ζ_Prime(s) = ∏ (1 - N(p)^{-s})^{-1}

A(z) = (mat-div monodromy (z - 0)) + ...

(defclass prime-puncture ()

  ((seal-id    :initarg :seal-id)

   (witness    :initarg :witness)

   (monodromy  :initarg :monodromy)

   (value-flow :initarg :value-flow)))

(defun prime-zeta (punctures s)

  "Euler product over prime seal punctures."

  (reduce #'*

    (mapcar (lambda (p)

              (/ 1 (- 1 (expt (value-flow p) (- s)))))

            punctures)))