Properties

Label 2304.55
Modulus $2304$
Conductor $128$
Order $32$
Real no
Primitive no
Minimal no
Parity odd

Related objects

Learn more

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(2304, base_ring=CyclotomicField(32))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([16,11,0]))
 
pari: [g,chi] = znchar(Mod(55,2304))
 

Basic properties

Modulus: \(2304\)
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 \(\chi_{128}(35,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 2304.bk

\(\chi_{2304}(55,\cdot)\) \(\chi_{2304}(199,\cdot)\) \(\chi_{2304}(343,\cdot)\) \(\chi_{2304}(487,\cdot)\) \(\chi_{2304}(631,\cdot)\) \(\chi_{2304}(775,\cdot)\) \(\chi_{2304}(919,\cdot)\) \(\chi_{2304}(1063,\cdot)\) \(\chi_{2304}(1207,\cdot)\) \(\chi_{2304}(1351,\cdot)\) \(\chi_{2304}(1495,\cdot)\) \(\chi_{2304}(1639,\cdot)\) \(\chi_{2304}(1783,\cdot)\) \(\chi_{2304}(1927,\cdot)\) \(\chi_{2304}(2071,\cdot)\) \(\chi_{2304}(2215,\cdot)\)

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

\((1279,2053,1793)\) → \((-1,e\left(\frac{11}{32}\right),1)\)

Values

\(-1\)\(1\)\(5\)\(7\)\(11\)\(13\)\(17\)\(19\)\(23\)\(25\)\(29\)\(31\)
\(-1\)\(1\)\(e\left(\frac{11}{32}\right)\)\(e\left(\frac{15}{16}\right)\)\(e\left(\frac{23}{32}\right)\)\(e\left(\frac{5}{32}\right)\)\(e\left(\frac{5}{8}\right)\)\(e\left(\frac{13}{32}\right)\)\(e\left(\frac{5}{16}\right)\)\(e\left(\frac{11}{16}\right)\)\(e\left(\frac{9}{32}\right)\)\(i\)
value at e.g. 2