\\ Pari/GP code for working with number field 30.0.8221408887534945302579972677458642036796803806187.1

\\ (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 + 15*x^28 - 12*x^27 + 131*x^26 - 92*x^25 + 755*x^24 - 449*x^23 + 3202*x^22 - 1648*x^21 + 10173*x^20 - 4368*x^19 + 24856*x^18 - 8980*x^17 + 46255*x^16 - 13276*x^15 + 65515*x^14 - 15154*x^13 + 68312*x^12 - 11198*x^11 + 51310*x^10 - 6592*x^9 + 25719*x^8 - 1518*x^7 + 8148*x^6 - 588*x^5 + 1330*x^4 + 56*x^3 + 92*x^2 - 8*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]])