\\ Pari/GP code for working with number field 44.0.114960548321016780585007182194561118164129919569806438859981042930068127481856.2

\\ (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^44 + 2*x^42 + 4*x^40 + 8*x^38 + 16*x^36 + 32*x^34 + 64*x^32 + 128*x^30 + 256*x^28 + 512*x^26 + 1024*x^24 + 2048*x^22 + 4096*x^20 + 8192*x^18 + 16384*x^16 + 32768*x^14 + 65536*x^12 + 131072*x^10 + 262144*x^8 + 524288*x^6 + 1048576*x^4 + 2097152*x^2 + 4194304, 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]])