\\ Pari/GP code for working with number field 26.2.955936936346220716198217427028321533203125.1

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

\\ Define the number field: 
K = bnfinit(y^26 - 4*y^25 - y^24 + 12*y^23 - 20*y^22 - 91*y^21 + 245*y^20 + 945*y^19 + 237*y^18 - 2538*y^17 - 3465*y^16 + 4625*y^15 + 16764*y^14 + 17173*y^13 + 6911*y^12 - 948*y^11 + 1857*y^10 + 6384*y^9 + 2100*y^8 - 1050*y^7 + 280*y^6 + 490*y^5 - 352*y^4 - 172*y^3 - 11*y^2 + 8*y - 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

\\ Analytic class number formula: 
# self-contained Pari/GP code snippet to compute the analytic class number formula
K = bnfinit(x^26 - 4*x^25 - x^24 + 12*x^23 - 20*x^22 - 91*x^21 + 245*x^20 + 945*x^19 + 237*x^18 - 2538*x^17 - 3465*x^16 + 4625*x^15 + 16764*x^14 + 17173*x^13 + 6911*x^12 - 948*x^11 + 1857*x^10 + 6384*x^9 + 2100*x^8 - 1050*x^7 + 280*x^6 + 490*x^5 - 352*x^4 - 172*x^3 - 11*x^2 + 8*x - 1, 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]])