\\ Pari/GP code for working with number field 30.0.13209167403604364499542354001933559191813355687.1

\\ (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 + 5*x^28 - 6*x^27 + 20*x^26 - 27*x^25 + 75*x^24 - 46*x^23 + 211*x^22 - 109*x^21 + 617*x^20 - 357*x^19 + 1911*x^18 - 1372*x^17 + 2909*x^16 - 2210*x^15 + 4354*x^14 - 2262*x^13 + 5693*x^12 + 2042*x^11 + 3092*x^10 + 1302*x^9 + 2375*x^8 + 290*x^7 + 1798*x^6 - 511*x^5 + 146*x^4 - 41*x^3 + 12*x^2 - 3*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]])