Why this isn't a simple rate table
Straight from the Illinois Attorney General's own instructions: "The Illinois Estate Tax will be determined using an interrelated calculation. The calculator at the Illinois Attorney General's website may be used for this computation" — rather than a preparer "performing numerous trials to obtain a figure" by hand. This is genuinely unusual: even experienced estate attorneys use the state's own online tool rather than computing it manually.
Verified official examples
The AG's own fact sheet publishes exact reference points: a $4,000,000 estate (all Illinois property) owes $0. A $5,000,000 estate (all Illinois property) owes $285,714. The same $5,000,000 estate split 50% Illinois / 50% Florida owes exactly half, $142,857 — confirming the tax apportions cleanly by where the property sits.
A genuine cliff above the exclusion
Once the estate exceeds $4,000,000, the tax is computed on the whole taxable base, not just the amount over the exclusion — the same cliff mechanic used by a handful of other states, though Illinois reaches its number through this interrelated, iterative calculation rather than a published rate table applied directly.