# Rewriting number field related Magma code in Sage

I have the following Magma code, which I want to rewrite in Sage:

G := Sz(8);
T := CharacterTable(G);
M := GModule(T:SparseCyclo := false);
N := AbsoluteModuleOverMinimalField(M);


Currently, I have something like this:

from sage.all import *
proof.arithmetic(False)

G = SuzukiGroup(8)
T = gap(G).CharacterTable()
print(gap.eval("Display(%s)"%T.name()))


Though, I do not know how to rewrite the rest in Sage. Sz in Magma is Suzuki group. The result of M here is GModule M of dimension 14 over Cyclotomic Field of order 52 and degree 24. Also, the result of T in Magma is T = ( 14, -2, 2*zeta(4)_4, -2*zeta(4)_4, -1, 0, 0, 0, 1, 1, 1 ). AbsoluteModuleOverMinimalField is defined here.

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Unfortunately, it is hard to extract the needed information from the documentation of GModule starting from here: GModule

The following extracts the character table:

G = SuzukiGroup(8)
T = G.character_table()
for k in range(3): # 3 instead of 11 here, no space 4 more
print T[k]


with results:

(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1)
(14, 0, 0, 0, -1, 1, 1, 1, -2, -2*zeta364^91, 2*zeta364^91)
(14, 0, 0, 0, -1, 1, 1, 1, -2, 2*zeta364^91, -2*zeta364^91)


and T has for instance for its last component

sage: a = T[-1]; a
2*zeta364^91
sage: a.parent()
Cyclotomic Field of order 364 and degree 144
sage: a.absolute_minpoly()
x^2 + 4


Which is question in this context?