Properties

Label 1152.19
Modulus $1152$
Conductor $128$
Order $32$
Real no
Primitive no
Minimal yes
Parity odd

Related objects

Learn more

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(1152, base_ring=CyclotomicField(32))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([16,23,0]))
 
pari: [g,chi] = znchar(Mod(19,1152))
 

Basic properties

Modulus: \(1152\)
Conductor: \(128\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(32\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{128}(19,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 1152.bk

\(\chi_{1152}(19,\cdot)\) \(\chi_{1152}(91,\cdot)\) \(\chi_{1152}(163,\cdot)\) \(\chi_{1152}(235,\cdot)\) \(\chi_{1152}(307,\cdot)\) \(\chi_{1152}(379,\cdot)\) \(\chi_{1152}(451,\cdot)\) \(\chi_{1152}(523,\cdot)\) \(\chi_{1152}(595,\cdot)\) \(\chi_{1152}(667,\cdot)\) \(\chi_{1152}(739,\cdot)\) \(\chi_{1152}(811,\cdot)\) \(\chi_{1152}(883,\cdot)\) \(\chi_{1152}(955,\cdot)\) \(\chi_{1152}(1027,\cdot)\) \(\chi_{1152}(1099,\cdot)\)

sage: chi.galois_orbit()
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Related number fields

Field of values: \(\Q(\zeta_{32})\)
Fixed field: 32.0.3138550867693340381917894711603833208051177722232017256448.1

Values on generators

\((127,901,641)\) → \((-1,e\left(\frac{23}{32}\right),1)\)

Values

\(-1\)\(1\)\(5\)\(7\)\(11\)\(13\)\(17\)\(19\)\(23\)\(25\)\(29\)\(31\)
\(-1\)\(1\)\(e\left(\frac{23}{32}\right)\)\(e\left(\frac{11}{16}\right)\)\(e\left(\frac{19}{32}\right)\)\(e\left(\frac{25}{32}\right)\)\(e\left(\frac{1}{8}\right)\)\(e\left(\frac{1}{32}\right)\)\(e\left(\frac{9}{16}\right)\)\(e\left(\frac{7}{16}\right)\)\(e\left(\frac{13}{32}\right)\)\(i\)
value at e.g. 2