Measurements are reported of the magnetic field dependence of excitations in the quantum critical state of the spin S=1/2 linear chain Heisenberg antiferromagnet copper pyrazine dinitrate (CuPzN). The complete spectrum was measured at k(B)T/J< or =0.025 for H=0 and H=8.7 T, where the system is approximately 30% magnetized. At H=0, the results are in agreement with exact calculations of the dynamic spin correlation function for a two-spinon continuum. At H=8.7 T, there are multiple overlapping continua with incommensurate soft modes. The boundaries of these continua confirm long-standing predictions, and the intensities are consistent with exact diagonalization and Bethe ansatz calculations.