\\ Pari/GP code for working with number field 28.0.20444429365013571404907915184985572799247638801.1 \\ (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^28 - 6*x^27 + 18*x^26 + 6*x^25 - 69*x^24 + 47*x^23 + 257*x^22 - 674*x^21 + 321*x^20 + 545*x^19 - 15*x^18 - 692*x^17 + 1854*x^16 - 6800*x^15 + 5094*x^14 + 6261*x^13 - 5929*x^12 + 6262*x^11 - 14458*x^10 - 7839*x^9 + 27851*x^8 - 6775*x^7 + 6005*x^6 - 1487*x^5 - 35142*x^4 + 22011*x^3 + 18446*x^2 - 12525*x + 2675, 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]])