\\ Pari/GP code for working with number field 26.0.1674969840842867253564530506487708596884007.1

\\ (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^26 - 8*x^25 + 22*x^24 - 43*x^23 + 115*x^22 - 151*x^21 + 220*x^20 - 577*x^19 + 509*x^18 - 1015*x^17 + 1547*x^16 - 884*x^15 + 2815*x^14 - 3027*x^13 + 2341*x^12 - 3581*x^11 + 6893*x^10 + 2193*x^9 + 12186*x^8 - 1094*x^7 + 906*x^6 - 2074*x^5 + 14041*x^4 + 14998*x^3 + 13037*x^2 + 4230*x + 1325, 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]])