\\ Pari/GP code for working with number field 47.47.60970910094493879171722397386843789409880004652500555557585849098686770857374286440784619980917859063722220141990715114417121369170889241.1

\\ Some of these functions may take a long time to execute (this depends on the field).

\\ Define the number field: 
K = bnfinit(y^47 - y^46 - 460*y^45 + 327*y^44 + 94524*y^43 - 38110*y^42 - 11539413*y^41 + 809932*y^40 + 937957195*y^39 + 272017844*y^38 - 53844657814*y^37 - 36415505127*y^36 + 2255802403789*y^35 + 2452634499322*y^34 - 70139481731357*y^33 - 106937338241973*y^32 + 1626084100876542*y^31 + 3250400054052522*y^30 - 27906088812601386*y^29 - 70884683396944095*y^28 + 346512540625848199*y^27 + 1118163243198969746*y^26 - 2955220812359278078*y^25 - 12685164476223506555*y^24 + 15046746180109293999*y^23 + 101582059147167915284*y^22 - 18312922973366227046*y^21 - 554548726919125907181*y^20 - 318711846399705268031*y^19 + 1938753789920516494271*y^18 + 2414984135254760303399*y^17 - 3792697335240007382545*y^16 - 8178953624841789295386*y^15 + 2279595290530927592625*y^14 + 14681478777833447802999*y^13 + 5435523725560836559149*y^12 - 12942546360599189199808*y^11 - 11501227765200381452105*y^10 + 3183515530405052075328*y^9 + 7591082677180116655272*y^8 + 2077754691851067407232*y^7 - 1323128253866746375290*y^6 - 896927209808036028574*y^5 - 132715131473527952574*y^4 + 23448602689225942698*y^3 + 8115247135424866684*y^2 + 574328145019154892*y - 1980612833005069, 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

\\ Analytic class number formula: 
# self-contained Pari/GP code snippet to compute the analytic class number formula
K = bnfinit(x^47 - x^46 - 460*x^45 + 327*x^44 + 94524*x^43 - 38110*x^42 - 11539413*x^41 + 809932*x^40 + 937957195*x^39 + 272017844*x^38 - 53844657814*x^37 - 36415505127*x^36 + 2255802403789*x^35 + 2452634499322*x^34 - 70139481731357*x^33 - 106937338241973*x^32 + 1626084100876542*x^31 + 3250400054052522*x^30 - 27906088812601386*x^29 - 70884683396944095*x^28 + 346512540625848199*x^27 + 1118163243198969746*x^26 - 2955220812359278078*x^25 - 12685164476223506555*x^24 + 15046746180109293999*x^23 + 101582059147167915284*x^22 - 18312922973366227046*x^21 - 554548726919125907181*x^20 - 318711846399705268031*x^19 + 1938753789920516494271*x^18 + 2414984135254760303399*x^17 - 3792697335240007382545*x^16 - 8178953624841789295386*x^15 + 2279595290530927592625*x^14 + 14681478777833447802999*x^13 + 5435523725560836559149*x^12 - 12942546360599189199808*x^11 - 11501227765200381452105*x^10 + 3183515530405052075328*x^9 + 7591082677180116655272*x^8 + 2077754691851067407232*x^7 - 1323128253866746375290*x^6 - 896927209808036028574*x^5 - 132715131473527952574*x^4 + 23448602689225942698*x^3 + 8115247135424866684*x^2 + 574328145019154892*x - 1980612833005069, 1);
[polcoeff (lfunrootres (lfuncreate (K))[1][1][2], -1), 2^K.r1 * (2*Pi)^K.r2 * K.reg * K.no / (K.tu[1] * sqrt (abs (K.disc)))]

\\ Intermediate fields: 
L = nfsubfields(K); L[2..length(b)]

\\ Galois group: 
polgalois(K.pol)

\\ Frobenius cycle types: 
\\ to obtain a list of $[e_i,f_i]$ for the factorization of the ideal $p\mathcal{O}_K$ for $p=7$ in Pari:
p = 7; pfac = idealprimedec(K, p); vector(length(pfac), j, [pfac[j][3], pfac[j][4]])