\\ Pari/GP code for working with number field 33.33.23681050358190252966666038984115482490423545779778728084912954382239302601.1 \\ (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^33 - 8*x^32 - 86*x^31 + 690*x^30 + 3527*x^29 - 25876*x^28 - 92162*x^27 + 549745*x^26 + 1676544*x^25 - 7221169*x^24 - 21518451*x^23 + 59984529*x^22 + 192193744*x^21 - 307177110*x^20 - 1170053321*x^19 + 864215343*x^18 + 4741699040*x^17 - 637264044*x^16 - 12404482875*x^15 - 3656463713*x^14 + 19997642137*x^13 + 12376322490*x^12 - 18399788371*x^11 - 16849661483*x^10 + 8289542908*x^9 + 11391691466*x^8 - 842642325*x^7 - 3707258605*x^6 - 522452271*x^5 + 463178377*x^4 + 128777001*x^3 - 2389174*x^2 - 1929880*x + 90889, 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]])