\\ Pari/GP code for working with number field 28.28.642581186433047492874742549394260203375244140625.1 \\ (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 - x^27 - 40*x^26 + 35*x^25 + 667*x^24 - 497*x^23 - 6073*x^22 + 3733*x^21 + 33381*x^20 - 16356*x^19 - 116335*x^18 + 43955*x^17 + 264151*x^16 - 74631*x^15 - 396001*x^14 + 80966*x^13 + 391804*x^12 - 55684*x^11 - 251669*x^10 + 23519*x^9 + 101079*x^8 - 5634*x^7 - 23674*x^6 + 574*x^5 + 2842*x^4 + 28*x^3 - 133*x^2 - 7*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]])