^4 + 9*z^3 + 11*z^2 + 8,
4*z^35 + 7*z^34 + 3*z^33 + 11*z^32 + 11*z^30 + 5*z^29 + 11*z^28 + 12*z^27 + 5*z^26 + 4*z^25 + 3*z^24 + 12*z^23 + 11*z^20 + 7*z^19 + 7*z^18 + 11*z^17 + 12*z^14 + 3*z^13 + 4*z^12 + 5*z^11 + 12*z^10 + 11*z^9 + 5*z^8 + 11*z^7 + 11*z^5 + 3*z^4 + 7*z^3 + 4*z^2 + 7,
6*z^35 + 12*z^33 + 3*z^32 + 3*z^30 + 4*z^29 + 12*z^28 + 9*z^27 + 4*z^26 + 6*z^25 + 12*z^24 + 9*z^23 + 7*z^22 + 7*z^21 + 12*z^20 + 12*z^17 + 7*z^16 + 7*z^15 + 9*z^14 + 12*z^13 + 6*z^12 + 4*z^11 + 9*z^10 + 12*z^9 + 4*z^8 + 3*z^7 + 3*z^5 + 12*z^4 + 6*z^2 + 11,
3*z^34 + z^33 + 10*z^32 + 10*z^30 + 10*z^27 + z^24 + 10*z^23 + 12*z^22 + 12*z^21 + 3*z^19 + 3*z^18 + 12*z^16 + 12*z^15 + 10*z^14 + z^13 + 10*z^10 + 10*z^7 + 10*z^5 + z^4 + 3*z^3 + 11,
9*z^35 + 11*z^34 + 11*z^33 + 9*z^32 + 9*z^30 + 11*z^29 + 7*z^28 + z^27 + 11*z^26 + 9*z^25 + 11*z^24 + z^23 + 7*z^20 + 11*z^19 + 11*z^18 + 7*z^17 + z^14 + 11*z^13 + 9*z^12 + 11*z^11 + z^10 + 7*z^9 + 11*z^8 + 9*z^7 + 9*z^5 + 11*z^4 + 11*z^3 + 9*z^2 + 1,
8*z^35 + 10*z^34 + 9*z^33 + 12*z^32 + 12*z^30 + 10*z^29 + 6*z^28 + 3*z^27 + 10*z^26 + 8*z^25 + 9*z^24 + 3*z^23 + 3*z^22 + 3*z^21 + 6*z^20 + 10*z^19 + 10*z^18 + 6*z^17 + 3*z^16 + 3*z^15 + 3*z^14 + 9*z^13 + 8*z^12 + 10*z^11 + 3*z^10 + 6*z^9 + 10*z^8 + 12*z^7 + 12*z^5 + 9*z^4 + 10*z^3 + 8*z^2 + 3,
6*z^35 + 3*z^34 + 10*z^32 + 10*z^30 + 6*z^29 + 6*z^28 + z^27 + 6*z^26 + 6*z^25 + z^23 + 11*z^22 + 11*z^21 + 6*z^20 + 3*z^19 + 3*z^18 + 6*z^17 + 11*z^16 + 11*z^15 + z^14 + 6*z^12 + 6*z^11 + z^10 + 6*z^9 + 6*z^8 + 10*z^7 + 10*z^5 + 3*z^3 + 6*z^2 + 12,
11*z^35 + 12*z^34 + 4*z^33 + 5*z^29 + 12*z^27 + 5*z^26 + 11*z^25 + 4*z^24 + 12*z^23 + 4*z^22 + 4*z^21 + 12*z^19 + 12*z^18 + 4*z^16 + 4*z^15 + 12*z^14 + 4*z^13 + 11*z^12 + 5*z^11 + 12*z^10 + 5*z^8 + 4*z^4 + 12*z^3 + 11*z^2 + 6,
3*z^35 + 8*z^34 + 2*z^33 + 6*z^32 + 6*z^30 + 5*z^29 + 5*z^28 + 9*z^27 + 5*z^26 + 3*z^25 + 2*z^24 + 9*z^23 + 7*z^22 + 7*z^21 + 5*z^20 + 8*z^19 + 8*z^18 + 5*z^17 + 7*z^16 + 7*z^15 + 9*z^14 + 2*z^13 + 3*z^12 + 5*z^11 + 9*z^10 + 5*z^9 + 5*z^8 + 6*z^7 + 6*z^5 + 2*z^4 + 8*z^3 + 3*z^2 + 5,
3*z^35 + 11*z^34 + 9*z^33 + 6*z^32 + 6*z^30 + 12*z^29 + 9*z^28 + z^27 + 12*z^26 + 3*z^25 + 9*z^24 + z^23 + 2*z^22 + 2*z^21 + 9*z^20 + 11*z^19 + 11*z^18 + 9*z^17 + 2*z^16 + 2*z^15 + z^14 + 9*z^13 + 3*z^12 + 12*z^11 + z^10 + 9*z^9 + 12*z^8 + 6*z^7 + 6*z^5 + 9*z^4 + 11*z^3 + 3*z^2,
z^35 + 6*z^34 + 5*z^32 + 5*z^30 + 5*z^29 + 12*z^28 + 12*z^27 + 5*z^26 + z^25 + 12*z^23 + 12*z^22 + 12*z^21 + 12*z^20 + 6*z^19 + 6*z^18 + 12*z^17 + 12*z^16 + 12*z^15 + 12*z^14 + z^12 + 5*z^11 + 12*z^10 + 12*z^9 + 5*z^8 + 5*z^7 + 5*z^5 + 6*z^3 + z^2 + 4,
3*z^35 + z^34 + 5*z^33 + 4*z^32 + 4*z^30 + 10*z^29 + 8*z^28 + 5*z^27 + 10*z^26 + 3*z^25 + 5*z^24 + 5*z^23 + 8*z^20 + z^19 + z^18 + 8*z^17 + 5*z^14 + 5*z^13 + 3*z^12 + 10*z^11 + 5*z^10 + 8*z^9 + 10*z^8 + 4*z^7 + 4*z^5 + 5*z^4 + z^3 + 3*z^2 + 6,
0,
0,
1
]
> &+[X^(i-1)*EE[i] : i in [1..38]];

>> &+[X^(i-1)*EE[i] : i in [1..38]];
             ^
Runtime error in '*': Bad argument types
Argument types given: RngUPolElt, RngUPolResElt
> R;
Univariate Polynomial Ring in X over Univariate Quotient Polynomial Algebra in z over GF(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
> f;
X^37 + (2*z^35 + 10*z^34 + 7*z^33 + 2*z^32 + 2*z^30 + 10*z^29 + 11*z^28 + 5*z^27 + 10*z^26 + 2*z^25 + 7*z^24 + 5*z^23 + z^22 + z^21 + 11*z^20 + 10*z^19 + 10*z^18 + 11*z^17 + z^16 + z^15 + 5*z^14 + 7*z^13 + 2*z^12 + 10*z^11 + 5*z^10 + 11*z^9 + 10*z^8 + 2*z^7 + 2*z^5 + 7*z^4 + 10*z^3 + 2*z^2 + 3)*X^34 + (12*z^35 + 12*z^34 + 4*z^33 + 11*z^32 + 11*z^30 + 11*z^29 + 5*z^28 + 11*z^27 + 11*z^26 + 12*z^25 + 4*z^24 + 11*z^23 + 4*z^22 + 4*z^21 + 5*z^20 + 12*z^19 + 12*z^18 + 5*z^17 + 4*z^16 + 4*z^15 + 11*z^14 + 4*z^13 + 12*z^12 + 11*z^11 + 11*z^10 + 5*z^9 + 11*z^8 + 11*z^7 + 11*z^5 + 4*z^4 + 12*z^3 + 12*z^2 + 3)*X^33 + (6*z^35 + 10*z^34 + 9*z^33 + 11*z^32 + 11*z^30 + 12*z^29 + 8*z^28 + 6*z^27 + 12*z^26 + 6*z^25 + 9*z^24 + 6*z^23 + 3*z^22 + 3*z^21 + 8*z^20 + 10*z^19 + 10*z^18 + 8*z^17 + 3*z^16 + 3*z^15 + 6*z^14 + 9*z^13 + 6*z^12 + 12*z^11 + 6*z^10 + 8*z^9 + 12*z^8 + 11*z^7 + 11*z^5 + 9*z^4 + 10*z^3 + 6*z^2 + 10)*X^32 + (12*z^35 + 10*z^34 + 2*z^33 + 6*z^32 + 6*z^30 + 4*z^29 + 5*z^28 + 2*z^27 + 4*z^26 + 12*z^25 + 2*z^24 + 2*z^23 + 3*z^22 + 3*z^21 + 5*z^20 + 10*z^19 + 10*z^18 + 5*z^17 + 3*z^16 + 3*z^15 + 2*z^14 + 2*z^13 + 12*z^12 + 4*z^11 + 2*z^10 + 5*z^9 + 4*z^8 + 6*z^7 + 6*z^5 + 2*z^4 + 10*z^3 + 12*z^2 + 2)*X^31 + (6*z^35 + 2*z^34 + 7*z^33 + z^32 + z^30 + 6*z^29 + z^28 + 2*z^27 + 6*z^26 + 6*z^25 + 7*z^24 + 2*z^23 + 2*z^22 + 2*z^21 + z^20 + 2*z^19 + 2*z^18 + z^17 + 2*z^16 + 2*z^15 + 2*z^14 + 7*z^13 + 6*z^12 + 6*z^11 + 2*z^10 + z^9 + 6*z^8 + z^7 + z^5 + 7*z^4 + 2*z^3 + 6*z^2 + 8)*X^30 + (7*z^35 + 7*z^34 + 8*z^32 + 8*z^30 + 5*z^29 + 10*z^28 + 5*z^26 + 7*z^25 + 4*z^22 + 4*z^21 + 10*z^20 + 7*z^19 + 7*z^18 + 10*z^17 + 4*z^16 + 4*z^15 + 7*z^12 + 5*z^11 + 10*z^9 + 5*z^8 + 8*z^7 + 8*z^5 + 7*z^3 + 7*z^2 + 6)*X^29 + (z^35 + 5*z^34 + 2*z^33 + 8*z^32 + 8*z^30 + 8*z^29 + 2*z^28 + 11*z^27 + 8*z^26 + z^25 + 2*z^24 + 11*z^23 + 4*z^22 + 4*z^21 + 2*z^20 + 5*z^19 + 5*z^18 + 2*z^17 + 4*z^16 + 4*z^15 + 11*z^14 + 2*z^13 + z^12 + 8*z^11 + 11*z^10 + 2*z^9 + 8*z^8 + 8*z^7 + 8*z^5 + 2*z^4 + 5*z^3 + z^2 + 8)*X^28 + (2*z^35 + 4*z^34 + 2*z^33 + 5*z^32 + 5*z^30 + 4*z^29 + 2*z^28 + 11*z^27 + 4*z^26 + 2*z^25 + 2*z^24 + 11*z^23 + 2*z^20 + 4*z^19 + 4*z^18 + 2*z^17 + 11*z^14 + 2*z^13 + 2*z^12 + 4*z^11 + 11*z^10 + 2*z^9 + 4*z^8 + 5*z^7 + 5*z^5 + 2*z^4 + 4*z^3 + 2*z^2 + 5)*X^27 + (z^35 + 10*z^32 + 10*z^30 + 12*z^29 + 3*z^28 + 12*z^26 + z^25 + 10*z^22 + 10*z^21 + 3*z^20 + 3*z^17 + 10*z^16 + 10*z^15 + z^12 + 12*z^11 + 3*z^9 + 12*z^8 + 10*z^7 + 10*z^5 + z^2 + 11)*X^26 + (6*z^35 + 7*z^34 + 11*z^33 + 3*z^32 + 3*z^30 + z^29 + 7*z^28 + 6*z^27 + z^26 + 6*z^25 + 11*z^24 + 6*z^23 + 10*z^22 + 10*z^21 + 7*z^20 + 7*z^19 + 7*z^18 + 7*z^17 + 10*z^16 + 10*z^15 + 6*z^14 + 11*z^13 + 6*z^12 + z^11 + 6*z^10 + 7*z^9 + z^8 + 3*z^7 + 3*z^5 + 11*z^4 + 7*z^3 + 6*z^2 + 5)*X^25 + (12*z^35 + 9*z^34 + z^33 + 8*z^32 + 8*z^30 + 9*z^29 + 3*z^28 + 7*z^27 + 9*z^26 + 12*z^25 + z^24 + 7*z^23 + 7*z^22 + 7*z^21 + 3*z^20 + 9*z^19 + 9*z^18 + 3*z^17 + 7*z^16 + 7*z^15 + 7*z^14 + z^13 + 12*z^12 + 9*z^11 + 7*z^10 + 3*z^9 + 9*z^8 + 8*z^7 + 8*z^5 + z^4 + 9*z^3 + 12*z^2 + 3)*X^24 + (10*z^35 + 2*z^34 + 9*z^33 + 10*z^32 + 10*z^30 + 11*z^28 + 3*z^27 + 10*z^25 + 9*z^24 + 3*z^23 + 11*z^22 + 11*z^21 + 11*z^20 + 2*z^19 + 2*z^18 + 11*z^17 + 11*z^16 + 11*z^15 + 3*z^14 + 9*z^13 + 10*z^12 + 3*z^10 + 11*z^9 + 10*z^7 + 10*z^5 + 9*z^4 + 2*z^3 + 10*z^2 + 10)*X^23 + (6*z^35 + 9*z^34 + 12*z^33 + 5*z^32 + 5*z^30 + 4*z^29 + 12*z^28 + 7*z^27 + 4*z^26 + 6*z^25 + 12*z^24 + 7*z^23 + 6*z^22 + 6*z^21 + 12*z^20 + 9*z^19 + 9*z^18 + 12*z^17 + 6*z^16 + 6*z^15 + 7*z^14 + 12*z^13 + 6*z^12 + 4*z^11 + 7*z^10 + 12*z^9 + 4*z^8 + 5*z^7 + 5*z^5 + 12*z^4 + 9*z^3 + 6*z^2 + 5)*X^22 + (2*z^35 + z^34 + 7*z^33 + 3*z^29 + 6*z^28 + 3*z^27 + 3*z^26 + 2*z^25 + 7*z^24 + 3*z^23 + 10*z^22 + 10*z^21 + 6*z^20 + z^19 + z^18 + 6*z^17 + 10*z^16 + 10*z^15 + 3*z^14 + 7*z^13 + 2*z^12 + 3*z^11 + 3*z^10 + 6*z^9 + 3*z^8 + 7*z^4 + z^3 + 2*z^2 + 1)*X^21 + (6*z^35 + 6*z^33 + 8*z^32 + 8*z^30 + 6*z^25 + 6*z^24 + 6*z^22 + 6*z^21 + 6*z^16 + 6*z^15 + 6*z^13 + 6*z^12 + 8*z^7 + 8*z^5 + 6*z^4 + 6*z^2 + 7)*X^20 + (5*z^35 + 6*z^34 + 7*z^33 + 12*z^32 + 12*z^30 + 6*z^29 + 5*z^28 + 6*z^27 + 6*z^26 + 5*z^25 + 7*z^24 + 6*z^23 + 5*z^20 + 6*z^19 + 6*z^18 + 5*z^17 + 6*z^14 + 7*z^13 + 5*z^12 + 6*z^11 + 6*z^10 + 5*z^9 + 6*z^8 + 12*z^7 + 12*z^5 + 7*z^4 + 6*z^3 + 5*z^2 + 2)*X^19 + (7*z^35 + 4*z^34 + 8*z^33 + 10*z^29 + 6*z^28 + 11*z^27 + 10*z^26 + 7*z^25 + 8*z^24 + 11*z^23 + z^22 + z^21 + 6*z^20 + 4*z^19 + 4*z^18 + 6*z^17 + z^16 + z^15 + 11*z^14 + 8*z^13 + 7*z^12 + 10*z^11 + 11*z^10 + 6*z^9 + 10*z^8 + 8*z^4 + 4*z^3 + 7*z^2 + 6)*X^18 + (z^35 + 12*z^34 + 10*z^33 + 5*z^32 + 5*z^30 + 11*z^29 + 7*z^28 + 11*z^26 + z^25 + 10*z^24 + 4*z^22 + 4*z^21 + 