import Mathlib

set_option maxHeartbeats 0

open BigOperators Real Nat Topology Rat

theorem amc12a_2021_p12
  (a b c d : ℝ)
  (f : ℂ → ℂ)
  (h₀ : ∀ z, f z = z^6 - 10 * z^5 + a * z^4 + b * z^3 + c * z^2 + d * z + 16)
  (h₁ : ∀ z, f z = 0 → (z.im = 0 ∧ 0 < z.re ∧ ↑(Int.floor z.re) = z.re)) :
  b = -88 := by sorry