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Spectral line positions and emission probabilities of the B′ 1Σu+ → X 1Σg+ and D 1Πu → X 1Σg+ band systems of molecular hydrogen have been calculated by solving a system of four coupled Schrödinger equations. A great number of rotational lines, emitted by a low-pressure electric discharge in H2, have been identified from 122 nm down to 78 nm. All the 69 bands of the B′ 1Σu+ → X 1Σg+ system and many high-J lines of 145 bands of the D 1Πu → X 1Σg+ system are reported for the first time. Improved molecular constants are derived for the (unperturbed) electronic excited state D 1Πu−.