7*z^20 + 12*z^19 + 12*z^18 + 7*z^17 + 4*z^16 + 4*z^15 + 10*z^13 + z^12 + 11*z^11 + 7*z^9 + 11*z^8 + 5*z^7 + 5*z^5 + 10*z^4 + 12*z^3 + z^2)*X^17 + (9*z^35 + 8*z^33 + 2*z^32 + 2*z^30 + 6*z^29 + z^27 + 6*z^26 + 9*z^25 + 8*z^24 + z^23 + z^22 + z^21 + z^16 + z^15 + z^14 + 8*z^13 + 9*z^12 + 6*z^11 + z^10 + 6*z^8 + 2*z^7 + 2*z^5 + 8*z^4 + 9*z^2 + 4)*X^16 + (2*z^35 + 7*z^34 + 4*z^33 + 3*z^32 + 3*z^30 + 12*z^29 + 6*z^28 + 6*z^27 + 12*z^26 + 2*z^25 + 4*z^24 + 6*z^23 + 5*z^22 + 5*z^21 + 6*z^20 + 7*z^19 + 7*z^18 + 6*z^17 + 5*z^16 + 5*z^15 + 6*z^14 + 4*z^13 + 2*z^12 + 12*z^11 + 6*z^10 + 6*z^9 + 12*z^8 + 3*z^7 + 3*z^5 + 4*z^4 + 7*z^3 + 2*z^2 + 3)*X^15 + (7*z^34 + 2*z^33 + 3*z^32 + 3*z^30 + 6*z^29 + 2*z^28 + 11*z^27 + 6*z^26 + 2*z^24 + 11*z^23 + 12*z^22 + 12*z^21 + 2*z^20 + 7*z^19 + 7*z^18 + 2*z^17 + 12*z^16 + 12*z^15 + 11*z^14 + 2*z^13 + 6*z^11 + 11*z^10 + 2*z^9 + 6*z^8 + 3*z^7 + 3*z^5 + 2*z^4 + 7*z^3 + 8)*X^14 + (12*z^35 + 5*z^34 + 9*z^33 + 10*z^32 + 10*z^30 + 8*z^29 + 6*z^28 + 6*z^27 + 8*z^26 + 12*z^25 + 9*z^24 + 6*z^23 + 3*z^22 + 3*z^21 + 6*z^20 + 5*z^19 + 5*z^18 + 6*z^17 + 3*z^16 + 3*z^15 + 6*z^14 + 9*z^13 + 12*z^12 + 8*z^11 + 6*z^10 + 6*z^9 + 8*z^8 + 10*z^7 + 10*z^5 + 9*z^4 + 5*z^3 + 12*z^2 + 12)*X^13 + (2*z^35 + z^34 + 6*z^33 + 4*z^32 + 4*z^30 + 5*z^28 + 2*z^27 + 2*z^25 + 6*z^24 + 2*z^23 + 9*z^22 + 9*z^21 + 5*z^20 + z^19 + z^18 + 5*z^17 + 9*z^16 + 9*z^15 + 2*z^14 + 6*z^13 + 2*z^12 + 2*z^10 + 5*z^9 + 4*z^7 + 4*z^5 + 6*z^4 + z^3 + 2*z^2 + 3)*X^12 + (7*z^35 + 5*z^34 + 2*z^33 + z^32 + z^30 + 10*z^29 + 7*z^28 + 7*z^27 + 10*z^26 + 7*z^25 + 2*z^24 + 7*z^23 + 6*z^22 + 6*z^21 + 7*z^20 + 5*z^19 + 5*z^18 + 7*z^17 + 6*z^16 + 6*z^15 + 7*z^14 + 2*z^13 + 7*z^12 + 10*z^11 + 7*z^10 + 7*z^9 + 10*z^8 + z^7 + z^5 + 2*z^4 + 5*z^3 + 7*z^2 + 11)*X^11 + (8*z^35 + 8*z^34 + 3*z^33 + 11*z^29 + 4*z^28 + 7*z^27 + 11*z^26 + 8*z^25 + 3*z^24 + 7*z^23 + 8*z^22 + 8*z^21 + 4*z^20 + 8*z^19 + 8*z^18 + 4*z^17 + 8*z^16 + 8*z^15 + 7*z^14 + 3*z^13 + 8*z^12 + 11*z^11 + 7*z^10 + 4*z^9 + 11*z^8 + 3*z^4 + 8*z^3 + 8*z^2 + 3)*X^10 + (9*z^35 + 5*z^33 + 11*z^29 + 6*z^28 + 10*z^27 + 11*z^26 + 9*z^25 + 5*z^24 + 10*z^23 + 8*z^22 + 8*z^21 + 6*z^20 + 6*z^17 + 8*z^16 + 8*z^15 + 10*z^14 + 5*z^13 + 9*z^12 + 11*z^11 + 10*z^10 + 6*z^9 + 11*z^8 + 5*z^4 + 9*z^2 + 10)*X^9 + (8*z^35 + 9*z^34 + 9*z^33 + 4*z^32 + 4*z^30 + z^29 + 4*z^28 + 8*z^27 + z^26 + 8*z^25 + 9*z^24 + 8*z^23 + 3*z^22 + 3*z^21 + 4*z^20 + 9*z^19 + 9*z^18 + 4*z^17 + 3*z^16 + 3*z^15 + 8*z^14 + 9*z^13 + 8*z^12 + z^11 + 8*z^10 + 4*z^9 + z^8 + 4*z^7 + 4*z^5 + 9*z^4 + 9*z^3 + 8*z^2 + 12)*X^8 + (11*z^35 + z^34 + 5*z^33 + 9*z^32 + 9*z^30 + 8*z^29 + 4*z^28 + 5*z^27 + 8*z^26 + 11*z^25 + 5*z^24 + 5*z^23 + 10*z^22 + 10*z^21 + 4*z^20 + z^19 + z^18 + 4*z^17 + 10*z^16 + 10*z^15 + 5*z^14 + 5*z^13 + 11*z^12 + 8*z^11 + 5*z^10 + 4*z^9 + 8*z^8 + 9*z^7 + 9*z^5 + 5*z^4 + z^3 + 11*z^2 + 7)*X^7 + (8*z^35 + 12*z^34 + z^33 + 4*z^32 + 4*z^30 + 9*z^29 + 11*z^28 + 9*z^27 + 9*z^26 + 8*z^25 + z^24 + 9*z^23 + 7*z^22 + 7*z^21 + 11*z^20 + 12*z^19 + 12*z^18 + 11*z^17 + 7*z^16 + 7*z^15 + 9*z^14 + z^13 + 8*z^12 + 9*z^11 + 9*z^10 + 11*z^9 + 9*z^8 + 4*z^7 + 4*z^5 + z^4 + 12*z^3 + 8*z^2 + 7)*X^6 + (5*z^34 + 9*z^33 + 2*z^32 + 2*z^30 + z^29 + 12*z^28 + z^27 + z^26 + 9*z^24 + z^23 + 4*z^22 + 4*z^21 + 12*z^20 + 5*z^19 + 5*z^18 + 12*z^17 + 4*z^16 + 4*z^15 + z^14 + 9*z^13 + z^11 + z^10 + 12*z^9 + z^8 + 2*z^7 + 2*z^5 + 9*z^4 + 5*z^3 + 2)*X^5 + (9*z^35 + 11*z^34 + z^33 + 4*z^32 + 4*z^30 + 4*z^29 + 10*z^28 + 2*z^27 + 4*z^26 + 9*z^25 + z^24 + 2*z^23 + 2*z^22 + 2*z^21 + 10*z^20 + 11*z^19 + 11*z^18 + 10*z^17 + 2*z^16 + 2*z^15 + 2*z^14 + z^13 + 9*z^12 + 4*z^11 + 2*z^10 + 10*z^9 + 4*z^8 + 4*z^7 + 4*z^5 + z^4 + 11*z^3 + 9*z^2 + 9)*X^4 + (11*z^35 + 8*z^33 + z^32 + z^30 + 6*z^29 + 5*z^28 + z^27 + 6*z^26 + 11*z^25 + 8*z^24 + z^23 + 9*z^22 + 9*z^21 + 5*z^20 + 5*z^17 + 9*z^16 + 9*z^15 + z^14 + 8*z^13 + 11*z^12 + 6*z^11 + z^10 + 5*z^9 + 6*z^8 + z^7 + z^5 + 8*z^4 + 11*z^2 + 5)*X^3 + (7*z^35 + 9*z^33 + 6*z^32 + 6*z^30 + 2*z^29 + 12*z^28 + 5*z^27 + 2*z^26 + 7*z^25 + 9*z^24 + 5*z^23 + 8*z^22 + 8*z^21 + 12*z^20 + 12*z^17 + 8*z^16 + 8*z^15 + 5*z^14 + 9*z^13 + 7*z^12 + 2*z^11 + 5*z^10 + 12*z^9 + 2*z^8 + 6*z^7 + 6*z^5 + 9*z^4 + 7*z^2 + 9)*X^2 + (9*z^35 + 7*z^34 + 5*z^33 + 9*z^32 + 9*z^30 + 5*z^29 + 11*z^28 + 4*z^27 + 5*z^26 + 9*z^25 + 5*z^24 + 4*z^23 + 3*z^22 + 3*z^21 + 11*z^20 + 7*z^19 + 7*z^18 + 11*z^17 + 3*z^16 + 3*z^15 + 4*z^14 + 5*z^13 + 9*z^12 + 5*z^11 + 4*z^10 + 11*z^9 + 5*z^8 + 9*z^7 + 9*z^5 + 5*z^4 + 7*z^3 + 9*z^2 + 8)*X + 8*z^35 + 6*z^34 + 10*z^32 + 10*z^30 + 8*z^29 + 8*z^28 + 5*z^27 + 8*z^26 + 8*z^25 + 5*z^23 + 7*z^22 + 7*z^21 + 8*z^20 + 6*z^19 + 6*z^18 + 8*z^17 + 7*z^16 + 7*z^15 + 5*z^14 + 8*z^12 + 8*z^11 + 5*z^10 + 8*z^9 + 8*z^8 + 10*z^7 + 10*z^5 + 6*z^3 + 8*z^2 + 6
> tr_alpha;
(8*z^35 + 11*z^34 + 11*z^33 + 10*z^32 + 10*z^30 + 6*z^29 + 5*z^28 + 8*z^27 + 6*z^26 + 8*z^25 + 11*z^24 + 8*z^23 + 11*z^22 + 11*z^21 + 5*z^20 + 11*z^19 + 11*z^18 + 5*z^17 + 11*z^16 + 11*z^15 + 8*z^14 + 11*z^13 + 8*z^12 + 6*z^11 + 8*z^10 + 5*z^9 + 6*z^8 + 10*z^7 + 10*z^5 + 11*z^4 + 11*z^3 + 8*z^2 + 9)*w^34 + (5*z^35 + 12*z^34 + z^33 + 5*z^32 + 5*z^30 + 6*z^29 + 5*z^28 + 9*z^27 + 6*z^26 + 5*z^25 + z^24 + 9*z^23 + 11*z^22 + 11*z^21 + 5*z^20 + 12*z^19 + 12*z^18 + 5*z^17 + 11*z^16 + 11*z^15 + 9*z^14 + z^13 + 5*z^12 + 6*z^11 + 9*z^10 + 5*z^9 + 6*z^8 + 5*z^7 + 5*z^5 + z^4 + 12*z^3 + 5*z^2 + 9)*w^33 + (2*z^35 + 5*z^34 + 2*z^33 + 10*z^32 + 10*z^30 + 6*z^29 + 12*z^28 + z^27 + 6*z^26 + 2*z^25 + 2*z^24 + z^23 + 10*z^22 + 10*z^21 + 12*z^20 + 5*z^19 + 5*z^18 + 12*z^17 + 10*z^16 + 10*z^15 + z^14 + 2*z^13 + 2*z^12 + 6*z^11 + z^10 + 12*z^9 + 6*z^8 + 10*z^7 + 10*z^5 + 2*z^4 + 5*z^3 + 2*z^2 + 9)*w^26 + (2*z^35 + 10*z^34 + 6*z^33 + 9*z^32 + 9*z^30 + 8*z^29 + 6*z^27 + 8*z^26 + 2*z^25 + 6*z^24 + 6*z^23 + 9*z^22 + 9*z^21 + 10*z^19 + 10*z^18 + 9*z^16 + 9*z^15 + 6*z^14 + 6*z^13 + 2*z^12 + 8*z^11 + 6*z^10 + 8*z^8 + 9*z^7 + 9*z^5 + 6*z^4 + 10*z^3 + 2*z^2)*w^16 + (6*z^35 + 6*z^34 + 4*z^33 + z^32 + z^30 + 7*z^29 + z^28 + z^27 + 7*z^26 + 6*z^25 + 4*z^24 + z^23 + z^20 + 6*z^19 + 6*z^18 + z^17 + z^14 + 4*z^13 + 6*z^12 + 7*z^11 + z^10 + z^9 + 7*z^8 + z^7 + z^5 + 4*z^4 + 6*z^3 + 6*z^2 + 3)*w^12 + (z^35 + 4*z^34 + z^33 + 2*z^32 + 2*z^30 + z^29 + 10*z^28 + 10*z^27 + z^26 + z^25 + z^24 + 10*z^23 + 10*z^22 + 10*z^21 + 10*z^20 + 4*z^19 + 4*z^18 + 10*z^17 + 10*z^16 + 10*z^15 + 10*z^14 + z^13 + z^12 + z^11 + 10*z^10 + 10*z^9 + z^8 + 2*z^7 + 2*z^5 + z^4 + 4*z^3 + z^2 + 7)*w^10 + (9*z^35 + 6*z^34 + 4*z^33 + 8*z^32 + 8*z^30 + 4*z^29 + 4*z^28 + 4*z^26 + 9*z^25 + 4*z^24 + 6*z^22 + 6*z^21 + 4*z^20 + 6*z^19 + 6*z^18 + 4*z^17 + 6*z^16 + 6*z^15 + 4*z^13 + 9*z^12 + 4*z^11 + 4*z^9 + 4*z^8 + 8*z^7 + 8*z^5 + 4*z^4 + 6*z^3 + 9*z^2)*w^9 + (3*z^35 + 8*z^34 + 8*z^33 + 6*z^32 + 6*z^30 + 11*z^29 + 2*z^28 + 3*z^27 + 11*z^26 + 3*z^25 + 8*z^24 + 3*z^23 + 7*z^22 + 7*z^21 + 2*z^20 + 8*z^19 + 8*z^18 + 2*z^17 + 7*z^16 + 7*z^15 + 3*z^14 + 8*z^13 + 3*z^12 + 11*z^11 + 3*z^10 + 2*z^9 + 11*z^8 + 6*z^7 + 6*z^5 + 8*z^4 + 8*z^3 + 3*z^2 + 11)*w^7 + 4*w
> &+[Coefficient(f,i)*tr_alpha^i : i in [0..37]];
0
> &+[del(Coefficient(f,i))*tr_alpha^i : i in [0..37]];
