\\ Pari/GP code for working with number field 30.0.1097586964004374803146658147777020931243896484375.1

\\ (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 - 7*x^29 + 48*x^28 - 257*x^27 + 1124*x^26 - 4108*x^25 + 12894*x^24 - 35106*x^23 + 82734*x^22 - 166828*x^21 + 288975*x^20 - 424231*x^19 + 515389*x^18 - 443551*x^17 + 184757*x^16 + 79835*x^15 - 29816*x^14 - 348911*x^13 + 993639*x^12 - 2148173*x^11 + 1765791*x^10 + 384577*x^9 - 1489368*x^8 + 2068027*x^7 - 1731374*x^6 - 444980*x^5 + 2213182*x^4 - 1190713*x^3 - 21588*x^2 + 127306*x + 52081, 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]])