NMAX=16 NS=3200 primes<=100000 (9591) prec=300

sup over s in [1,2] of |[z^i] d_s^r H(s,z)|, and the ratio to 3^-i:
   i            r=0            r=1            r=2   |h''|3^i/i^2
   1   8.187914e-01   1.102181e+00   2.612119e+00       7.8364
   2   4.363339e-01   1.222375e+00   4.599433e+00      10.3487
   3   1.577210e-01   6.788361e-01   3.590363e+00      10.7711
   4   4.787708e-02   2.787034e-01   1.889894e+00       9.5676
   5   1.141040e-02   8.462048e-02   7.089635e-01       6.8911
   6   2.574717e-03   2.295473e-02   2.250387e-01       4.5570
   7   4.513346e-04   4.811084e-03   5.504959e-02       2.4570
   8   9.353172e-05   1.105222e-03   1.361876e-02       1.3961
   9   1.167298e-05   1.648224e-04   2.270133e-03       0.5516
  10   3.660649e-06   5.027822e-05   6.441547e-04       0.3804
  11   4.964941e-07   5.912106e-06   4.922598e-05       0.0721
  12   2.576539e-07   3.858892e-06   4.621834e-05       0.1706
  13   7.545006e-08   1.168556e-06   1.324586e-05       0.1250
  14   2.640279e-08   4.443534e-07   5.724107e-06       0.1397
  15   8.702431e-09   1.553511e-07   2.117369e-06       0.1350
  16   2.919666e-09   5.541327e-08   8.124397e-07       0.1366

G_2 = d_s^2 H (1-z/3)^3 :  S = sup_s sum_{j<=16} |g_j| 3^j
  computed per s-box from the signed coefficients (see the loop).

S (head, j <= 16) = 7890.6376   attained in s-box 1/3200
C_2 ~ S/6 = 1315.1063

C_2 = max_i |h_i''| 3^i / i^2 = 10.7711
C = C_2/18 = 0.598394   [in |R_k| <= C (k+3)^3 3^-k]
K0 = 33

NOTE: C_2 here is a max over i <= NMAX.  Extending it to all i needs
a tail argument -- the Cauchy bound on the pole-free part supplies
one, and is only needed for i > NMAX where it is far less lossy.