(10*z^35 + 11*z^34 + 7*z^33 + 3*z^32 + 3*z^30 + 4*z^29 + 4*z^28 + 5*z^27 + 4*z^26 + 10*z^25 + 7*z^24 + 5*z^23 + 2*z^22 + 2*z^21 + 4*z^20 + 11*z^19 + 11*z^18 + 4*z^17 + 2*z^16 + 2*z^15 + 5*z^14 + 7*z^13 + 10*z^12 + 4*z^11 + 5*z^10 + 4*z^9 + 4*z^8 + 3*z^7 + 3*z^5 + 7*z^4 + 11*z^3 + 10*z^2 + 11)*w^36 + (7*z^35 + 7*z^34 + 7*z^33 + 8*z^32 + 8*z^30 + z^29 + 12*z^28 + 11*z^27 + z^26 + 7*z^25 + 7*z^24 + 11*z^23 + 12*z^22 + 12*z^21 + 12*z^20 + 7*z^19 + 7*z^18 + 12*z^17 + 12*z^16 + 12*z^15 + 11*z^14 + 7*z^13 + 7*z^12 + z^11 + 11*z^10 + 12*z^9 + z^8 + 8*z^7 + 8*z^5 + 7*z^4 + 7*z^3 + 7*z^2 + 10)*w^35 + (6*z^35 + z^33 + 9*z^32 + 9*z^30 + 6*z^29 + 3*z^28 + z^27 + 6*z^26 + 6*z^25 + z^24 + z^23 + 4*z^22 + 4*z^21 + 3*z^20 + 3*z^17 + 4*z^16 + 4*z^15 + z^14 + z^13 + 6*z^12 + 6*z^11 + z^10 + 3*z^9 + 6*z^8 + 9*z^7 + 9*z^5 + z^4 + 6*z^2 + 7)*w^34 + (11*z^35 + z^34 + 3*z^33 + 10*z^32 + 10*z^30 + 9*z^29 + z^28 + 9*z^26 + 11*z^25 + 3*z^24 + 11*z^22 + 11*z^21 + z^20 + z^19 + z^18 + z^17 + 11*z^16 + 11*z^15 + 3*z^13 + 11*z^12 + 9*z^11 + z^9 + 9*z^8 + 10*z^7 + 10*z^5 + 3*z^4 + z^3 + 11*z^2 + 9)*w^33 + (6*z^35 + 5*z^34 + 8*z^33 + 4*z^32 + 4*z^30 + 11*z^29 + 11*z^28 + 9*z^27 + 11*z^26 + 6*z^25 + 8*z^24 + 9*z^23 + 12*z^22 + 12*z^21 + 11*z^20 + 5*z^19 + 5*z^18 + 11*z^17 + 12*z^16 + 12*z^15 + 9*z^14 + 8*z^13 + 6*z^12 + 11*z^11 + 9*z^10 + 11*z^9 + 11*z^8 + 4*z^7 + 4*z^5 + 8*z^4 + 5*z^3 + 6*z^2 + 8)*w^32 + (6*z^35 + z^33 + 5*z^32 + 5*z^30 + 12*z^29 + 7*z^28 + 2*z^27 + 12*z^26 + 6*z^25 + z^24 + 2*z^23 + 4*z^22 + 4*z^21 + 7*z^20 + 7*z^17 + 4*z^16 + 4*z^15 + 2*z^14 + z^13 + 6*z^12 + 12*z^11 + 2*z^10 + 7*z^9 + 12*z^8 + 5*z^7 + 5*z^5 + z^4 + 6*z^2 + 5)*w^31 + (z^34 + 5*z^33 + z^32 + z^30 + 6*z^29 + 4*z^28 + 11*z^27 + 6*z^26 + 5*z^24 + 11*z^23 + 11*z^22 + 11*z^21 + 4*z^20 + z^19 + z^18 + 4*z^17 + 11*z^16 + 11*z^15 + 11*z^14 + 5*z^13 + 6*z^11 + 11*z^10 + 4*z^9 + 6*z^8 + z^7 + z^5 + 5*z^4 + z^3 + 6)*w^30 + (2*z^35 + 9*z^34 + 4*z^33 + 12*z^32 + 12*z^30 + 7*z^28 + 3*z^27 + 2*z^25 + 4*z^24 + 3*z^23 + 7*z^20 + 9*z^19 + 9*z^18 + 7*z^17 + 3*z^14 + 4*z^13 + 2*z^12 + 3*z^10 + 7*z^9 + 12*z^7 + 12*z^5 + 4*z^4 + 9*z^3 + 2*z^2 + 1)*w^29 + (4*z^35 + z^34 + 10*z^33 + 4*z^32 + 4*z^30 + 6*z^29 + 2*z^28 + 8*z^27 + 6*z^26 + 4*z^25 + 10*z^24 + 8*z^23 + 2*z^22 + 2*z^21 + 2*z^20 + z^19 + z^18 + 2*z^17 + 2*z^16 + 2*z^15 + 8*z^14 + 10*z^13 + 4*z^12 + 6*z^11 + 8*z^10 + 2*z^9 + 6*z^8 + 4*z^7 + 4*z^5 + 10*z^4 + z^3 + 4*z^2 + 7)*w^28 + (4*z^35 + 2*z^34 + 11*z^32 + 11*z^30 + 3*z^29 + z^28 + 12*z^27 + 3*z^26 + 4*z^25 + 12*z^23 + 7*z^22 + 7*z^21 + z^20 + 2*z^19 + 2*z^18 + z^17 + 7*z^16 + 7*z^15 + 12*z^14 + 4*z^12 + 3*z^11 + 12*z^10 + z^9 + 3*z^8 + 11*z^7 + 11*z^5 + 2*z^3 + 4*z^2 + 2)*w^27 + (4*z^35 + 8*z^34 + 5*z^33 + 2*z^32 + 2*z^30 + 11*z^29 + 4*z^28 + 3*z^27 + 11*z^26 + 4*z^25 + 5*z^24 + 3*z^23 + 2*z^22 + 2*z^21 + 4*z^20 + 8*z^19 + 8*z^18 + 4*z^17 + 2*z^16 + 2*z^15 + 3*z^14 + 5*z^13 + 4*z^12 + 11*z^11 + 3*z^10 + 4*z^9 + 11*z^8 + 2*z^7 + 2*z^5 + 5*z^4 + 8*z^3 + 4*z^2 + 7)*w^26 + (11*z^35 + 11*z^34 + 4*z^33 + 4*z^32 + 4*z^30 + 11*z^29 + 5*z^28 + 11*z^27 + 11*z^26 + 11*z^25 + 4*z^24 + 11*z^23 + 5*z^22 + 5*z^21 + 5*z^20 + 11*z^19 + 11*z^18 + 5*z^17 + 5*z^16 + 5*z^15 + 11*z^14 + 4*z^13 + 11*z^12 + 11*z^11 + 11*z^10 + 5*z^9 + 11*z^8 + 4*z^7 + 4*z^5 + 4*z^4 + 11*z^3 + 11*z^2)*w^25 + (9*z^35 + 12*z^32 + 12*z^30 + 5*z^29 + 11*z^28 + 11*z^27 + 5*z^26 + 9*z^25 + 11*z^23 + 3*z^22 + 3*z^21 + 11*z^20 + 11*z^17 + 3*z^16 + 3*z^15 + 11*z^14 + 9*z^12 + 5*z^11 + 11*z^10 + 11*z^9 + 5*z^8 + 12*z^7 + 12*z^5 + 9*z^2 + 8)*w^24 + (3*z^35 + 12*z^34 + 7*z^33 + z^29 + 11*z^28 + z^26 + 3*z^25 + 7*z^24 + 8*z^22 + 8*z^21 + 11*z^20 + 12*z^19 + 12*z^18 + 11*z^17 + 8*z^16 + 8*z^15 + 7*z^13 + 3*z^12 + z^11 + 11*z^9 + z^8 + 7*z^4 + 12*z^3 + 3*z^2)*w^23 + (z^35 + z^34 + 2*z^33 + 7*z^32 + 7*z^30 + 11*z^29 + 6*z^28 + 9*z^27 + 11*z^26 + z^25 + 2*z^24 + 9*z^23 + 8*z^22 + 8*z^21 + 6*z^20 + z^19 + z^18 + 6*z^17 + 8*z^16 + 8*z^15 + 9*z^14 + 2*z^13 + z^12 + 11*z^11 + 9*z^10 + 6*z^9 + 11*z^8 + 7*z^7 + 7*z^5 + 2*z^4 + z^3 + z^2 + 1)*w^22 + (5*z^35 + 10*z^34 + 4*z^33 + 8*z^32 + 8*z^30 + 6*z^29 + 11*z^28 + 6*z^27 + 6*z^26 + 5*z^25 + 4*z^24 + 6*z^23 + 4*z^22 + 4*z^21 + 11*z^20 + 10*z^19 + 10*z^18 + 11*z^17 + 4*z^16 + 4*z^15 + 6*z^14 + 4*z^13 + 5*z^12 + 6*z^11 + 6*z^10 + 11*z^9 + 6*z^8 + 8*z^7 + 8*z^5 + 4*z^4 + 10*z^3 + 5*z^2 + 2)*w^21 + (11*z^35 + 6*z^34 + 10*z^33 + 6*z^32 + 6*z^30 + 9*z^29 + 8*z^28 + 6*z^27 + 9*z^26 + 11*z^25 + 10*z^24 + 6*z^23 + z^22 + z^21 + 8*z^20 + 6*z^19 + 6*z^18 + 8*z^17 + z^16 + z^15 + 6*z^14 + 10*z^13 + 11*z^12 + 9*z^11 + 6*z^10 + 8*z^9 + 9*z^8 + 6*z^7 + 6*z^5 + 10*z^4 + 6*z^3 + 11*z^2 + 11)*w^20 + (z^34 + z^33 + 4*z^32 + 4*z^30 + 11*z^29 + 5*z^28 + 11*z^26 + z^24 + 7*z^22 + 7*z^21 + 5*z^20 + z^19 + z^18 + 5*z^17 + 7*z^16 + 7*z^15 + z^13 + 11*z^11 + 5*z^9 + 11*z^8 + 4*z^7 + 4*z^5 + z^4 + z^3 + 1)*w^19 + (10*z^35 + 4*z^34 + z^33 + 2*z^32 + 2*z^30 + 9*z^29 + 6*z^28 + 2*z^27 + 9*z^26 + 10*z^25 + z^24 + 2*z^23 + 10*z^22 + 10*z^21 + 6*z^20 + 4*z^19 + 4*z^18 + 6*z^17 + 10*z^16 + 10*z^15 + 2*z^14 + z^13 + 10*z^12 + 9*z^11 + 2*z^10 + 6*z^9 + 9*z^8 + 2*z^7 + 2*z^5 + z^4 + 4*z^3 + 10*z^2 + 6)*w^18 + (4*z^35 + 2*z^34 + 6*z^33 + 10*z^32 + 10*z^30 + 9*z^29 + 5*z^28 + 2*z^27 + 9*z^26 + 4*z^25 + 6*z^24 + 2*z^23 + 9*z^22 + 9*z^21 + 5*z^20 + 2*z^19 + 2*z^18 + 5*z^17 + 9*z^16 + 9*z^15 + 2*z^14 + 6*z^13 + 4*z^12 + 9*z^11 + 2*z^10 + 5*z^9 + 9*z^8 + 10*z^7 + 10*z^5 + 6*z^4 + 2*z^3 + 4*z^2 + 12)*w^17 + (z^35 + 8*z^34 + 3*z^33 + 12*z^32 + 12*z^30 + 12*z^29 + 9*z^28 + 5*z^27 + 12*z^26 + z^25 + 3*z^24 + 5*z^23 + 8*z^22 + 8*z^21 + 9*z^20 + 8*z^19 + 8*z^18 + 9*z^17 + 8*z^16 + 8*z^15 + 5*z^14 + 3*z^13 + z^12 + 12*z^11 + 5*z^10 + 9*z^9 + 12*z^8 + 12*z^7 + 12*z^5 + 3*z^4 + 8*z^3 + z^2 + 5)*w^16 + (6*z^35 + 8*z^34 + z^33 + 11*z^32 + 11*z^30 + 8*z^29 + z^28 + z^27 + 8*z^26 + 6*z^25 + z^24 + z^23 + 2*z^22 + 2*z^21 + z^20 + 8*z^19 + 8*z^18 + z^17 + 2*z^16 + 2*z^15 + z^14 + z^13 + 6*z^12 + 8*z^11 + z^10 + z^9 + 8*z^8 + 11*z^7 + 11*z^5 + z^4 + 8*z^3 + 6*z^2 + 6)*w^15 + (10*z^35 + 7*z^34 + 7*z^33 + 5*z^32 + 5*z^30 + 3*z^29 + 9*z^28 + 2*z^27 + 3*z^26 + 10*z^25 + 7*z^24 + 2*z^23 + 6*z^22 + 6*z^21 + 9*z^20 + 7*z^19 + 7*z^18 + 9*z^17 + 6*z^16 + 6*z^15 + 2*z^14 + 7*z^13 + 10*z^12 + 3*z^11 + 2*z^10 + 9*z^9 + 3*z^8 + 5*z^7 + 5*z^5 + 7*z^4 + 7*z^3 + 10*z^2 + 6)*w^14 + (10*z^35 + z^34 + 12*z^33 + 8*z^32 + 8*z^30 + 8*z^29 + 3*z^28 + 8*z^26 + 10*z^25 + 12*z^24 + 10*z^22 + 10*z^21 + 3*z^20 + z^19 + z^18 + 3*z^17 + 10*z^16 + 10*z^15 + 12*z^13 + 10*z^12 + 8*z^11 + 3*z^9 + 8*z^8 + 8*z^7 + 8*z^5 + 12*z^4 + z^3 + 10*z^2 + 11)*w^13 + (5*z^34 + z^33 + 4*z^32 + 4*z^30 + 4*z^29 + 9*z^28 + 9*z^27 + 4*z^26 + z^24 + 9*z^23 + 2*z^22 + 2*z^21 + 9*z^20 + 5*z^19 + 5*z^18 + 9*z^17 + 2*z^16 + 2*z^15 + 9*z^14 + z^13 + 4*z^11 + 9*z^10 + 9*z^9 + 4*z^8 + 4*z^7 + 4*z^5 + z^4 + 5*z^3 + 10)*w^12 + (6*z^35 + 8*z^34 + 7*z^33 + 6*z^32 + 6*z^30 + 11*z^29 + 8*z^28 + 10*z^27 + 11*z^26 + 6*z^25 + 7*z^24 + 10*z^23 + z^22 + z^21 + 8*z^20 + 8*z^19 + 8*z^18 + 8*z^17 + z^16 + z^15 + 10*z^14 + 7*z^13 + 6*z^12 + 11*z^11 + 10*z^10 + 8*z^9 + 11*z^8 + 6*z^7 + 6*z^5 + 7*z^4 + 8*z^3 + 6*z^2 + 1)*w^11 + (3*z^35 + 11*z^34 + 2*z^33 + 10*z^32 + 10*z^30 + 7*z^29 + 11*z^28 + 6*z^27 + 7*z^26 + 3*z^25 + 2*z^24 + 6*z^23 + 11*z^20 + 11*z^19 + 11*z^18 + 11*z^17 + 6*z^14 + 2*z^13 + 3*z^12 + 7*z^11 + 6*z^10 + 11*z^9 + 7*z^8 + 10*z^7 + 10*z^5 + 2*z^4 + 11*z^3 + 3*z^2 + 3)*w^10 + (10*z^35 + 12*z^34 + 6*z^33 + 8*z^29 + z^28 + z^27 + 8*z^26 + 10*z^25 + 6*z^24 + z^23 + 12*z^22 + 12*z^21 + z^20 + 12*z^19 + 12*z^18 + z^17 + 12*z^16 + 12*z^15 + z^14 + 6*z^13 + 10*z^12 + 8*z^11 + z^10 + z^9 + 8*z^8 + 6*z^4 + 12*z^3 + 10*z^2 + 3)*w^9 + (5*z^35 + 10*z^34 + 7*z^32 + 7*z^30 + 3*z^29 + 4*z^28 + 10*z^27 + 3*z^26 + 5*z^25 + 10*z^23 + 3*z^22 + 3*z^21 + 4*z^20 + 10*z^19 + 10*z^18 + 4*z^17 + 3*z^16 + 3*z^15 + 10*z^14 + 5*z^12 + 3*z^11 + 10*z^10 + 4*z^9 + 3*z^8 + 7*z^7 + 7*z^5 + 10*z^3 + 5*z^2 + 8)*w^8 + (12*z^35 + 11*z^34 + 5*z^33 + 9*z^32 + 9*z^30 + 8*z^29 + 10*z^28 + z^27 + 8*z^26 + 12*z^25 + 5*z^24 + z^23 + 6*z^22 + 6*z^21 + 10*z^20 + 11*z^19 + 11*z^18 + 10*z^17 + 6*z^16 + 6*z^15 + z^14 + 5*z^13 + 12*z^12 + 8*z^11 + z^10 + 10*z^9 + 8*z^8 + 9*z^7 + 9*z^5 + 5*z^4 + 11*z^3 + 12*z^2 + 7)*w^7 + (6*z^35 + 9*z^33 + 7*z^32 + 7*z^30 + 8*z^29 + 11*z^28 + 9*z^27 + 8*z^26 + 6*z^25 + 9*z^24 + 9*z^23 + 9*z^22 + 9*z^21 + 11*z^20 + 11*z^17 + 9*z^16 + 9*z^15 + 9*z^14 + 9*z^13 + 6*z^12 + 8*z^11 + 9*z^10 + 11*z^9 + 8*z^8 + 7*z^7 + 7*z^5 + 9*z^4 + 6*z^2 + 10)*w^6 + (11*z^35 + 11*z^34 + 7*z^33 + 3*z^32 + 3*z^30 + 12*z^29 + z^28 + 3*z^27 + 12*z^26 + 11*z^25 + 7*z^24 + 3*z^23 + z^20 + 11*z^19 + 11*z^18 + z^17 + 3*z^14 + 7*z^13 + 11*z^12 + 12*z^11 + 