== ring L=64: |X| = 64, l0 = Lambda^+(x,x) = 5.332031, omega_1 = 0.009631, l0 |X| omega_1 = 3.286, 33 separations (4.18): max relative residual (|lhs - rhs| / sum of |terms|) at the exact lowest eigenvalue = 7.6e-13 (couplings from (0.01,0.02) to (-10,-10)) eta g1 g2 r2 4eta/(1-eta) r3 4eta^2/(1-eta) 0.05 5.861e-04 5.861e-04 7.46e-03 2.11e-01 3.11e-05 1.05e-02 ok 0.05 5.861e-04 -2.930e-04 1.87e-03 2.11e-01 4.45e-06 1.05e-02 ok 0.05 -5.861e-04 -1.954e-04 5.01e-03 2.11e-01 1.44e-05 1.05e-02 ok 0.25 2.930e-03 2.930e-03 3.67e-02 1.33e+00 7.73e-04 3.33e-01 ok 0.25 2.930e-03 -1.465e-03 9.26e-03 1.33e+00 1.11e-04 3.33e-01 ok 0.25 -2.930e-03 -9.768e-04 2.53e-02 1.33e+00 3.60e-04 3.33e-01 ok 0.50 5.861e-03 5.861e-03 7.19e-02 4.00e+00 3.07e-03 2.00e+00 ok 0.50 5.861e-03 -2.930e-03 1.83e-02 4.00e+00 4.42e-04 2.00e+00 ok 0.50 -5.861e-03 -1.954e-03 5.14e-02 4.00e+00 1.45e-03 2.00e+00 ok 0.90 1.055e-02 1.055e-02 1.25e-01 3.60e+01 9.81e-03 3.24e+01 ok 0.90 1.055e-02 -5.275e-03 3.23e-02 3.60e+01 1.43e-03 3.24e+01 ok 0.90 -1.055e-02 -3.516e-03 9.46e-02 3.60e+01 4.71e-03 3.24e+01 ok == square torus L=16: |X| = 256, l0 = Lambda^+(x,x) = 0.489924, omega_1 = 0.152241, l0 |X| omega_1 = 19.094, 45 separations (4.18): max relative residual (|lhs - rhs| / sum of |terms|) at the exact lowest eigenvalue = 5.2e-12 (couplings from (0.01,0.02) to (-10,-10)) eta g1 g2 r2 4eta/(1-eta) r3 4eta^2/(1-eta) 0.05 6.379e-03 6.379e-03 9.15e-03 2.11e-01 6.45e-05 1.05e-02 ok 0.05 6.379e-03 -3.189e-03 2.29e-03 2.11e-01 9.25e-06 1.05e-02 ok 0.05 -6.379e-03 -2.126e-03 6.17e-03 2.11e-01 3.00e-05 1.05e-02 ok 0.25 3.189e-02 3.189e-02 4.45e-02 1.33e+00 1.57e-03 3.33e-01 ok 0.25 3.189e-02 -1.595e-02 1.13e-02 1.33e+00 2.29e-04 3.33e-01 ok 0.25 -3.189e-02 -1.063e-02 3.15e-02 1.33e+00 7.64e-04 3.33e-01 ok 0.50 6.379e-02 6.379e-02 8.60e-02 4.00e+00 6.10e-03 2.00e+00 ok 0.50 6.379e-02 -3.189e-02 2.21e-02 4.00e+00 9.02e-04 2.00e+00 ok 0.50 -6.379e-02 -2.126e-02 6.46e-02 4.00e+00 3.13e-03 2.00e+00 ok 0.90 1.148e-01 1.148e-01 1.47e-01 3.60e+01 1.89e-02 3.24e+01 ok 0.90 1.148e-01 -5.741e-02 3.86e-02 3.60e+01 2.86e-03 3.24e+01 ok 0.90 -1.148e-01 -3.827e-02 1.21e-01 3.60e+01 1.05e-02 3.24e+01 ok == cubic torus L=8: |X| = 512, l0 = Lambda^+(x,x) = 0.224606, omega_1 = 0.585786, l0 |X| omega_1 = 67.364, 35 separations (4.18): max relative residual (|lhs - rhs| / sum of |terms|) at the exact lowest eigenvalue = 2.7e-11 (couplings from (0.01,0.02) to (-10,-10)) eta g1 g2 r2 4eta/(1-eta) r3 4eta^2/(1-eta) 0.05 1.391e-02 1.391e-02 9.27e-03 2.11e-01 6.72e-05 1.05e-02 ok 0.05 1.391e-02 -6.957e-03 2.33e-03 2.11e-01 9.61e-06 1.05e-02 ok 0.05 -1.391e-02 -4.638e-03 6.26e-03 2.11e-01 3.13e-05 1.05e-02 ok 0.25 6.957e-02 6.957e-02 4.51e-02 1.33e+00 1.64e-03 3.33e-01 ok 0.25 6.957e-02 -3.478e-02 1.14e-02 1.33e+00 2.38e-04 3.33e-01 ok 0.25 -6.957e-02 -2.319e-02 3.19e-02 1.33e+00 7.96e-04 3.33e-01 ok 0.50 1.391e-01 1.391e-01 8.71e-02 4.00e+00 6.34e-03 2.00e+00 ok 0.50 1.391e-01 -6.957e-02 2.24e-02 4.00e+00 9.39e-04 2.00e+00 ok 0.50 -1.391e-01 -4.638e-02 6.55e-02 4.00e+00 3.26e-03 2.00e+00 ok 0.90 2.504e-01 2.504e-01 1.49e-01 3.60e+01 1.96e-02 3.24e+01 ok 0.90 2.504e-01 -1.252e-01 3.91e-02 3.60e+01 2.98e-03 3.24e+01 ok 0.90 -2.504e-01 -8.348e-02 1.23e-01 3.60e+01 1.10e-02 3.24e+01 ok Ring L=4, g=(1,-1/2), d=2: exact delta = -1.74e-16; right side of (4.18) at delta=0: 5.55e-16