\\ Pari/GP code for working with number field 38.0.3600319611560698860610362435063272860144872381060102455880973038531255093138465367428016635904.1

\\ (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^38 + 181*x^36 + 14302*x^34 + 655785*x^32 + 19564842*x^30 + 403491764*x^28 + 5961216274*x^26 + 64460499272*x^24 + 516273473421*x^22 + 3076728313208*x^20 + 13620343868498*x^18 + 44444158242663*x^16 + 105381413708670*x^14 + 177560394917737*x^12 + 205585970435602*x^10 + 155336297697903*x^8 + 70268784621098*x^6 + 16089414412134*x^4 + 1207108975793*x^2 + 13841287201, 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]])