3*z^10 + z^9 + 12*z^8 + 3*z^7 + 3*z^5 + 7*z^4 + 11*z^3 + 11*z^2 + 3)*w^5 + (4*z^35 + 4*z^34 + 8*z^33 + 4*z^32 + 4*z^30 + 9*z^29 + 7*z^28 + 11*z^27 + 9*z^26 + 4*z^25 + 8*z^24 + 11*z^23 + 10*z^22 + 10*z^21 + 7*z^20 + 4*z^19 + 4*z^18 + 7*z^17 + 10*z^16 + 10*z^15 + 11*z^14 + 8*z^13 + 4*z^12 + 9*z^11 + 11*z^10 + 7*z^9 + 9*z^8 + 4*z^7 + 4*z^5 + 8*z^4 + 4*z^3 + 4*z^2 + 8)*w^4 + (3*z^35 + 8*z^34 + 12*z^33 + 10*z^32 + 10*z^30 + 6*z^29 + 5*z^28 + z^27 + 6*z^26 + 3*z^25 + 12*z^24 + z^23 + 6*z^22 + 6*z^21 + 5*z^20 + 8*z^19 + 8*z^18 + 5*z^17 + 6*z^16 + 6*z^15 + z^14 + 12*z^13 + 3*z^12 + 6*z^11 + z^10 + 5*z^9 + 6*z^8 + 10*z^7 + 10*z^5 + 12*z^4 + 8*z^3 + 3*z^2 + 7)*w^3 + (9*z^35 + 8*z^33 + 2*z^32 + 2*z^30 + 7*z^29 + 2*z^27 + 7*z^26 + 9*z^25 + 8*z^24 + 2*z^23 + 10*z^22 + 10*z^21 + 10*z^16 + 10*z^15 + 2*z^14 + 8*z^13 + 9*z^12 + 7*z^11 + 2*z^10 + 7*z^8 + 2*z^7 + 2*z^5 + 8*z^4 + 9*z^2 + 5)*w^2 + (5*z^35 + 7*z^34 + 4*z^33 + 8*z^32 + 8*z^30 + 11*z^28 + 5*z^27 + 5*z^25 + 4*z^24 + 5*z^23 + 7*z^22 + 7*z^21 + 11*z^20 + 7*z^19 + 7*z^18 + 11*z^17 + 7*z^16 + 7*z^15 + 5*z^14 + 4*z^13 + 5*z^12 + 5*z^10 + 11*z^9 + 8*z^7 + 8*z^5 + 4*z^4 + 7*z^3 + 5*z^2 + 3)*w + 3*z^35 + 3*z^34 + z^33 + 6*z^32 + 6*z^30 + 7*z^29 + 12*z^28 + 10*z^27 + 7*z^26 + 3*z^25 + z^24 + 10*z^23 + z^22 + z^21 + 12*z^20 + 3*z^19 + 3*z^18 + 12*z^17 + z^16 + z^15 + 10*z^14 + z^13 + 3*z^12 + 7*z^11 + 10*z^10 + 12*z^9 + 7*z^8 + 6*z^7 + 6*z^5 + z^4 + 3*z^3 + 3*z^2 + 12
> &+[del(Coefficient(f,i)*tr_alpha^i) : i in [0..37]];
0
> &+[del(Coefficient(f,i))*del(tr_alpha^i) : i in [0..37]];
0
> del(tr_alpha) - tr_alpha;
0
> del(tr_alpha^2) - tr_alpha^2;
(9*z^35 + 9*z^33 + z^32 + z^30 + 2*z^29 + 2*z^28 + 6*z^27 + 2*z^26 + 9*z^25 + 9*z^24 + 6*z^23 + 4*z^22 + 4*z^21 + 2*z^20 + 2*z^17 + 4*z^16 + 4*z^15 + 6*z^14 + 9*z^13 + 9*z^12 + 2*z^11 + 6*z^10 + 2*z^9 + 2*z^8 + z^7 + z^5 + 9*z^4 + 9*z^2 + 11)*w^35 + (3*z^35 + 5*z^34 + 11*z^33 + 6*z^32 + 6*z^30 + z^29 + z^28 + 9*z^27 + z^26 + 3*z^25 + 11*z^24 + 9*z^23 + z^20 + 5*z^19 + 5*z^18 + z^17 + 9*z^14 + 11*z^13 + 3*z^12 + z^11 + 9*z^10 + z^9 + z^8 + 6*z^7 + 6*z^5 + 11*z^4 + 5*z^3 + 3*z^2 + 12)*w^32 + (10*z^35 + 12*z^34 + z^33 + 11*z^32 + 11*z^30 + 3*z^29 + 5*z^28 + 8*z^27 + 3*z^26 + 10*z^25 + z^24 + 8*z^23 + z^22 + z^21 + 5*z^20 + 12*z^19 + 12*z^18 + 5*z^17 + z^16 + z^15 + 8*z^14 + z^13 + 10*z^12 + 3*z^11 + 8*z^10 + 5*z^9 + 3*z^8 + 11*z^7 + 11*z^5 + z^4 + 12*z^3 + 10*z^2 + 2)*w^31 + (8*z^35 + 6*z^34 + 5*z^32 + 5*z^30 + 7*z^29 + 5*z^28 + 5*z^27 + 7*z^26 + 8*z^25 + 5*z^23 + 3*z^22 + 3*z^21 + 5*z^20 + 6*z^19 + 6*z^18 + 5*z^17 + 3*z^16 + 3*z^15 + 5*z^14 + 8*z^12 + 7*z^11 + 5*z^10 + 5*z^9 + 7*z^8 + 5*z^7 + 5*z^5 + 6*z^3 + 8*z^2 + 9)*w^30 + (5*z^35 + 11*z^34 + 9*z^33 + z^32 + z^30 + 5*z^29 + 4*z^28 + 12*z^27 + 5*z^26 + 5*z^25 + 9*z^24 + 12*z^23 + 11*z^22 + 11*z^21 + 4*z^20 + 11*z^19 + 11*z^18 + 4*z^17 + 11*z^16 + 11*z^15 + 12*z^14 + 9*z^13 + 5*z^12 + 5*z^11 + 12*z^10 + 4*z^9 + 5*z^8 + z^7 + z^5 + 9*z^4 + 11*z^3 + 5*z^2 + 12)*w^29 + (5*z^34 + 3*z^33 + 3*z^32 + 3*z^30 + 5*z^29 + 9*z^28 + 10*z^27 + 5*z^26 + 3*z^24 + 10*z^23 + 2*z^22 + 2*z^21 + 9*z^20 + 5*z^19 + 5*z^18 + 9*z^17 + 2*z^16 + 2*z^15 + 10*z^14 + 3*z^13 + 5*z^11 + 10*z^10 + 9*z^9 + 5*z^8 + 3*z^7 + 3*z^5 + 3*z^4 + 5*z^3 + 12)*w^28 + (8*z^35 + 4*z^34 + 7*z^33 + 7*z^32 + 7*z^30 + 12*z^29 + 12*z^28 + 6*z^27 + 12*z^26 + 8*z^25 + 7*z^24 + 6*z^23 + 2*z^22 + 2*z^21 + 12*z^20 + 4*z^19 + 4*z^18 + 12*z^17 + 2*z^16 + 2*z^15 + 6*z^14 + 7*z^13 + 8*z^12 + 12*z^11 + 6*z^10 + 12*z^9 + 12*z^8 + 7*z^7 + 7*z^5 + 7*z^4 + 4*z^3 + 8*z^2 + 3)*w^26 + (8*z^34 + 11*z^33 + 2*z^32 + 2*z^30 + 5*z^29 + 5*z^28 + 4*z^27 + 5*z^26 + 11*z^24 + 4*z^23 + 3*z^22 + 3*z^21 + 5*z^20 + 8*z^19 + 8*z^18 + 5*z^17 + 3*z^16 + 3*z^15 + 4*z^14 + 11*z^13 + 5*z^11 + 4*z^10 + 5*z^9 + 5*z^8 + 2*z^7 + 2*z^5 + 11*z^4 + 8*z^3 + 10)*w^25 + (10*z^35 + 2*z^34 + z^33 + 2*z^32 + 2*z^30 + 9*z^29 + 8*z^28 + 10*z^27 + 9*z^26 + 10*z^25 + z^24 + 10*z^23 + 3*z^22 + 3*z^21 + 8*z^20 + 2*z^19 + 2*z^18 + 8*z^17 + 3*z^16 + 3*z^15 + 10*z^14 + z^13 + 10*z^12 + 9*z^11 + 10*z^10 + 8*z^9 + 9*z^8 + 2*z^7 + 2*z^5 + z^4 + 2*z^3 + 10*z^2 + 4)*w^23 + (2*z^35 + 3*z^34 + 6*z^32 + 6*z^30 + 5*z^29 + 4*z^28 + 9*z^27 + 5*z^26 + 2*z^25 + 9*z^23 + 3*z^22 + 3*z^21 + 4*z^20 + 3*z^19 + 3*z^18 + 4*z^17 + 3*z^16 + 3*z^15 + 9*z^14 + 2*z^12 + 5*z^11 + 9*z^10 + 4*z^9 + 5*z^8 + 6*z^7 + 6*z^5 + 3*z^3 + 2*z^2)*w^22 + (z^35 + 6*z^34 + 9*z^33 + 6*z^32 + 6*z^30 + 5*z^28 + 3*z^27 + z^25 + 9*z^24 + 3*z^23 + 10*z^22 + 10*z^21 + 5*z^20 + 6*z^19 + 6*z^18 + 5*z^17 + 10*z^16 + 10*z^15 + 3*z^14 + 9*z^13 + z^12 + 3*z^10 + 5*z^9 + 6*z^7 + 6*z^5 + 9*z^4 + 6*z^3 + z^2 + 6)*w^21 + (2*z^34 + 12*z^33 + 10*z^32 + 10*z^30 + 12*z^29 + 4*z^28 + 5*z^27 + 12*z^26 + 12*z^24 + 5*z^23 + 4*z^22 + 4*z^21 + 4*z^20 + 2*z^19 + 2*z^18 + 4*z^17 + 4*z^16 + 4*z^15 + 5*z^14 + 12*z^13 + 12*z^11 + 5*z^10 + 4*z^9 + 12*z^8 + 10*z^7 + 10*z^5 + 12*z^4 + 2*z^3 + 2)*w^19 + (10*z^35 + 9*z^33 + 2*z^32 + 2*z^30 + 2*z^29 + 8*z^28 + 8*z^27 + 2*z^26 + 10*z^25 + 9*z^24 + 8*z^23 + 3*z^22 + 3*z^21 + 8*z^20 + 8*z^17 + 3*z^16 + 3*z^15 + 8*z^14 + 9*z^13 + 10*z^12 + 2*z^11 + 8*z^10 + 8*z^9 + 2*z^8 + 2*z^7 + 2*z^5 + 9*z^4 + 10*z^2 + 7)*w^18 + (11*z^35 + 10*z^33 + 7*z^32 + 7*z^30 + 4*z^29 + 11*z^28 + 4*z^26 + 11*z^25 + 10*z^24 + 4*z^22 + 4*z^21 + 11*z^20 + 11*z^17 + 4*z^16 + 4*z^15 + 10*z^13 + 11*z^12 + 4*z^11 + 11*z^9 + 4*z^8 + 7*z^7 + 7*z^5 + 10*z^4 + 11*z^2 + 1)*w^17 + (9*z^35 + 3*z^34 + 9*z^33 + 6*z^32 + 6*z^30 + z^29 + 4*z^28 + 2*z^27 + z^26 + 9*z^25 + 9*z^24 + 2*z^23 + 6*z^22 + 6*z^21 + 4*z^20 + 3*z^19 + 3*z^18 + 4*z^17 + 6*z^16 + 6*z^15 + 2*z^14 + 9*z^13 + 9*z^12 + z^11 + 2*z^10 + 4*z^9 + z^8 + 6*z^7 + 6*z^5 + 9*z^4 + 3*z^3 + 9*z^2 + 3)*w^15 + (12*z^35 + 9*z^34 + z^33 + 4*z^32 + 4*z^30 + 5*z^29 + 7*z^28 + 11*z^27 + 5*z^26 + 12*z^25 + z^24 + 11*z^23 + 12*z^22 + 12*z^21 + 7*z^20 + 9*z^19 + 9*z^18 + 7*z^17 + 12*z^16 + 12*z^15 + 11*z^14 + z^13 + 12*z^12 + 5*z^11 + 11*z^10 + 7*z^9 + 5*z^8 + 4*z^7 + 4*z^5 + z^4 + 9*z^3 + 12*z^2 + 1)*w^13 + (12*z^35 + 8*z^34 + 8*z^33 + 4*z^32 + 4*z^30 + 2*z^29 + 9*z^28 + 7*z^27 + 2*z^26 + 12*z^25 + 8*z^24 + 7*z^23 + 10*z^22 + 10*z^21 + 9*z^20 + 8*z^19 + 8*z^18 + 9*z^17 + 10*z^16 + 10*z^15 + 7*z^14 + 8*z^13 + 12*z^12 + 2*z^11 + 7*z^10 + 9*z^9 + 2*z^8 + 4*z^7 + 4*z^5 + 8*z^4 + 8*z^3 + 12*z^2 + 1)*w^12 + (12*z^35 + 4*z^34 + 12*z^33 + z^32 + z^30 + 7*z^29 + 6*z^28 + 2*z^27 + 7*z^26 + 12*z^25 + 12*z^24 + 2*z^23 + 11*z^22 + 11*z^21 + 6*z^20 + 4*z^19 + 4*z^18 + 6*z^17 + 11*z^16 + 11*z^15 + 2*z^14 + 12*z^13 + 12*z^12 + 7*z^11 + 2*z^10 + 6*z^9 + 7*z^8 + z^7 + z^5 + 12*z^4 + 4*z^3 + 12*z^2 + 1)*w^10 + (5*z^34 + 8*z^32 + 8*z^30 + 3*z^29 + 2*z^28 + 10*z^27 + 3*z^26 + 10*z^23 + 2*z^22 + 2*z^21 + 2*z^20 + 5*z^19 + 5*z^18 + 2*z^17 + 2*z^16 + 2*z^15 + 10*z^14 + 3*z^11 + 10*z^10 + 2*z^9 + 3*z^8 + 8*z^7 + 8*z^5 + 5*z^3 + 1)*w^9 + (8*z^35 + 2*z^33 + 6*z^32 + 6*z^30 + z^29 + 4*z^28 + z^26 + 8*z^25 + 2*z^24 + 3*z^22 + 3*z^21 + 4*z^20 + 4*z^17 + 3*z^16 + 3*z^15 + 2*z^13 + 8*z^12 + z^11 + 4*z^9 + z^8 + 6*z^7 + 6*z^5 + 2*z^4 + 8*z^2)*w^8 + (8*z^35 + 9*z^34 + 9*z^33 + 11*z^32 + 11*z^30 + 2*z^29 + 4*z^28 + 3*z^27 + 2*z^26 + 8*z^25 + 9*z^24 + 3*z^23 + 10*z^22 + 10*z^21 + 4*z^20 + 9*z^19 + 9*z^18 + 4*z^17 + 10*z^16 + 10*z^15 + 3*z^14 + 9*z^13 + 8*z^12 + 2*z^11 + 3*z^10 + 4*z^9 + 2*z^8 + 11*z^7 + 11*z^5 + 9*z^4 + 9*z^3 + 8*z^2 + 5)*w^7 + (z^35 + 3*z^33 + 6*z^32 + 6*z^30 + 9*z^29 + 12*z^28 + 9*z^27 + 9*z^26 + z^25 + 3*z^24 + 9*z^23 + 5*z^22 + 5*z^21 + 12*z^20 + 12*z^17 + 5*z^16 + 5*z^15 + 9*z^14 + 3*z^13 + z^12 + 9*z^11 + 9*z^10 + 12*z^9 + 9*z^8 + 6*z^7 + 6*z^5 + 3*z^4 + z^2 + 1)*w^6 + (5*z^34 + 9*z^33 + 8*z^32 + 8*z^30 + 7*z^29 + 9*z^28 + 12*z^27 + 7*z^26 + 9*z^24 + 12*z^23 + 7*z^22 + 7*z^21 + 9*z^20 + 5*z^19 + 5*z^18 + 9*z^17 + 7*z^16 + 7*z^15 + 12*z^14 + 9*z^13 + 7*z^11 + 12*z^10 + 9*z^9 + 7*z^8 + 8*z^7 + 8*z^5 + 9*z^4 + 5*z^3 + 7)*w^5 + (8*z^35 + 6*z^34 + 12*z^33 + 12*z^32 + 12*z^30 + 9*z^29 + 5*z^27 + 9*z^26 + 8*z^25 + 12*z^24 + 5*z^23 + 5*z^22 + 5*z^21 + 6*z^19 + 6*z^18 + 5*z^16 + 5*z^15 + 5*z^14 + 12*z^13 + 8*z^12 + 9*z^11 + 5*z^10 + 9*z^8 + 12*z^7 + 12*z^5 + 12*z^4 + 6*z^3 + 8*z^2 + 3)*w^4 + (12*z^35 + 9*z^34 + z^33 + 12*z^32 + 12*z^30 + 2*z^29 + z^28 + 5*z^27 + 2*z^26 + 12*z^25 + z^24 + 5*z^23 + 7*z^22 + 7*z^21 + z^20 + 9*z^19 + 9*z^18 + z^17 + 7*z^16 + 7*z^15 + 5*z^14 + z^13 + 12*z^12 + 2*z^11 + 5*z^10 + z^9 + 2*z^8 + 12*z^7 + 12*z^5 + z^4 + 9*z^3 + 12*z^2 + 8)*w^3 + (3*z^35 + 2*z^34 + 8*z^33 + 11*z^32 + 11*z^30 + 4*z^29 + 5*z^28 + 6*z^27 + 4*z^26 + 3*z^25 + 8*z^24 + 6*z^23 + 5*z^22 + 5*z^21 + 5*z^20 + 2*z^19 + 2*z^18 + 5*z^17 + 5*z^16 + 5*z^15 + 6*z^14 + 8*z^13 + 3*z^12 + 4*z^11 + 6*z^10 + 5*z^9 + 4*z^8 + 11*z^7 + 11*z^5 + 8*z^4 + 2*z^3 + 3*z^2 + 3)*w
> del(tr_alpha)*del(tr_alpha) - del(tr_alpha^2);
(4*z^35 + 4*z^33 + 12*z^32 + 12*z^30 + 11*z^29 + 11*z^28 + 7*z^27 + 11*z^26 + 4*z^25 + 4*z^24 + 7*z^23 + 9*z^22 + 9*z^21 + 11*z^20 + 11*z^17 + 9*z^16 + 9*z^15 + 7*z^14 + 4*z^13 + 4*z^12 + 11*z^11 + 7*z^10 + 11*z^9 + 11*z^8 + 12*z^7 + 12*z^5 + 4*z^4 + 4*z^2 + 2)*w^35 + (10*z^35 + 8*z^34 + 2*z^33 + 7*z^32 + 7*z^30 + 12*z^29 + 12*z^28 + 4*z^27 + 12*z^26 + 10*z^25 + 2*z^24 + 4*z^23 + 12*z^20 + 8*z^19 + 8*z^18 + 12*z^17 + 4*z^14 + 2*z^13 + 10*z^12 + 12*z^11 + 4*z^10 + 12*z^9 + 12*z^8 + 7*z^7 + 7*z^5 + 2*z^4 + 8*z^3 + 10*z^2 + 1)*w^32 + (3*z^35 + z^34 + 12*z^33 + 2*z^32 + 2*z^30 + 10*z^29 + 8*z^28 + 5*z^27 + 10*z^26 + 3*z^25 + 12*z^24 + 5*z^23 + 12*z^22 + 12*z^21 + 8*z^20 + z^19 + z^18 + 8*z^17 + 12*z^16 + 12*z^15 + 5*z^14 + 12*z^13 + 3*z^12 + 10*z^11 + 5*z^10 + 8*z^9 + 10*z^8 + 2*z^7 + 2*z^5 + 12*z^4 + z^3 + 3*z^2 + 11)*w^31 + (5*z^35 + 7*z^34 + 8*z^32 + 8*z^30 + 6*z^29 + 8*z^28 + 8*z^27 + 6*z^26 + 5*z^25 + 8*z^23 + 10*z^22 + 10*z^21 + 8*z^20 + 7*z^19 + 7*z^18 + 8*z^17 + 10*z^16 + 10*z^15 + 8*z^14 + 5*z^12 + 6*z^11 + 8*z^10 + 8*z^9 + 6*z^8 + 8*z^7 + 8*z^5 + 7*z^3 + 5*z^2 + 4)*w^30 + (8*z^35 + 2*z^34 + 4*z^33 + 12*z^32 + 12*z^30 + 8*z^29 + 9*z^28 + z^27 + 8*z^26 + 8*z^25 + 4*z^24 + z^23 + 2*z^22 + 2*z^21 + 9*z^20 + 2*z^19 + 2*z^18 + 9*z^17 + 2*z^16 + 2*z^15 + z^14 + 4*z^13 + 8*z^12 + 8*z^11 + z^10 + 9*z^9 + 8*z^8 + 12*z^7 + 12*z^5 + 4*z^4 + 2*z^3 + 8*z^2 + 1)*w^29 + (8*z^34 + 10*z^33 + 10*z^32 + 10*z^30 + 8*z^29 + 4*z^28 + 3*z^27 + 8*z^26 + 10*z^24 + 3*z^23 + 11*z^22 + 11*z^21 + 4*z^20 + 8*z^19 + 8*z^18 + 4*z^17 + 11*z^16 + 11*z^15 + 3*z^14 + 10*z^13 + 8*z^11 + 3*z^10 + 4*z^9 + 8*z^8 + 10*z^7 + 10*z^5 + 10*z^4 + 8*z^3 + 1)*w^28 + (5*z^35 + 9*z^34 + 6*z^33 + 6*z^32 + 6*z^30 + z^29 + z^28 + 7*z^27 + z^26 + 5*z^25 + 6*z^24 + 7*z^23 + 11*z^22 + 11*z^21 + z^20 + 9*z^19 + 9*z^18 + z^17 + 11*z^16 + 11*z^15 + 7*z^14 + 6*z^13 + 5*z^12 + z^11 + 7*z^10 + z^9 + z^8 + 6*z^7 + 6*z^5 + 6*z^4 + 9*z^3 + 5*z^2 + 10)*w^26 + (5*z^34 + 2*z^33 + 11*z^32 + 11*z^30 + 8*z^29 + 8*z^28 + 9*z^27 + 8*z^26 + 2*z^24 + 9*z^23 + 10*z^22 + 10*z^21 + 8*z^20 + 5*z^19 + 5*z^18 + 8*z^17 + 10*z^16 + 10*z^15 + 9*z^14 + 2*z^13 + 8*z^11 + 9*z^10 + 8*z^9 + 8*z^8 + 11*z^7 + 11*z^5 + 2*z^4 + 5*z^3 + 3)*w^25 + (3*z^35 + 11*z^34 + 12*z^33 + 11*z^32 + 11*z^30 + 4*z^29 + 5*z^28 + 3*z^27 + 4*z^26 + 3*z^25 + 12*z^24 + 3*z^23 + 10*z^22 + 10*z^21 + 5*z^20 + 11*z^19 + 11*z^18 + 5*z^17 + 10*z^16 + 10*z^15 + 3*z^14 + 12*z^13 + 3*z^12 + 4*z^11 + 3*z^10 + 5*z^9 + 4*z^8 + 11*z^7 + 11*z^5 + 12*z^4 + 11*z^3 + 3*z^2 + 9)*w^23 + (11*z^35 + 10*z^34 + 7*z^32 + 7*z^30 + 8*z^29 + 9*z^28 + 4*z^27 + 8*z^26 + 11*z^25 + 4*z^23 + 10*z^22 + 10*z^21 + 9*z^20 + 10*z^19 + 10*z^18 + 9*z^17 + 10*z^16 + 10*z^15 + 4*z^14 + 11*z^12 + 8*z^11 + 4*z^10 + 9*z^9 + 8*z^8 + 7*z^7 + 7*z^5 + 10*z^3 + 11*z^2)*w^22 + (12*z^35 + 7*z^34 + 4*z^33 + 7*z^32 + 7*z^30 + 8*z^28 + 10*z^27 + 12*z^25 + 4*z^24 + 10*z^23 + 3*z^22 + 3*z^21 + 8*z^20 + 7*z^19 + 7*z^18 + 8*z^17 + 3*z^16 + 3*z^15 + 10*z^14 + 4*z^13 + 12*z^12 + 10*z^10 + 8*z^9 + 7*z^7 + 7*z^5 + 4*z^4 + 7*z^3 + 12*z^2 + 7)*w^21 + (11*z^34 + z^33 + 3*z^32 + 3*z^30 + z^29 + 9*z^28 + 8*z^27 + z^26 + z^24 + 8*z^23 + 9*z^22 + 9*z^21 + 9*z^20 + 11*z^19 + 11*z^18 + 9*z^17 + 9*z^16 + 9*z^15 + 8*z^14 + z^13 + z^11 + 8*z^10 + 9*z^9 + z^8 + 3*z^7 + 3*z^5 + z^4 + 11*z^3 + 11)*w^19 + (3*z^35 + 4*z^33 + 11*z^32 + 11*z^30 + 11*z^29 + 5*z^28 + 5*z^27 + 11*z^26 + 3*z^25 + 4*z^24 + 5*z^23 + 10*z^22 + 10*z^21 + 5*z^20 + 5*z^17 + 10*z^16 + 10*z^15 + 5*z^14 + 4*z^13 + 3*z^12 + 11*z^11 + 5*z^10 + 5*z^9 + 11*z^8 + 11*z^7 + 11*z^5 + 4*z^4 + 3*z^2 + 6)*w^18 + (2*z^35 + 3*z^33 + 6*z^32 + 6*z^30 + 9*z^29 + 2*z^28 + 9*z^26 + 2*z^25 + 3*z^24 + 9*z^22 + 9*z^21 + 2*z^20 + 2*z^17 + 9*z^16 + 9*z^15 + 3*z^13 + 2*z^12 + 9*z^11 + 2*z^9 + 9*z^8 + 6*z^7 + 6*z^5 + 3*z^4 + 2*z^2 + 12)*w^17 + (4*z^35 + 10*z^34 + 4*z^33 + 7*z^32 + 7*z^30 + 12*z^29 + 9*z^28 + 11*z^27 + 12*z^26 + 4*z^25 + 4*z^24 + 11*z^23 + 7*z^22 + 7*z^21 + 9*z^20 + 10*z^19 + 10*z^18 + 9*z^17 + 7*z^16 + 7*z^15 + 11*z^14 + 4*z^13 + 4*z^12 + 12*z^11 + 11*z^10 + 9*z^9 + 12*z^8 + 7*z^7 + 7*z^5 + 4*z^4 + 10*z^3 + 4*z^2 + 10)*w^15 + (z^35 + 4*z^34 + 12*z^33 + 9*z^32 + 9*z^30 + 8*z^29 + 6*z^28 + 2*z^27 + 8*z^26 + z^25 + 12*z^24 + 2*z^23 + z^22 + z^21 + 6*z^20 + 4*z^19 + 4*z^18 + 6*z^17 + z^16 + z^15 + 2*z^14 + 12*z^13 + z^12 + 8*z^11 + 2*z^10 + 6*z^9 + 8*z^8 + 9*z^7 + 9*z^5 + 12*z^4 + 4*z^3 + z^2 + 12)*w^13 + (z^35 + 5*z^34 + 5*z^33 + 9*z^32 + 9*z^30 + 11*z^29 + 4*z^28 + 6*z^27 + 11*z^26 + z^25 + 5*z^24 + 6*z^23 + 3*z^22 + 3*z^21 + 4*z^20 + 5*z^19 + 5*z^18 + 4*z^17 + 3*z^16 + 3*z^15 + 6*z^14 + 5*z^13 + z^12 + 11*z^11 + 6*z^10 + 4*z^9 + 11*z^8 + 9*z^7 + 9*z^5 + 5*z^4 + 5*z^3 + z^2 + 12)*w^12 + (z^35 + 9*z^34 + z^33 + 12*z^32 + 12*z^30 + 6*z^29 + 7*z^28 + 11*z^27 + 6*z^26 + z^25 + z^24 + 11*z^23 + 2*z^22 + 2*z^21 + 7*z^20 + 9*z^19 + 9*z^18 + 7*z^17 + 2*z^16 + 2*z^15 + 11*z^14 + z^13 + z^12 + 6*z^11 + 11*z^10 + 7*z^9 + 6*z^8 + 12*z^7 + 12*z^5 + z^4 + 9*z^3 + z^2 + 12)*w^10 + (8*z^34 + 5*z^32 + 5*z^30 + 10*z^29 + 11*z^28 + 3*z^27 + 10*z^26 + 3*z^23 + 11*z^22 + 11*z^21 + 11*z^20 + 8*z^19 + 8*z^18 + 11*z^17 + 11*z^16 + 11*z^15 + 3*z^14 + 10*z^11 + 3*z^10 + 11*z^9 + 10*z^8 + 5*z^7 + 5*z^5 + 8*z^3 + 12)*w^9 + (5*z^35 + 11*z^33 + 7*z^32 + 7*z^30 + 12*z^29 + 9*z^28 + 12*z^26 + 5*z^25 + 11*z^24 + 10*z^22 + 10*z^21 + 9*z^20 + 9*z^17 + 10*z^16 + 10*z^15 + 11*z^13 + 5*z^12 + 12*z^11 + 9*z^9 + 12*z^8 + 7*z^7 + 7*z^5 + 11*z^4 + 5*z^2)*w^8 + (5*z^35 + 4*z^34 + 4*z^33 + 2*z^32 + 2*z^30 + 11*z^29 + 9*z^28 + 10*z^27 + 11*z^26 + 5*z^25 + 4*z^24 + 10*z^23 + 3*z^22 + 3*z^21 + 9*z^20 + 4*z^19 + 4*z^18 + 9*z^17 + 3*z^16 + 3*z^15 + 10*z^14 + 4*z^13 + 5*z^12 + 11*z^11 + 10*z^10 + 9*z^9 + 11*z^8 + 2*z^7 + 2*z^5 + 4*z^4 + 4*z^3 + 5*z^2 + 8)*w^7 + (12*z^35 + 10*z^33 + 7*z^32 + 7*z^30 + 4*z^29 + z^28 + 4*z^27 + 4*z^26 + 12*z^25 + 10*z^24 + 4*z^23 + 8*z^22 + 8*z^21 + z^20 + z^17 + 8*z^16 + 8*z^15 + 4*z^14 + 10*z^13 + 12*z^12 + 4*z^11 + 4*z^10 + z^9 + 4*z^8 + 7*z^7 + 7*z^5 + 10*z^4 + 12*z^2 + 12)*w^6 + (8*z^34 + 4*z^33 + 5*z^32 + 5*z^30 + 6*z^29 + 4*z^28 + z^27 + 6*z^26 + 4*z^24 + z^23 + 6*z^22 + 6*z^21 + 4*z^20 + 8*z^19 + 8*z^18 + 4*z^17 + 6*z^16 + 6*z^15 + z^14 + 4*z^13 + 6*z^11 + z^10 + 4*z^9 + 6*z^8 + 5*z^7 + 5*z^5 + 4*z^4 + 8*z^3 + 6)*w^5 + (5*z^35 + 7*z^34 + z^33 + z^32 + z^30 + 4*z^29 + 8*z^27 + 4*z^26 + 5*z^25 + z^24 + 8*z^23 + 8*z^22 + 8*z^21 + 7*z^19 + 7*z^18 + 8*z^16 + 8*z^15 + 8*z^14 + z^13 + 5*z^12 + 4*z^11 + 8*z^10 + 4*z^8 + z^7 + z^5 + z^4 + 7*z^3 + 5*z^2 + 10)*w^4 + (z^35 + 4*z^34 + 12*z^33 + z^32 + z^30 + 11*z^29 + 12*z^28 + 8*z^27 + 11*z^26 + z^25 + 12*z^24 + 8*z^23 + 6*z^22 + 6*z^21 + 12*z^20 + 4*z^19 + 4*z^18 + 12*z^17 + 6*z^16 + 6*z^15 + 8*z^14 + 12*z^13 + z^12 + 11*z^11 + 8*z^10 + 12*z^9 + 11*z^8 + z^7 + z^5 + 12*z^4 + 4*z^3 + z^2 + 5)*w^3 + (10*z^35 + 11*z^34 + 5*z^33 + 2*z^32 + 2*z^30 + 9*z^29 + 8*z^28 + 7*z^27 + 9*z^26 + 10*z^25 + 5*z^24 + 7*z^23 + 8*z^22 + 8*z^21 + 8*z^20 + 11*z^19 + 11*z^18 + 8*z^17 + 8*z^16 + 8*z^15 + 7*z^14 + 5*z^13 + 10*z^12 + 9*z^11 + 7*z^10 + 8*z^9 + 9*z^8 + 2*z^7 + 2*z^5 + 5*z^4 + 11*z^3 + 10*z^2 + 10)*w
