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The conformal range, which is a horizontal projection of the Davis-Wielandtshell, can be considered as the hyperbolic version of the numerical range. Herewe explain (the analogue of) the elliptical range theorem of $2\times2$ complexmatrices for the conformal range. In that course, comparison to theDavis-Wielandt shell and the numerical range is made.

On the elliptical range theorems for the Davis-Wielandt shell, the numerical range, and the conformal range