G1  the operator T in M_2(Q[Z/2 wr Z])
     T11 = (-3/4)*1 + (-3/4)*e0 + (-1/4)*e1 + (3/4)*e01 + (3/4)*1 t^2 + (1/4)*e0 t^2 + (1/4)*e1 t^2 + (-1/4)*e01 t^2
     T12 = (-1/4)*1 + (1/4)*e0 + (1/4)*e1 + (-1/4)*e01
     T21 = (1/4)*1 t^2 + (-1/4)*e0 t^2 + (-1/4)*e1 t^2 + (1/4)*e01 t^2
     T22 = (-1)*1 + (-1/2)*e1 + (1/2)*e01 + (1/2)*1 t^2 + (1/2)*e0 t^2 + (1/2)*e1 t^2 + (-1/2)*e01 t^2
     chi^2 = chi alpha = chi beta = chi; T equals the hand expansion; 4T has integer coefficients: ok
G2  phi_K respects 3000 random products for every K <= 8: ok
G3  left and right multiplication by 4T on Q[G_K]^2 (no Fourier transform)
    K = 1: |G_K| =     2, matrix size     4 in 1 block(s); dim ker left = right = 3 (exact over Q and mod both primes); d_K =       3/2 = 1.5000000000  (0.0 s)
    K = 2: |G_K| =     8, matrix size    16 in 2 block(s); dim ker left = right = 10 (exact over Q and mod both primes); d_K =       5/4 = 1.2500000000  = Proposition 6.2  (0.0 s)
    K = 3: |G_K| =    24, matrix size    48 in 1 block(s); dim ker left = right = 8 (exact over Q and mod both primes); d_K =       1/3 = 0.3333333333  (0.0 s)
    K = 4: |G_K| =    64, matrix size   128 in 2 block(s); dim ker left = right = 24 (exact over Q and mod both primes); d_K =       3/8 = 0.3750000000  = Proposition 6.2  (0.0 s)
    K = 5: |G_K| =   160, matrix size   320 in 1 block(s); dim ker left = right = 32 (exact over Q and mod both primes); d_K =       1/5 = 0.2000000000  (2.8 s)
    K = 6: |G_K| =   384, matrix size   768 in 2 block(s); dim ker left = right = 80 (exact over Q and mod both primes); d_K =      5/24 = 0.2083333333  = Proposition 6.2  (7.0 s)
    K = 7: |G_K| =   896, matrix size  1792 in 1 block(s); dim ker left = right = 142 (mod both primes); d_K =    71/448 = 0.1584821429  (12.0 s)
    K = 8: |G_K| =  2048, matrix size  4096 in 2 block(s); dim ker left = right = 304 (mod both primes); d_K =    19/128 = 0.1484375000  = Proposition 6.2  (28.7 s)
G4  Remark 7.1: T in Q[Z/4 wr Z/K] via e_j -> 2 e_j
    K = 1: |Z/4 wr Z/1| = 4, 2 blocks; dim ker = 6; normalized 3/2 = d_K of Z/2 wr Z/1: ok  (0.0 s)
    K = 2: |Z/4 wr Z/2| = 32, 8 blocks; dim ker = 40; normalized 5/4 = d_K of Z/2 wr Z/2: ok  (0.0 s)
    K = 3: |Z/4 wr Z/3| = 192, 8 blocks; dim ker = 64; normalized 1/3 = d_K of Z/2 wr Z/3: ok  (0.0 s)
    K = 4: |Z/4 wr Z/4| = 1024, 32 blocks; dim ker = 384; normalized 3/8 = d_K of Z/2 wr Z/4: ok  (0.2 s)
G5  self-test: wrong operator (alpha = 1 + 2 pi'_0 pi_1, i.e. a = 3 at U)
    K = 6: d_6(wrong) = 17/96 differs from Proposition 6.2 (5/24): detected
TOTAL checks: 271, failures: 0; running time 52.3 s
ALL CHECKS PASSED