> del(w);

>> del(w);
       ^
User error: Identifier 'w' has not been declared or assigned
> 
L;
> 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
> w := L.1;
> del(w);
z^2
> del(w^2) - del(w)^2;
0
> del(w^2);
z^4
> del(w^35) - del(w)^35;
0
> f, L, K, del, tr_alpha := FindDegree37FieldMod(59);
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: 0.830

Finished computing trace of random element.
Computing minimal polynomial of trace(alpha), as an element of K[X]
Time: 1.880
> w := L.1;
> del(w^35) - del(w)^35;
(18*z^35 + 58*z^34 + 36*z^33 + 28*z^32 + 28*z^30 + 6*z^29 + 28*z^28 + 37*z^27 + 6*z^26 + 18*z^25 + 36*z^24 + 37*z^23 + 46*z^22 + 46*z^21 + 28*z^20 + 58*z^19 + 58*z^18 + 28*z^17 + 46*z^16 + 46*z^15 + 37*z^14 + 36*z^13 + 18*z^12 + 6*z^11 + 37*z^10 + 28*z^9 + 6*z^8 + 28*z^7 + 28*z^5 + 36*z^4 + 58*z^3 + 18*z^2 + 45)*w^23
> del(w^2) - del(w)^2;
0
> f, L, K, del, tr_alpha := FindDegree37FieldMod(59);
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: 0.300

Finished computing trace of random element.
Computing minimal polynomial of trace(alpha), as an element of K[X]
Time: 1.930
> w := L.1;
> del(w^2) - del(w)^2;
0
> del(w^35) - del(w)^35;
(5*z^35 + 47*z^34 + 25*z^33 + 22*z^32 + 22*z^30 + 34*z^29 + 34*z^28 + 47*z^27 + 34*z^26 + 5*z^25 + 25*z^24 + 47*z^23 + 11*z^22 + 11*z^21 + 34*z^20 + 47*z^19 + 47*z^18 + 34*z^17 + 11*z^16 + 11*z^15 + 47*z^14 + 25*z^13 + 5*z^12 + 34*z^11 + 47*z^10 + 34*z^9 + 34*z^8 + 22*z^7 + 22*z^5 + 25*z^4 + 47*z^3 + 5*z^2 + 25)*w^23
> f, L, K, del, tr_alpha := FindDegree37FieldMod(59);
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 + 43*z^35 + 31*z^34 + 9*z^33 + 19*z^32 + 44*z^31 + 49*z^30 + z^29 + 27*z^28 + 39*z^27 + 20*z^26 + 7*z^25 + 45*z^24 + 10*z^23 + 20*z^22 + 31*z^21 + 37*z^20 + 48*z^19 + 48*z^18 + 37*z^17 + 31*z^16 + 20*z^15 + 10*z^14 + 45*z^13 + 7*z^12 + 20*z^11 + 39*z^10 + 27*z^9 + z^8 + 49*z^7 + 44*z^6 + 19*z^5 + 9*z^4 + 31*z^3 + 43*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: 0.570

Finished computing trace of random element.
Computing minimal polynomial of trace(alpha), as an element of K[X]
Time: 1.840
> w := L.1;
> del(w^35) - del(w)^35;
(13*z^35 + 51*z^34 + 24*z^33 + 43*z^32 + 36*z^31 + 58*z^30 + 5*z^29 + 46*z^28 + 34*z^27 + 58*z^26 + 5*z^25 + 53*z^24 + 47*z^23 + 2*z^22 + 50*z^21 + 45*z^20 + 24*z^19 + 24*z^18 + 45*z^17 + 50*z^16 + 2*z^15 + 47*z^14 + 53*z^13 + 5*z^12 + 58*z^11 + 34*z^10 + 46*z^9 + 5*z^8 + 58*z^7 + 36*z^6 + 43*z^5 + 24*z^4 + 51*z^3 + 13*z^2 + 36)*w^23
> f, L, K, del, tr_alpha := FindDegree37FieldMod(59);
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 + 43*z^35 + 31*z^34 + 9*z^33 + 19*z^32 + 44*z^31 + 49*z^30 + z^29 + 27*z^28 + 39*z^27 + 20*z^26 + 7*z^25 + 45*z^24 + 10*z^23 + 20*z^22 + 31*z^21 + 37*z^20 + 48*z^19 + 48*z^18 + 37*z^17 + 31*z^16 + 20*z^15 + 10*z^14 + 45*z^13 + 7*z^12 + 20*z^11 + 39*z^10 + 27*z^9 + z^8 + 49*z^7 + 44*z^6 + 19*z^5 + 9*z^4 + 31*z^3 + 43*z^2 + 42
Computing trace of random element (alpha = w
)
34 steps: [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
1, [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
2, [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
3, [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
4, [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
5, [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
6, [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
7, [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
8, [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
9, [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
10, [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
11, [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
12, [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
13, [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
14, [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
15, [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
16, [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
17, [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
18, [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
19, [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
20, [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
21, [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
22, [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
23, [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
24, [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
25, [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
26, [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
27, [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
28, [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
29, [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
30, [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
31, [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
32, [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
33, [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
34, [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
Time: 0.590

Finished computing trace of random element.
Computing minimal polynomial of trace(alpha), as an element of K[X]
Time: 1.960
> f, L, K, del, tr_alpha := FindDegree37FieldMod(59);
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 + 43*z^35 + 31*z^34 + 9*z^33 + 19*z^32 + 44*z^31 + 49*z^30 + z^29 + 27*z^28 + 39*z^27 + 20*z^26 + 7*z^25 + 45*z^24 + 10*z^23 + 20*z^22 + 31*z^21 + 37*z^20 + 48*z^19 + 48*z^18 + 37*z^17 + 31*z^16 + 20*z^15 + 10*z^14 + 45*z^13 + 7*z^12 + 20*z^11 + 39*z^10 + 27*z^9 + z^8 + 49*z^7 + 44*z^6 + 19*z^5 + 9*z^4 + 31*z^3 + 43*z^2 + 42
Computing trace of random element (alpha = w
)
34 steps: [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
1, [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
2, [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
3, [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
4, [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
5, [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
6, [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
7, [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
8, [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
9, [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
10, [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
11, [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
12, [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
13, [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
14, [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
15, [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
16, [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
17, [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
18, [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
19, [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
20, [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
21, [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
22, [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
23, [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
24, [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
25, [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
26, [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
27, [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
28, [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
29, [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
30, [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
31, [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
32, [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
33, [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
34, [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
Time: 0.600

Finished computing trace of random element.
