(1) degree-1 omega, r = 1/2:
    p=  4.000:  max_a lam_max = 0.9661806441  at a = 0.95000
    p=  8.000:  max_a lam_max = 0.9798503284  at a = 0.95000
    p= 11.000:  max_a lam_max = 0.9926568494  at a = 0.95000
    p= 11.900:  max_a lam_max = 0.9980947401  at a = 0.78937
    p= 12.000:  max_a lam_max = 0.9998805530  at a = 0.77529
    p= 12.005:  max_a lam_max = 0.9999723367  at a = 0.77466
    p= 12.006:  max_a lam_max = 0.9999907199  at a = 0.77453
    p= 12.007:  max_a lam_max = 1.0000091120  at a = 0.77440
    p= 12.010:  max_a lam_max = 1.0000643410  at a = 0.77403
    p= 12.100:  max_a lam_max = 1.0017561156  at a = 0.76346
    p= 13.000:  max_a lam_max = 1.0212773583  at a = 0.69720
    bisection:  F(p) = 1  at  p_1 ~ 12.006505   (critical a ~ 0.77447)   [3s]
(2) local optimality at p = p_1 (value without perturbation: 1.0000000000):
    extra Blaschke zero (1-0.02) e^(i beta), beta = 0..pi:  change of the maximum: -1.90e-01 -1.37e-01 -8.42e-02 -4.82e-02 -2.38e-02 -8.48e-03 -1.33e-03
    extra singular factor exp(-0.02 P_beta),          beta = 0..pi:  change of the maximum: -1.89e-01 -1.36e-01 -8.39e-02 -4.80e-02 -2.37e-02 -8.43e-03 -1.32e-03
    extra Blaschke zero (1-0.005) e^(i beta), beta = 0..pi:  change of the maximum: -9.86e-02 -7.33e-02 -4.45e-02 -2.46e-02 -1.17e-02 -2.52e-03 -3.93e-04
    extra singular factor exp(-0.005 P_beta),          beta = 0..pi:  change of the maximum: -9.85e-02 -7.32e-02 -4.45e-02 -2.45e-02 -1.17e-02 -2.52e-03 -3.92e-04
    [6s]
(3) global search at p = 12.0, zeros of omega capped at modulus 0.97:
    degree 2: best lam_max over 14 restarts = 0.9981254278  at zeros [-0.1063+0.9642j -0.0922+0.8365j]   [12s]
    degree 3: best lam_max over 14 restarts = 0.9973763837  at zeros [-0.8885+0.1459j -0.9572+0.1572j -0.9572+0.1572j]   [50s]
    (for comparison: degree 1 at p = 12.0 gives 0.9998805530)
