Spectroscopy data Fig 2c Three DAT files of raw spectroscopic data shown in Figure 2C. Each dat file has 3 columns in the order of: sweep frequency (Hz), in-phase voltage (mV) and quadrature voltage (mV). In addition there are several lines of headers to record experimental parameters tuned for acquiring the spectroscopy data. The three files represent the measurement done near bare modes 1, 2 and 3 respectively and named "Fig 2C sweep mode {1,2,3}.dat". Ordered set of EP coordinates in stereographic projection (shown in Fig 3b,c; 4b,c; 5b,c) "ordered knot list.csv" contains the coordinates of the steregraphically projected knot of EPs. The coordinates are ordered, as in the manuscript. 2D sheets of Arg(D) as shown in Fig 3a; 4a; 5a Three csv files of 2D sheets of Arg(D). Filenames identify the sheets, as in the manuscript. Each file has 3 columns: control parameter 1, control parameter 2 and Arg(D). Loops in parameter space Experimental control and stereographically projected coordinates of loops shown in the manuscript. Each datafile contains 7 columns: First four correspond to experimental control parameters and the last 3 columns contain the corresponding stereographically projected coordinates. The location of each loop are described below alongside filenames and filenames identify loops.Loop 1: Green loop in Fig 3. Located exclusively in the 2D sheet P3=78uW delta=60kHz Loop 2: Blue loop in Fig 3 and 4. Located in two 2D sheets P3=78uW delta=60kHz and P3=78uW delta=75_6kHz Loop 3: Red loop shown in Fig 4. Located in three 2D sheets P3=78uW delta=60kHz, P3=78uW delta=75_6kHz and P2=289uW delta=75_6kHz Loop 4: Red loop shown in Fig 5. Located in two 2D sheets P3=78uW delta=75_6kHz and P2=289uW delta=75_6kHz Loop 5: Blue loop shown in Fig 5. Located in two 2D sheets P3=78uW delta=75_6kHz and P2=289uW delta=75_6kHz Eigenvalue braids Eigenvalue braids corresponding to control loops. Filenames identify eigenvalue braids and their corresponding control loops. Each csv file has 7 columns: First column - \rho: index along the braid (and corresponding loop), 2nd and 3rd column: Re and Im parts of eigenvalue 1, 4th and 5th column: Re and Im parts of eigenvalue 2, 6thand 7th column: Re and Im parts of eigenvalue 3.