\\ Pari/GP code for working with number field 32.0.6649076259173893054484111016591360000000000000000.1

\\ (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 - 8*x^31 + 22*x^30 - 40*x^29 + 178*x^28 - 712*x^27 + 1264*x^26 + 844*x^25 - 9359*x^24 + 23304*x^23 - 31738*x^22 + 20712*x^21 + 4242*x^20 - 53384*x^19 + 309318*x^18 - 1090772*x^17 + 2225756*x^16 - 2949980*x^15 + 2866688*x^14 - 2095500*x^13 + 1173576*x^12 - 535544*x^11 + 258862*x^10 - 119572*x^9 + 42617*x^8 - 13676*x^7 + 3860*x^6 - 916*x^5 + 264*x^4 - 80*x^3 + 20*x^2 - 4*x + 1, 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]])