Multimode squeezed states of light are a resource for achieving quantum advantage in computing and sensing, where spatial or temporal modes have been the experimental norm. In our experiments, we generated highly frequency-multimode infrared quantum light, and show how adiabatic frequency conversion can be used to convert the quantum state to visible wavelengths, while concurrently manipulating the joint spectrum by realizing a configurable many-port frequency-domain-beamsplitter unitary transformation. We report near-unity-efficiency quantum frequency conversion over a bandwidth >45 THz, which allowed us to measure the state with an electron-multiplying CCD (EMCCD) camera-based spectrometer, at non-cryogenic temperatures. The parametric amplification and conversion of >400 frequency modes yielded an overall mean of approximately 700 visible photons per shot, and photon statistics consistent with squeezing. Our work shows how many-mode quantum states of light can be generated, manipulated, and measured with efficient use of hardware resources, motivating the use of frequency encoding in quantum optics.