9.0.0 Game Currency »« 8.10.0 Lilith Souls
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From time to time, an event will give souls or fragments of those souls. Keep in mind that many of these fragments will also double as currency in the store, so make sure you know what your options are before cashing in fragments for souls.
Most of the event souls produce 4* characters, so they're great to stock up on for those sacrifice events. Also, since there seems at this time to be no limit on fragments, keeping them in fragment form until you're ready to do something with them can keep your soul inventory lower than continually converting them.