In previous work, the author has extended the concept of regular and
irregular primes to the setting of arbitrary totally real number fields
k_{0}, using the values of the zeta function \zeta_{k_{0}} at negative
integers as our ``higher Bernoulli numbers''. In the case where k_{0} is a
real quadratic field, Siegel presented two formulas for calculating these
zeta-values: one using entirely elementary methods and one which is derived
from the theory of modular forms. (The author would like to thank Henri
Cohen for suggesting an analysis of the second formula.) We briefly
discuss several algorithms based on these formulas and compare the running
time involved in using them to determine the index of k_{0}-irregularity
(more generally, ``quadratic irregularity'') of a prime number.