? #
   timer = 1 (on)
? read("CongruencesR
CongruencesRoutines.gp   CongruencesRoutines.gp~
? read("CongruencesRoutines.gp");
time = 4 ms.
? \r E1
E17a1example.txt   E17a1example.txt~
? \r E17a1example.txt
   realprecision = 115 significant digits (100 digits displayed)
time = 612 ms.
The class groups of the degree 20 extension is [24]
time = 4 ms.
time = 41,072 ms.
time = 1,561 ms.
time = 3,080 ms.
The matrix of generators of the first test has size [13, 5]
This part should be run in different processes to speed up
time = 1h, 39min, 26,156 ms.
The characters having a Galois closure of degree at most 5^4 are:  [[1, 0, 0, 4, 0], 
[1, 0, 1, 2, 3], [1, 0, 2, 0, 1], [1, 0, 3, 3, 4], [1, 0, 4, 1, 2], [1, 1, 0, 1, 4], 
[1, 1, 1, 4, 2], [1, 1, 2, 2, 0], [1, 1, 3, 0, 3], [1, 1, 4, 3, 1], [1, 2, 0, 3, 3], 
[1, 2, 1, 1, 1], [1, 2, 2, 4, 4], [1, 2, 3, 2, 2], [1, 2, 4, 0, 0], [1, 3, 0, 0, 2], 
[1, 3, 1, 3, 0], [1, 3, 2, 1, 3], [1, 3, 3, 4, 1], [1, 3, 4, 2, 4], [1, 4, 0, 2, 1], 
[1, 4, 0, 2, 2], [1, 4, 1, 0, 4], [1, 4, 1, 4, 0], [1, 4, 2, 1, 3], [1, 4, 2, 3, 2], 
[1, 4, 3, 1, 0], [1, 4, 3, 3, 1], [1, 4, 4, 0, 4], [1, 4, 4, 4, 3], [0, 1, 0, 2, 4], 
[0, 1, 1, 0, 2], [0, 1, 2, 3, 0], [0, 1, 3, 1, 3], [0, 1, 4, 4, 1], [0, 0, 1, 2, 3], [0, 0, 1, 3, 3]]
time = 2h, 57min, 15,761 ms.
The third test in each element gives the following number of order 30 elts:  [0, 0, 0, 0, 0, 2401, 2401, 2401, 2401, 2401, 2401, 2401, 2401, 2401, 2401, 2401, 2401, 2401, 2401, 2401, 2401, 2397, 2401, 2418, 2415, 2401, 2401, 2410, 2385, 2401, 2401, 2401, 2401, 2401, 2401, 2425, 0]
This can we writen as the union of the spaces <[1,0,0,0,2],[0,0,0,1,3],[1,2,3,0,0]> <[1,0,4,0,3],[0,0,0,1,1]> and the first one has a 2-dimensional subspace which does not pass test 3
The computation with a unique ramified prime gives
time = 985 ms.
time = 2,168 ms.
The matrix of generators of the first test has size [7, 2]
time = 38,240 ms.
The characters having a Galois closure of degree at most 5^4 are:  [[1, 1], [1, 3]]
time = 7min, 2,625 ms.
The third test in each element gives the following number of order 30 elts:  [2425, 0]
The evaluation of the first character at the primes above 113 is:
time = 372 ms.
[Mod(0, 5), Mod(0, 5), Mod(2, 5), Mod(4, 5), Mod(1, 5), Mod(3, 5)]~