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Superconducting metamaterials are a promising resource for quantum-information science. In the context of circuit QED, they provide a means to engineer on-chip dispersion relations and a band structure that could ultimately be utilized for generating complex entangled states of quantum circuitry, for quantum-reservoir engineering, and as an element for quantum-simulation architectures. Here we report on the development and measurement at millikelvin temperatures of a particular type of circuit metamaterial resonator composed of planar superconducting lumped-element reactances in the form of a discrete left-handed transmission line that is compatible with circuit QED architectures. We discuss the details of the design, fabrication, and circuit properties of this system. As well, we provide an extensive characterization of the dense mode spectrum in these metamaterial resonators, which we conduct using both …