Real quadratic fields with 3-class group of type (3,3).
Like all quadratic fields K of 3-class rank 2,
they have 4 unramified cyclic cubic extensions N1,...,N4
whose non-Galois cubic subfields L1,...,L4
share the same (fundamental) discriminant as the quadratic field K.
Before 1982, it was unknown,
if the complete 3-class group of K can become principal
in any of the extensions Ni, provided that K is real.
The numerical investigations  of F.-P. Heider and B. Schmithals in 1982
showed that this phenomenon occurs indeed for the 5 smallest discriminants
These were the first examples of principal factorization type Alpha1.
For d = 62501, the quadruplet of PFT's appears in pure form (A,A,A,A),
for the other four discriminants in mixed form (A,A,A,D)
with a single case of principal factorization type Delta1
(having only a 1-dimensional capitulation of ideal classes).
In the time from January 15th, 2006, to February 6th, 2006,
we investigated the sequence of these discriminants further  and found that
behave completely like the first 5 smallest discriminants. We have (known from  already)
pure PFT (A,A,A,A) for d = 152949, and mixed PFT's (A,A,A,D) otherwise.
However, on January 28th, 2006,
we were extremely surprised when we discovered 
that all four totally real cubic fields of discriminant
are of principal factorization type Delta1.
Of course we were very curious about the capitulation type
and on January 30th, 2006, we determined it to be G.19, (4321).
On April 28th, 2006, we found further occurrences of
quadruplets (D,D,D,D) with principal factorization type Delta1 for
and on June 13th, 2006, we calculated their capitulation types as
E.9, (4134) and D.10, (1341), respectively.
Thus we have solved the last open questions for unramified extensions in
Ennola and Turunen's range 0 < d < 500000 of totally real cubic discriminants 
and we are pushing forward to the mysterious region 500000 < d < 1000000.