\\ Pari/GP code for working with number field 19.1.49578494467761916312526550343.1 \\ (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^19 - 9*x^18 + 24*x^17 - 6*x^16 - 42*x^15 + 4*x^14 + 34*x^13 + 74*x^12 + 46*x^11 - 238*x^10 - 49*x^9 + 181*x^8 + 195*x^7 + 116*x^6 - 193*x^5 - 275*x^4 + 106*x^3 - 8*x^2 + 121*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]])