lattice h = 0.005, 616 atoms, L = 16384
  x = +0.005, lam =  40000.00: exact 0.797882898545095; |fft - exact| = 3.7e-11, |float closed form - exact| = 1.7e-11
  x = +0.010, lam =  10000.00: exact 0.797877911792565; |fft - exact| = 3.4e-12, |float closed form - exact| = 1.6e-11
  x = +0.025, lam =   1600.00: exact 0.797843005398046; |fft - exact| = 7.6e-13, |float closed form - exact| = 3.1e-13
  x = +0.050, lam =    400.00: exact 0.797718352201322; |fft - exact| = 1.6e-13, |float closed form - exact| = 1.8e-13
  x = +0.150, lam =     44.44: exact 0.798604253319036; |fft - exact| = 1.1e-13, |float closed form - exact| = 8.9e-16
  x = +0.300, lam =     11.11: exact 0.795410236291197; |fft - exact| = 2.7e-14, |float closed form - exact| = 2.1e-15
  x = +0.420, lam =      5.67: exact 0.801899045207263; |fft - exact| = 5.8e-15, |float closed form - exact| = 5.6e-16
  x = -0.005, lam =  40000.00: exact 0.797882898545095; |fft - exact| = 1.0e-10, |float closed form - exact| = 1.7e-11
  x = -0.035, lam =    816.33: exact 0.797910573062322; |fft - exact| = 1.0e-12, |float closed form - exact| = 5.3e-13
  x = -0.250, lam =     16.00: exact 0.793740252977247; |fft - exact| = 1.1e-13, |float closed form - exact| = 2.2e-16
(a) max |fft - exact| = 1.0e-10; max |float closed form - exact| = 1.7e-11
(b) law of a40i's objective test 'all' (wpos 0.9) on this lattice: atoms x = [-1.49, -0.79, -0.54, -0.09, -0.005], rate at x = -0.005: 8916, total rate 8988
    eps = 1e-06: central difference 0.0098658950, analytic 0.0098172239, |difference| = 4.9e-05
    eps = 1e-05: central difference 0.0098167114, analytic 0.0098172239, |difference| = 5.1e-07
    eps = 1e-04: central difference 0.0098175972, analytic 0.0098172239, |difference| = 3.7e-07
    eps = 1e-03: central difference 0.0098172411, analytic 0.0098172239, |difference| = 1.7e-08
(c) E|Z| with L = 2^14, 2^15, 2^16: ['0.79340097175559', '0.79340097174525', '0.79340097166786']; spread 8.8e-11
