We report results of largescale groundstate density matrix renormalization group (DMRG) calculations on t
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${t}^{\prime}$ J cylinders with circumferences 6 and 8. We determine a rough phase diagram that appears to approximate the twodimensional (2D) system. While for many properties, positive and negative${t}^{\prime}$ values (${t}^{\prime}/t=\pm 0.2$ ) appear to correspond to electron and holedoped cuprate systems, respectively, the behavior of superconductivity itself shows an inconsistency between the model and the materials. The${t}^{\prime}<0$ (holedoped) region shows antiferromagnetism limited to very low doping, stripes more generally, and the familiar Fermi surface of the holedoped cuprates. However, we find${t}^{\prime}<0$ strongly suppresses superconductivity. The${t}^{\prime}>0$ (electrondoped) region shows the expected circular Fermi pocket of holes around the$\left(\pi ,\pi \right)$ point and a broad lowdoped region of coexisting antiferromagnetism and dwave pairing with a triplet p component at wavevector$\left(\pi ,\pi \right)$ induced by the antiferromagnetism and dwave pairing. The pairing for the electron lowdoped system with${t}^{\prime}>0$ is strong and unambiguous in the DMRG simulations. At larger doping another broad region with stripes in addition to weaker dwave pairing and striped pwave pairing appears. In a small doping region near$x=0.08$ for${t}^{\prime}\sim 0.2$ , we find an unconventional type of stripe involving unpaired holes located predominantly on chains spaced three lattice spacings apart. The undopedmore »