\\ Pari/GP code for working with number field 25.25.1269734648531914468903714880493455422104626762401.1

\\ (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^25 - x^24 - 48*x^23 + 43*x^22 + 946*x^21 - 752*x^20 - 9993*x^19 + 6962*x^18 + 62052*x^17 - 37341*x^16 - 234195*x^15 + 119366*x^14 + 538390*x^13 - 226505*x^12 - 737819*x^11 + 249907*x^10 + 571793*x^9 - 151052*x^8 - 224456*x^7 + 42136*x^6 + 35494*x^5 - 2561*x^4 - 1633*x^3 + 57*x^2 + 19*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]])