\\ Pari/GP code for working with number field 30.30.254863675513583304379979153001217903140700917991797.1

\\ (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^30 - x^29 - 30*x^28 + 30*x^27 + 404*x^26 - 404*x^25 - 3223*x^24 + 3223*x^23 + 16927*x^22 - 16927*x^21 - 61503*x^20 + 61503*x^19 + 158101*x^18 - 158101*x^17 - 288950*x^16 + 288950*x^15 + 371908*x^14 - 371908*x^13 - 329002*x^12 + 329002*x^11 + 191674*x^10 - 191674*x^9 - 68664*x^8 + 68664*x^7 + 13548*x^6 - 13548*x^5 - 1208*x^4 + 1208*x^3 + 32*x^2 - 32*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]])