All characters between ASCII 32 and 126 are supported with the exception of " (double quote) and ' (single quote/apostrophe), which TPAM architecture does not allow support of.
TPAM does not allow characters with an ASCII code of 127 or above (i.e., no †‡‰§£, etc.)
The full list of allowed non-alphanumeric characters is:
The (space) character is also allowed.
The above is also detailed in the TPAM System Administration Guide under the section "Password Rules"; and there is also further detail visible form the blue Help Bubbles when generating the Password Rules.
The detailed list from TPAM 2.5.922 System Administration Guide:
BFER 8979 was submitted as a feature enhancement to consider adding the pound symbol (£) as a supported character for password management.
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