\\ Pari/GP code for working with number field 32.32.2283054469939826689646603434893544205211768622361793362696380065480141214463295488.1

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

\\ Define the number field: 
K = bnfinit(y^32 - 992*y^30 + 445904*y^28 - 120117312*y^26 + 21610391400*y^24 - 2739237167680*y^22 + 251483043048160*y^20 - 16928401412041856*y^18 + 836368832263692948*y^16 - 30060792811796500160*y^14 + 770922695655253881376*y^12 - 13656344894464497327232*y^10 + 158755009398149781429072*y^8 - 1115784195608048666238336*y^6 + 4117775007601131982546240*y^4 - 6007107069912239598067456*y^2 + 1454846243494370527656962, 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^32 - 992*x^30 + 445904*x^28 - 120117312*x^26 + 21610391400*x^24 - 2739237167680*x^22 + 251483043048160*x^20 - 16928401412041856*x^18 + 836368832263692948*x^16 - 30060792811796500160*x^14 + 770922695655253881376*x^12 - 13656344894464497327232*x^10 + 158755009398149781429072*x^8 - 1115784195608048666238336*x^6 + 4117775007601131982546240*x^4 - 6007107069912239598067456*x^2 + 1454846243494370527656962, 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]])