Computing minimal polynomial of trace(alpha), as an element of K[X]
Time: 2.080
> f, L, K, del, tr_alpha := FindDegree37FieldMod(59);
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: [ 0, -111, -37, -222, -222, 0, -222, -148, -74, -37, -148, -111, -222, -37, -37, -37, -74, -37, -37, -74, -37, -37, -37, -222, -111, -148, -37, -74, -148, -222, 0, -222, -222, -37, -111, 0 ]
1, [ 0, -111, -37, -222, -222, 0, -222, -148, -74, -37, -148, -111, -222, -37, -37, -37, -74, -37, -37, -74, -37, -37, -37, -222, -111, -148, -37, -74, -148, -222, 0, -222, -222, -37, -111, 0 ]
2, [ 0, -111, -37, -222, -222, 0, -222, -148, -74, -37, -148, -111, -222, -37, -37, -37, -74, -37, -37, -74, -37, -37, -37, -222, -111, -148, -37, -74, -148, -222, 0, -222, -222, -37, -111, 0 ]
3, [ 0, -111, -37, -222, -222, 0, -222, -148, -74, -37, -148, -111, -222, -37, -37, -37, -74, -37, -37, -74, -37, -37, -37, -222, -111, -148, -37, -74, -148, -222, 0, -222, -222, -37, -111, 0 ]
4, [ 0, -111, -37, -222, -222, 0, -222, -148, -74, -37, -148, -111, -222, -37, -37, -37, -74, -37, -37, -74, -37, -37, -37, -222, -111, -148, -37, -74, -148, -222, 0, -222, -222, -37, -111, 0 ]
5, [ 0, -111, -37, -222, -222, 0, -222, -148, -74, -37, -148, -111, -222, -37, -37, -37, -74, -37, -37, -74, -37, -37, -37, -222, -111, -148, -37, -74, -148, -222, 0, -222, -222, -37, -111, 0 ]
6, [ 0, -111, -37, -222, -222, 0, -222, -148, -74, -37, -148, -111, -222, -37, -37, -37, -74, -37, -37, -74, -37, -37, -37, -222, -111, -148, -37, -74, -148, -222, 0, -222, -222, -37, -111, 0 ]
7, [ 0, -111, -37, -222, -222, 0, -222, -148, -74, -37, -148, -111, -222, -37, -37, -37, -74, -37, -37, -74, -37, -37, -37, -222, -111, -148, -37, -74, -148, -222, 0, -222, -222, -37, -111, 0 ]
8, [ 0, -111, -37, -222, -222, 0, -222, -148, -74, -37, -148, -111, -222, -37, -37, -37, -74, -37, -37, -74, -37, -37, -37, -222, -111, -148, -37, -74, -148, -222, 0, -222, -222, -37, -111, 0 ]
9, [ 0, -111, -37, -222, -222, 0, -222, -148, -74, -37, -148, -111, -222, -37, -37, -37, -74, -37, -37, -74, -37, -37, -37, -222, -111, -148, -37, -74, -148, -222, 0, -222, -222, -37, -111, 0 ]
10, [ 0, -111, -37, -222, -222, 0, -222, -148, -74, -37, -148, -111, -222, -37, -37, -37, -74, -37, -37, -74, -37, -37, -37, -222, -111, -148, -37, -74, -148, -222, 0, -222, -222, -37, -111, 0 ]
11, [ 0, -111, -37, -222, -222, 0, -222, -148, -74, -37, -148, -111, -222, -37, -37, -37, -74, -37, -37, -74, -37, -37, -37, -222, -111, -148, -37, -74, -148, -222, 0, -222, -222, -37, -111, 0 ]
12, [ 0, -111, -37, -222, -222, 0, -222, -148, -74, -37, -148, -111, -222, -37, -37, -37, -74, -37, -37, -74, -37, -37, -37, -222, -111, -148, -37, -74, -148, -222, 0, -222, -222, -37, -111, 0 ]
13, [ 0, -111, -37, -222, -222, 0, -222, -148, -74, -37, -148, -111, -222, -37, -37, -37, -74, -37, -37, -74, -37, -37, -37, -222, -111, -148, -37, -74, -148, -222, 0, -222, -222, -37, -111, 0 ]
14, [ 0, -111, -37, -222, -222, 0, -222, -148, -74, -37, -148, -111, -222, -37, -37, -37, -74, -37, -37, -74, -37, -37, -37, -222, -111, -148, -37, -74, -148, -222, 0, -222, -222, -37, -111, 0 ]
15, [ 0, -111, -37, -222, -222, 0, -222, -148, -74, -37, -148, -111, -222, -37, -37, -37, -74, -37, -37, -74, -37, -37, -37, -222, -111, -148, -37, -74, -148, -222, 0, -222, -222, -37, -111, 0 ]
16, [ 0, -111, -37, -222, -222, 0, -222, -148, -74, -37, -148, -111, -222, -37, -37, -37, -74, -37, -37, -74, -37, -37, -37, -222, -111, -148, -37, -74, -148, -222, 0, -222, -222, -37, -111, 0 ]
17, [ 0, -111, -37, -222, -222, 0, -222, -148, -74, -37, -148, -111, -222, -37, -37, -37, -74, -37, -37, -74, -37, -37, -37, -222, -111, -148, -37, -74, -148, -222, 0, -222, -222, -37, -111, 0 ]
18, [ 0, -111, -37, -222, -222, 0, -222, -148, -74, -37, -148, -111, -222, -37, -37, -37, -74, -37, -37, -74, -37, -37, -37, -222, -111, -148, -37, -74, -148, -222, 0, -222, -222, -37, -111, 0 ]
19, [ 0, -111, -37, -222, -222, 0, -222, -148, -74, -37, -148, -111, -222, -37, -37, -37, -74, -37, -37, -74, -37, -37, -37, -222, -111, -148, -37, -74, -148, -222, 0, -222, -222, -37, -111, 0 ]
20, [ 0, -111, -37, -222, -222, 0, -222, -148, -74, -37, -148, -111, -222, -37, -37, -37, -74, -37, -37, -74, -37, -37, -37, -222, -111, -148, -37, -74, -148, -222, 0, -222, -222, -37, -111, 0 ]
21, [ 0, -111, -37, -222, -222, 0, -222, -148, -74, -37, -148, -111, -222, -37, -37, -37, -74, -37, -37, -74, -37, -37, -37, -222, -111, -148, -37, -74, -148, -222, 0, -222, -222, -37, -111, 0 ]
22, [ 0, -111, -37, -222, -222, 0, -222, -148, -74, -37, -148, -111, -222, -37, -37, -37, -74, -37, -37, -74, -37, -37, -37, -222, -111, -148, -37, -74, -148, -222, 0, -222, -222, -37, -111, 0 ]
23, [ 0, -111, -37, -222, -222, 0, -222, -148, -74, -37, -148, -111, -222, -37, -37, -37, -74, -37, -37, -74, -37, -37, -37, -222, -111, -148, -37, -74, -148, -222, 0, -222, -222, -37, -111, 0 ]
24, [ 0, -111, -37, -222, -222, 0, -222, -148, -74, -37, -148, -111, -222, -37, -37, -37, -74, -37, -37, -74, -37, -37, -37, -222, -111, -148, -37, -74, -148, -222, 0, -222, -222, -37, -111, 0 ]
25, [ 0, -111, -37, -222, -222, 0, -222, -148, -74, -37, -148, -111, -222, -37, -37, -37, -74, -37, -37, -74, -37, -37, -37, -222, -111, -148, -37, -74, -148, -222, 0, -222, -222, -37, -111, 0 ]
26, [ 0, -111, -37, -222, -222, 0, -222, -148, -74, -37, -148, -111, -222, -37, -37, -37, -74, -37, -37, -74, -37, -37, -37, -222, -111, -148, -37, -74, -148, -222, 0, -222, -222, -37, -111, 0 ]
27, [ 0, -111, -37, -222, -222, 0, -222, -148, -74, -37, -148, -111, -222, -37, -37, -37, -74, -37, -37, -74, -37, -37, -37, -222, -111, -148, -37, -74, -148, -222, 0, -222, -222, -37, -111, 0 ]
28, [ 0, -111, -37, -222, -222, 0, -222, -148, -74, -37, -148, -111, -222, -37, -37, -37, -74, -37, -37, -74, -37, -37, -37, -222, -111, -148, -37, -74, -148, -222, 0, -222, -222, -37, -111, 0 ]
29, [ 0, -111, -37, -222, -222, 0, -222, -148, -74, -37, -148, -111, -222, -37, -37, -37, -74, -37, -37, -74, -37, -37, -37, -222, -111, -148, -37, -74, -148, -222, 0, -222, -222, -37, -111, 0 ]
30, [ 0, -111, -37, -222, -222, 0, -222, -148, -74, -37, -148, -111, -222, -37, -37, -37, -74, -37, -37, -74, -37, -37, -37, -222, -111, -148, -37, -74, -148, -222, 0, -222, -222, -37, -111, 0 ]
31, [ 0, -111, -37, -222, -222, 0, -222, -148, -74, -37, -148, -111, -222, -37, -37, -37, -74, -37, -37, -74, -37, -37, -37, -222, -111, -148, -37, -74, -148, -222, 0, -222, -222, -37, -111, 0 ]
32, [ 0, -111, -37, -222, -222, 0, -222, -148, -74, -37, -148, -111, -222, -37, -37, -37, -74, -37, -37, -74, -37, -37, -37, -222, -111, -148, -37, -74, -148, -222, 0, -222, -222, -37, -111, 0 ]
33, [ 0, -111, -37, -222, -222, 0, -222, -148, -74, -37, -148, -111, -222, -37, -37, -37, -74, -37, -37, -74, -37, -37, -37, -222, -111, -148, -37, -74, -148, -222, 0, -222, -222, -37, -111, 0 ]
34, [ 0, -111, -37, -222, -222, 0, -222, -148, -74, -37, -148, -111, -222, -37, -37, -37, -74, -37, -37, -74, -37, -37, -37, -222, -111, -148, -37, -74, -148, -222, 0, -222, -222, -37, -111, 0 ]
Time: 0.450

Finished computing trace of random element.
Computing minimal polynomial of trace(alpha), as an element of K[X]
Time: 0.880
> f, L, K, del, tr_alpha := FindDegree37FieldMod(59);
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: [ 0, -3, -1, -6, -6, 0, -6, -4, -2, -1, -4, -3, -6, -1, -1, -1, -2, -1, -1, -2, -1, -1, -1, -6, -3, -4, -1, -2, -4, -6, 0, -6, -6, -1, -3, 0 ]
1, [ 0, -3, -1, -6, -6, 0, -6, -4, -2, -1, -4, -3, -6, -1, -1, -1, -2, -1, -1, -2, -1, -1, -1, -6, -3, -4, -1, -2, -4, -6, 0, -6, -6, -1, -3, 0 ]
2, [ 0, -3, -1, -6, -6, 0, -6, -4, -2, -1, -4, -3, -6, -1, -1, -1, -2, -1, -1, -2, -1, -1, -1, -6, -3, -4, -1, -2, -4, -6, 0, -6, -6, -1, -3, 0 ]
3, [ 0, -3, -1, -6, -6, 0, -6, -4, -2, -1, -4, -3, -6, -1, -1, -1, -2, -1, -1, -2, -1, -1, -1, -6, -3, -4, -1, -2, -4, -6, 0, -6, -6, -1, -3, 0 ]
4, [ 0, -3, -1, -6, -6, 0, -6, -4, -2, -1, -4, -3, -6, -1, -1, -1, -2, -1, -1, -2, -1, -1, -1, -6, -3, -4, -1, -2, -4, -6, 0, -6, -6, -1, -3, 0 ]
5, [ 0, -3, -1, -6, -6, 0, -6, -4, -2, -1, -4, -3, -6, -1, -1, -1, -2, -1, -1, -2, -1, -1, -1, -6, -3, -4, -1, -2, -4, -6, 0, -6, -6, -1, -3, 0 ]
6, [ 0, -3, -1, -6, -6, 0, -6, -4, -2, -1, -4, -3, -6, -1, -1, -1, -2, -1, -1, -2, -1, -1, -1, -6, -3, -4, -1, -2, -4, -6, 0, -6, -6, -1, -3, 0 ]
7, [ 0, -3, -1, -6, -6, 0, -6, -4, -2, -1, -4, -3, -6, -1, -1, -1, -2, -1, -1, -2, -1, -1, -1, -6, -3, -4, -1, -2, -4, -6, 0, -6, -6, -1, -3, 0 ]
8, [ 0, -3, -1, -6, -6, 0, -6, -4, -2, -1, -4, -3, -6, -1, -1, -1, -2, -1, -1, -2, -1, -1, -1, -6, -3, -4, -1, -2, -4, -6, 0, -6, -6, -1, -3, 0 ]
9, [ 0, -3, -1, -6, -6, 0, -6, -4, -2, -1, -4, -3, -6, -1, -1, -1, -2, -1, -1, -2, -1, -1, -1, -6, -3, -4, -1, -2, -4, -6, 0, -6, -6, -1, -3, 0 ]
10, [ 0, -3, -1, -6, -6, 0, -6, -4, -2, -1, -4, -3, -6, -1, -1, -1, -2, -1, -1, -2, -1, -1, -1, -6, -3, -4, -1, -2, -4, -6, 0, -6, -6, -1, -3, 0 ]
11, [ 0, -3, -1, -6, -6, 0, -6, -4, -2, -1, -4, -3, -6, -1, -1, -1, -2, -1, -1, -2, -1, -1, -1, -6, -3, -4, -1, -2, -4, -6, 0, -6, -6, -1, -3, 0 ]
12, [ 0, -3, -1, -6, -6, 0, -6, -4, -2, -1, -4, -3, -6, -1, -1, -1, -2, -1, -1, -2, -1, -1, -1, -6, -3, -4, -1, -2, -4, -6, 0, -6, -6, -1, -3, 0 ]
13, [ 0, -3, -1, -6, -6, 0, -6, -4, -2, -1, -4, -3, -6, -1, -1, -1, -2, -1, -1, -2, -1, -1, -1, -6, -3, -4, -1, -2, -4, -6, 0, -6, -6, -1, -3, 0 ]
14, [ 0, -3, -1, -6, -6, 0, -6, -4, -2, -1, -4, -3, -6, -1, -1, -1, -2, -1, -1, -2, -1, -1, -1, -6, -3, -4, -1, -2, -4, -6, 0, -6, -6, -1, -3, 0 ]
15, [ 0, -3, -1, -6, -6, 0, -6, -4, -2, -1, -4, -3, -6, -1, -1, -1, -2, -1, -1, -2, -1, -1, -1, -6, -3, -4, -1, -2, -4, -6, 0, -6, -6, -1, -3, 0 ]
16, [ 0, -3, -1, -6, -6, 0, -6, -4, -2, -1, -4, -3, -6, -1, -1, -1, -2, -1, -1, -2, -1, -1, -1, -6, -3, -4, -1, -2, -4, -6, 0, -6, -6, -1, -3, 0 ]
17, [ 0, -3, -1, -6, -6, 0, -6, -4, -2, -1, -4, -3, -6, -1, -1, -1, -2, -1, -1, -2, -1, -1, -1, -6, -3, -4, -1, -2, -4, -6, 0, -6, -6, -1, -3, 0 ]
18, [ 0, -3, -1, -6, -6, 0, -6, -4, -2, -1, -4, -3, -6, -1, -1, -1, -2, -1, -1, -2, -1, -1, -1, -6, -3, -4, -1, -2, -4, -6, 0, -6, -6, -1, -3, 0 ]
19, [ 0, -3, -1, -6, -6, 0, -6, -4, -2, -1, -4, -3, -6, -1, -1, -1, -2, -1, -1, -2, -1, -1, -1, -6, -3, -4, -1, -2, -4, -6, 0, -6, -6, -1, -3, 0 ]
20, [ 0, -3, -1, -6, -6, 0, -6, -4, -2, -1, -4, -3, -6, -1, -1, -1, -2, -1, -1, -2, -1, -1, -1, -6, -3, -4, -1, -2, -4, -6, 0, -6, -6, -1, -3, 0 ]
21, [ 0, -3, -1, -6, -6, 0, -6, -4, -2, -1, -4, -3, -6, -1, -1, -1, -2, -1, -1, -2, -1, -1, -1, -6, -3, -4, -1, -2, -4, -6, 0, -6, -6, -1, -3, 0 ]
22, [ 0, -3, -1, -6, -6, 0, -6, -4, -2, -1, -4, -3, -6, -1, -1, -1, -2, -1, -1, -2, -1, -1, -1, -6, -3, -4, -1, -2, -4, -6, 0, -6, -6, -1, -3, 0 ]
23, [ 0, -3, -1, -6, -6, 0, -6, -4, -2, -1, -4, -3, -6, -1, -1, -1, -2, -1, -1, -2, -1, -1, -1, -6, -3, -4, -1, -2, -4, -6, 0, -6, -6, -1, -3, 0 ]
24, [ 0, -3, -1, -6, -6, 0, -6, -4, -2, -1, -4, -3, -6, -1, -1, -1, -2, -1, -1, -2, -1, -1, -1, -6, -3, -4, -1, -2, -4, -6, 0, -6, -6, -1, -3, 0 ]
25, [ 0, -3, -1, -6, -6, 0, -6, -4, -2, -1, -4, -3, -6, -1, -1, -1, -2, -1, -1, -2, -1, -1, -1, -6, -3, -4, -1, -2, -4, -6, 0, -6, -6, -1, -3, 0 ]
26, [ 0, -3, -1, -6, -6, 0, -6, -4, -2, -1, -4, -3, -6, -1, -1, -1, -2, -1, -1, -2, -1, -1, -1, -6, -3, -4, -1, -2, -4, -6, 0, -6, -6, -1, -3, 0 ]
27, [ 0, -3, -1, -6, -6, 0, -6, -4, -2, -1, -4, -3, -6, -1, -1, -1, -2, -1, -1, -2, -1, -1, -1, -6, -3, -4, -1, -2, -4, -6, 0, -6, -6, -1, -3, 0 ]
28, [ 0, -3, -1, -6, -6, 0, -6, -4, -2, -1, -4, -3, -6, -1, -1, -1, -2, -1, -1, -2, -1, -1, -1, -6, -3, -4, -1, -2, -4, -6, 0, -6, -6, -1, -3, 0 ]
29, [ 0, -3, -1, -6, -6, 0, -6, -4, -2, -1, -4, -3, -6, -1, -1, -1, -2, -1, -1, -2, -1, -1, -1, -6, -3, -4, -1, -2, -4, -6, 0, -6, -6, -1, -3, 0 ]
30, [ 0, -3, -1, -6, -6, 0, -6, -4, -2, -1, -4, -3, -6, -1, -1, -1, -2, -1, -1, -2, -1, -1, -1, -6, -3, -4, -1, -2, -4, -6, 0, -6, -6, -1, -3, 0 ]
31, [ 0, -3, -1, -6, -6, 0, -6, -4, -2, -1, -4, -3, -6, -1, -1, -1, -2, -1, -1, -2, -1, -1, -1, -6, -3, -4, -1, -2, -4, -6, 0, -6, -6, -1, -3, 0 ]
32, [ 0, -3, -1, -6, -6, 0, -6, -4, -2, -1, -4, -3, -6, -1, -1, -1, -2, -1, -1, -2, -1, -1, -1, -6, -3, -4, -1, -2, -4, -6, 0, -6, -6, -1, -3, 0 ]
33, [ 0, -3, -1, -6, -6, 0, -6, -4, -2, -1, -4, -3, -6, -1, -1, -1, -2, -1, -1, -2, -1, -1, -1, -6, -3, -4, -1, -2, -4, -6, 0, -6, -6, -1, -3, 0 ]
34, [ 0, -3, -1, -6, -6, 0, -6, -4, -2, -1, -4, -3, -6, -1, -1, -1, -2, -1, -1, -2, -1, -1, -1, -6, -3, -4, -1, -2, -4, -6, 0, -6, -6, -1, -3, 0 ]
Time: 0.880

Finished computing trace of random element.
