Program tnfd.
MODULUS for linear algebra = 1073741789
Verbose output? (0/1) Enter level: >>>Level 97	dimension = 8
Split into W-eigenspaces (0/1)? Multiplicity 1 eigenspaces only? (0/1)? Use just one T_p (1) or a linear combination (0)? Computing T_p for p = 2...done.
char poly = [-3 28 -54 -54 47 22 -13 -2 1]
NTL char poly square-free factors = [[[-3 28 -54 -54 47 22 -13 -2 1] 1]]
Factors of multiplicity 1 are:
1:	[-3 1]	(degree 1)
2:	[-1 3 4 1]	(degree 3)
3:	[-1 6 -1 -3 1]	(degree 4)
Enter factor number: Degree = 4
(unscaled) min poly = [1 -3 -1 6 -1 ]
(rescaled) min poly = [-1 6 -1 -3 1]
finished constructing S, now restricting T_p to S
done.  now combining S and SW
4*Matrix of T(2) restricted to S is [-4,8,4,0;0,4,0,8;-4,4,8,-4;-4,8,4,4]

The former poly is the min poly of alpha_1 = 4*alpha
The latter is the min poly of alpha, which is the eigenvalue of T(2)
Finished computing (dual) subspace S
S has denom 4, cumulative denom = 4
W     = [1,-4,0,-256;0,8,16,512;0,4,16,320;0,0,48,256]

W^(-1)= (1/128)*[128,-64,256,-64;0,176,-320,48;0,16,-32,8;0,-3,6,-1]

Basis for Hecke eigenvalues, in terms of powers of alpha:
(1/8)*[2,0,0,0]
(1/8)*[-1,11,4,-3]
(1/8)*[4,-20,-8,6]
(1/8)*[-1,3,2,-1]
Number of ap? 4*Matrix of T(2) = [-4,8,4,0;0,4,0,8;-4,4,8,-4;-4,8,4,4]
char poly = [ -1 6 -1 -3 1 ]
a_2 = [0,4,0,8]
4*Matrix of T(3) = [4,4,0,-12;8,-8,-8,-8;-4,8,8,0;0,-4,-4,-4]
char poly = [ 4 -1 -5 0 1 ]
a_3 = [8,-8,-8,-8]
4*Matrix of T(5) = [8,-8,-4,0;0,0,0,-8;4,-4,-4,4;4,-8,-4,0]
char poly = [ 2 1 -4 -1 1 ]
a_5 = [0,0,0,-8]
4*Matrix of T(7) = [8,-4,0,4;-8,16,16,0;12,-16,-20,0;0,0,4,8]
char poly = [ -16 23 -6 -3 1 ]
a_7 = [-8,16,16,0]
4*Matrix of T(11) = [8,-24,-12,16;0,-8,-16,-8;-4,4,20,12;12,-16,-12,0]
char poly = [ 92 47 -14 -5 1 ]
a_11 = [0,-8,-16,-8]
4*Matrix of T(13) = [-4,-16,-12,0;16,-40,-40,-16;-20,28,40,12;12,-20,-20,-20]
char poly = [ -122 -167 -29 6 1 ]
a_13 = [16,-40,-40,-16]
4*Matrix of T(17) = [-4,20,12,-4;-8,24,24,16;8,-12,-20,-12;-12,20,16,12]
char poly = [ 74 15 -20 -3 1 ]
a_17 = [-8,24,24,16]
4*Matrix of T(19) = [-12,0,0,8;0,-8,-8,8;-8,8,12,0;0,4,0,-4]
char poly = [ 4 -11 -5 3 1 ]
a_19 = [0,-8,-8,8]
4*Matrix of T(23) = [12,-16,-4,32;-16,32,8,16;4,-12,16,4;4,4,4,28]
char poly = [ -368 -265 151 -22 1 ]
a_23 = [-16,32,8,16]
4*Matrix of T(29) = [-12,32,16,-8;0,16,8,24;-8,8,12,-16;-16,28,16,12]
char poly = [ -254 199 -27 -7 1 ]
a_29 = [0,16,8,24]
4*Matrix of T(31) = [-8,44,20,-36;8,8,16,8;0,4,-16,-20;-20,24,16,0]
char poly = [ 592 -79 -67 4 1 ]
a_31 = [8,8,16,8]
4*Matrix of T(37) = [-12,-24,-12,24;0,-24,-24,0;-12,12,24,12;12,-12,-12,-12]
char poly = [ 162 -81 -27 6 1 ]
a_37 = [0,-24,-24,0]
4*Matrix of T(41) = [48,-12,-8,-36;8,8,16,-48;28,-24,-44,8;8,-32,-12,0]
char poly = [ 5506 131 -158 -3 1 ]
a_41 = [8,8,16,-48]
4*Matrix of T(43) = [20,-4,-4,-12;8,0,-8,-16;0,4,12,4;4,-12,-8,4]
char poly = [ -44 9 20 -9 1 ]
a_43 = [8,0,-8,-16]
4*Matrix of T(47) = [36,8,0,-32;16,8,-8,-24;0,8,20,0;0,-12,-8,12]
char poly = [ 16 -161 99 -19 1 ]
a_47 = [16,8,-8,-24]
4*Matrix of T(53) = [-4,24,4,-40;32,-40,-40,-16;-28,44,48,-4;-4,-4,-12,-20]
char poly = [ 1262 -123 -75 4 1 ]
a_53 = [32,-40,-40,-16]
4*Matrix of T(59) = [-8,24,4,-32;32,-40,-48,-8;-36,52,68,-4;-4,0,-12,-16]
char poly = [ 772 3 -98 -1 1 ]
a_59 = [32,-40,-48,-8]
4*Matrix of T(61) = [12,28,12,-44;8,8,24,-16;16,-12,-44,-12;-12,4,8,-4]
char poly = [ -1046 -627 -74 7 1 ]
a_61 = [8,8,24,-16]
4*Matrix of T(67) = [-32,12,16,36;-40,48,64,48;28,-48,-76,-16;-16,40,36,16]
char poly = [ -1604 -1069 -86 11 1 ]
a_67 = [-40,48,64,48]
4*Matrix of T(71) = [0,28,8,-28;24,-16,-32,0;-28,40,60,-8;-8,8,-4,0]
char poly = [ -656 413 -24 -11 1 ]
a_71 = [24,-16,-32,0]
4*Matrix of T(73) = [-40,12,16,36;-40,40,64,48;28,-48,-84,-16;-16,40,36,8]
char poly = [ -3982 -1249 4 19 1 ]
a_73 = [-40,40,64,48]
4*Matrix of T(79) = [-12,16,-4,-48;48,-80,-72,-32;-44,68,72,4;4,-20,-28,-44]
char poly = [ 1952 -1303 -73 16 1 ]
a_79 = [48,-80,-72,-32]
4*Matrix of T(83) = [-24,64,32,-16;0,32,16,48;-16,16,24,-32;-32,56,32,24]
char poly = [ -4064 1592 -108 -14 1 ]
a_83 = [0,32,16,48]
4*Matrix of T(89) = [-16,-44,-12,52;-40,16,48,8;40,-60,-96,12;12,-8,8,-8]
char poly = [ -5762 -1449 91 26 1 ]
a_89 = [-40,16,48,8]
4*Matrix of W(97) = [-4,0,0,0;0,-4,0,0;0,0,-4,0;0,0,0,-4]
char poly = [ 1 4 6 4 1 ]
w_97 = [0,0,0,0]

Enter level: