\\ Pari/GP code for working with number field 32.0.272292877590407567597186433188495333554574218609249.1

\\ (Note that not all these functions may be available, and some may take a long time to execute.)

\\ Define the number field: 
K = bnfinit(x^32 - x^31 - x^30 + 3*x^29 - x^28 - 5*x^27 + 7*x^26 + 3*x^25 - 17*x^24 + 11*x^23 + 23*x^22 - 45*x^21 - x^20 + 91*x^19 - 89*x^18 - 93*x^17 + 271*x^16 - 186*x^15 - 356*x^14 + 728*x^13 - 16*x^12 - 1440*x^11 + 1472*x^10 + 1408*x^9 - 4352*x^8 + 1536*x^7 + 7168*x^6 - 10240*x^5 - 4096*x^4 + 24576*x^3 - 16384*x^2 - 32768*x + 65536, 1)

\\ Defining polynomial: 
K.pol

\\ Degree over Q: 
poldegree(K.pol)

\\ Signature: 
K.sign

\\ Discriminant: 
K.disc

\\ Ramified primes: 
factor(abs(K.disc))[,1]~

\\ Integral basis: 
K.zk

\\ Class group: 
K.clgp

\\ Unit rank: 
K.fu

\\ Generator for roots of unity: 
K.tu[2]

\\ Fundamental units: 
K.fu

\\ Regulator: 
K.reg

\\ Galois group: 
polgalois(K.pol)

\\ Frobenius cycle types: 
p = 7;  \\ to obtain a list of $[e_i,f_i]$ for the factorization of the ideal $p\mathcal{O}_K$:
idealfactors = idealprimedec(K, p); \\ get the data
vector(length(idealfactors), j, [idealfactors[j][3], idealfactors[j][4]])