Computing minimal polynomial of trace(alpha), as an element of K[X]
Time: 1.790
> L, del := FindDegree37Field();
Forming field L.
Time: 0.000
L =  Univariate Quotient Polynomial Algebra in w over Cyclotomic Field of order 37 and degree 36
with modulus w^37 + 227554939220387001560181536043561236415684097905471324064108760413512735882211*z^35 - 748469965909445841121220656728096768986581374221957775796923397895739785679909*z^34 + 422937946274095144851355914765192796187368468424673347782850149678661221314766*z^33 + 987155020300395873684192072284494315727261476296223805812965362006473792003461*z^32 + 987155020300395873684192072284494315727261476296223805812965362006473792003461*z^30 + 1642559888262520802436174977647040780318296562574593002685224533085994719859703*z^29 + 453281345181236267145694170456596752887580518039782437819337989575823897625214*z^28 + 1043308013271809150417090498695323153095792631362883429099350371767608400203784*z^27 + 1642559888262520802436174977647040780318296562574593002685224533085994719859703*z^26 + 227554939220387001560181536043561236415684097905471324064108760413512735882211*z^25 + 422937946274095144851355914765192796187368468424673347782850149678661221314766*z^24 + 1043308013271809150417090498695323153095792631362883429099350371767608400203784*z^23 - 397951139482377025177712741609695316497385537225146905069164519558759827367816*z^22 - 397951139482377025177712741609695316497385537225146905069164519558759827367816*z^21 + 453281345181236267145694170456596752887580518039782437819337989575823897625214*z^20 - 748469965909445841121220656728096768986581374221957775796923397895739785679909*z^19 - 748469965909445841121220656728096768986581374221957775796923397895739785679909*z^18 + 453281345181236267145694170456596752887580518039782437819337989575823897625214*z^17 - 397951139482377025177712741609695316497385537225146905069164519558759827367816*z^16 - 397951139482377025177712741609695316497385537225146905069164519558759827367816*z^15 + 1043308013271809150417090498695323153095792631362883429099350371767608400203784*z^14 + 422937946274095144851355914765192796187368468424673347782850149678661221314766*z^13 + 227554939220387001560181536043561236415684097905471324064108760413512735882211*z^12 + 1642559888262520802436174977647040780318296562574593002685224533085994719859703*z^11 + 1043308013271809150417090498695323153095792631362883429099350371767608400203784*z^10 + 453281345181236267145694170456596752887580518039782437819337989575823897625214*z^9 + 1642559888262520802436174977647040780318296562574593002685224533085994719859703*z^8 + 987155020300395873684192072284494315727261476296223805812965362006473792003461*z^7 + 987155020300395873684192072284494315727261476296223805812965362006473792003461*z^5 + 422937946274095144851355914765192796187368468424673347782850149678661221314766*z^4 - 748469965909445841121220656728096768986581374221957775796923397895739785679909*z^3 + 227554939220387001560181536043561236415684097905471324064108760413512735882211*z^2 - 1109057779204797647220483387753958150300552237984728549445619892366735836842023
> w := L.1;
> del(w^2) - del(w)^2;
0
> del(w^35) - del(w)^35;
(118354602498740743488678697520167371185009250176611503181192252864778121094478934404358036170622489705293053070123827761489835122999680165213607649743889988679395105040008484086767404575770582182962*z^35 + 174357516569030032403566592136040673023681923460478676503517386238603666353390803168583266593857972275438855775239172908087466555583400445210873271197812347126617643106108407104496773975955757366253*z^34 + 123153107339021474495456256324183675875232019904863071762801899453007931144867672002468133235146474741749455244599218163453847201028583471678991032450837805213442725702791476739105423643669377608207*z^33 + 34004358006379039623208823813673870417695328596641854854482214690176323052210092665864993009872075261808718375658082185788535120563637100920513188454871869496258889178356532877147413124356859551134*z^32 + 34004358006379039623208823813673870417695328596641854854482214690176323052210092665864993009872075261808718375658082185788535120563637100920513188454871869496258889178356532877147413124356859551134*z^30 + 72735934587297739622329473794561783729538373589746590445358866013856318456554558654865579564213975256144860196986626865209220273623313267833654956194383911384344357497379198340166088315051605125658*z^29 + 70143053040219628132847522609474041764336330257076045179514688356569513791383968823351510703957952766715370530882685390281592234247774504008955498364306815978753427193053531789946252937403786387514*z^28 + 53448305391764860301961376999598274409660317730947694786011425289248081924418886509894122081931692294303864728286648267336582794467187956507836851030911714582765775576594572490731182510694069953563*z^27 + 72735934587297739622329473794561783729538373589746590445358866013856318456554558654865579564213975256144860196986626865209220273623313267833654956194383911384344357497379198340166088315051605125658*z^26 + 118354602498740743488678697520167371185009250176611503181192252864778121094478934404358036170622489705293053070123827761489835122999680165213607649743889988679395105040008484086767404575770582182962*z^25 + 123153107339021474495456256324183675875232019904863071762801899453007931144867672002468133235146474741749455244599218163453847201028583471678991032450837805213442725702791476739105423643669377608207*z^24 + 53448305391764860301961376999598274409660317730947694786011425289248081924418886509894122081931692294303864728286648267336582794467187956507836851030911714582765775576594572490731182510694069953563*z^23 - 29950917449907337409599911096715375636172400874568100138974581313195932622929677549416964179736257555006688768827498950485898306268253360717845904562679878948146727730297284711428384012572936040433*z^22 - 29950917449907337409599911096715375636172400874568100138974581313195932622929677549416964179736257555006688768827498950485898306268253360717845904562679878948146727730297284711428384012572936040433*z^21 + 70143053040219628132847522609474041764336330257076045179514688356569513791383968823351510703957952766715370530882685390281592234247774504008955498364306815978753427193053531789946252937403786387514*z^20 + 174357516569030032403566592136040673023681923460478676503517386238603666353390803168583266593857972275438855775239172908087466555583400445210873271197812347126617643106108407104496773975955757366253*z^19 + 174357516569030032403566592136040673023681923460478676503517386238603666353390803168583266593857972275438855775239172908087466555583400445210873271197812347126617643106108407104496773975955757366253*z^18 + 70143053040219628132847522609474041764336330257076045179514688356569513791383968823351510703957952766715370530882685390281592234247774504008955498364306815978753427193053531789946252937403786387514*z^17 - 29950917449907337409599911096715375636172400874568100138974581313195932622929677549416964179736257555006688768827498950485898306268253360717845904562679878948146727730297284711428384012572936040433*z^16 - 29950917449907337409599911096715375636172400874568100138974581313195932622929677549416964179736257555006688768827498950485898306268253360717845904562679878948146727730297284711428384012572936040433*z^15 + 53448305391764860301961376999598274409660317730947694786011425289248081924418886509894122081931692294303864728286648267336582794467187956507836851030911714582765775576594572490731182510694069953563*z^14 + 123153107339021474495456256324183675875232019904863071762801899453007931144867672002468133235146474741749455244599218163453847201028583471678991032450837805213442725702791476739105423643669377608207*z^13 + 118354602498740743488678697520167371185009250176611503181192252864778121094478934404358036170622489705293053070123827761489835122999680165213607649743889988679395105040008484086767404575770582182962*z^12 + 72735934587297739622329473794561783729538373589746590445358866013856318456554558654865579564213975256144860196986626865209220273623313267833654956194383911384344357497379198340166088315051605125658*z^11 + 53448305391764860301961376999598274409660317730947694786011425289248081924418886509894122081931692294303864728286648267336582794467187956507836851030911714582765775576594572490731182510694069953563*z^10 + 70143053040219628132847522609474041764336330257076045179514688356569513791383968823351510703957952766715370530882685390281592234247774504008955498364306815978753427193053531789946252937403786387514*z^9 + 72735934587297739622329473794561783729538373589746590445358866013856318456554558654865579564213975256144860196986626865209220273623313267833654956194383911384344357497379198340166088315051605125658*z^8 + 34004358006379039623208823813673870417695328596641854854482214690176323052210092665864993009872075261808718375658082185788535120563637100920513188454871869496258889178356532877147413124356859551134*z^7 + 34004358006379039623208823813673870417695328596641854854482214690176323052210092665864993009872075261808718375658082185788535120563637100920513188454871869496258889178356532877147413124356859551134*z^5 + 123153107339021474495456256324183675875232019904863071762801899453007931144867672002468133235146474741749455244599218163453847201028583471678991032450837805213442725702791476739105423643669377608207*z^4 + 174357516569030032403566592136040673023681923460478676503517386238603666353390803168583266593857972275438855775239172908087466555583400445210873271197812347126617643106108407104496773975955757366253*z^3 + 118354602498740743488678697520167371185009250176611503181192252864778121094478934404358036170622489705293053070123827761489835122999680165213607649743889988679395105040008484086767404575770582182962*z^2 - 60763015272938917065803194623650231841348488905989475895996385875521508903409345140545727030643312833538075517616458984411626358212364589149669481200266613490554278590815548757921788030102906149416)*w^23
> w^37;
-227554939220387001560181536043561236415684097905471324064108760413512735882211*z^35 + 748469965909445841121220656728096768986581374221957775796923397895739785679909*z^34 - 422937946274095144851355914765192796187368468424673347782850149678661221314766*z^33 - 987155020300395873684192072284494315727261476296223805812965362006473792003461*z^32 - 987155020300395873684192072284494315727261476296223805812965362006473792003461*z^30 - 1642559888262520802436174977647040780318296562574593002685224533085994719859703*z^29 - 453281345181236267145694170456596752887580518039782437819337989575823897625214*z^28 - 1043308013271809150417090498695323153095792631362883429099350371767608400203784*z^27 - 1642559888262520802436174977647040780318296562574593002685224533085994719859703*z^26 - 227554939220387001560181536043561236415684097905471324064108760413512735882211*z^25 - 422937946274095144851355914765192796187368468424673347782850149678661221314766*z^24 - 1043308013271809150417090498695323153095792631362883429099350371767608400203784*z^23 + 397951139482377025177712741609695316497385537225146905069164519558759827367816*z^22 + 397951139482377025177712741609695316497385537225146905069164519558759827367816*z^21 - 453281345181236267145694170456596752887580518039782437819337989575823897625214*z^20 + 748469965909445841121220656728096768986581374221957775796923397895739785679909*z^19 + 748469965909445841121220656728096768986581374221957775796923397895739785679909*z^18 - 453281345181236267145694170456596752887580518039782437819337989575823897625214*z^17 + 397951139482377025177712741609695316497385537225146905069164519558759827367816*z^16 + 397951139482377025177712741609695316497385537225146905069164519558759827367816*z^15 - 1043308013271809150417090498695323153095792631362883429099350371767608400203784*z^14 - 422937946274095144851355914765192796187368468424673347782850149678661221314766*z^13 - 227554939220387001560181536043561236415684097905471324064108760413512735882211*z^12 - 1642559888262520802436174977647040780318296562574593002685224533085994719859703*z^11 - 1043308013271809150417090498695323153095792631362883429099350371767608400203784*z^10 - 453281345181236267145694170456596752887580518039782437819337989575823897625214*z^9 - 1642559888262520802436174977647040780318296562574593002685224533085994719859703*z^8 - 987155020300395873684192072284494315727261476296223805812965362006473792003461*z^7 - 987155020300395873684192072284494315727261476296223805812965362006473792003461*z^5 - 422937946274095144851355914765192796187368468424673347782850149678661221314766*z^4 + 748469965909445841121220656728096768986581374221957775796923397895739785679909*z^3 - 227554939220387001560181536043561236415684097905471324064108760413512735882211*z^2 + 1109057779204797647220483387753958150300552237984728549445619892366735836842023
> eta := w^37;
> del(eta^2)-del(eta)^2;
0
> [del(eta^i)-del(eta)^i : i in [3..35]];
[
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
]
>