Properties

Label 2304.2249
Modulus $2304$
Conductor $384$
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([0,11,16]))
 
pari: [g,chi] = znchar(Mod(2249,2304))
 

Basic properties

Modulus: \(2304\)
Conductor: \(384\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(32\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{384}(221,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 2304.bn

\(\chi_{2304}(89,\cdot)\) \(\chi_{2304}(233,\cdot)\) \(\chi_{2304}(377,\cdot)\) \(\chi_{2304}(521,\cdot)\) \(\chi_{2304}(665,\cdot)\) \(\chi_{2304}(809,\cdot)\) \(\chi_{2304}(953,\cdot)\) \(\chi_{2304}(1097,\cdot)\) \(\chi_{2304}(1241,\cdot)\) \(\chi_{2304}(1385,\cdot)\) \(\chi_{2304}(1529,\cdot)\) \(\chi_{2304}(1673,\cdot)\) \(\chi_{2304}(1817,\cdot)\) \(\chi_{2304}(1961,\cdot)\) \(\chi_{2304}(2105,\cdot)\) \(\chi_{2304}(2249,\cdot)\)

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: 32.0.135104323545903136978453058557785670637514001130337144105502507008.1

Values on generators

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

Values

\(-1\)\(1\)\(5\)\(7\)\(11\)\(13\)\(17\)\(19\)\(23\)\(25\)\(29\)\(31\)
\(-1\)\(1\)\(e\left(\frac{27}{32}\right)\)\(e\left(\frac{7}{16}\right)\)\(e\left(\frac{23}{32}\right)\)\(e\left(\frac{5}{32}\right)\)\(e\left(\frac{1}{8}\right)\)\(e\left(\frac{29}{32}\right)\)\(e\left(\frac{5}{16}\right)\)\(e\left(\frac{11}{16}\right)\)\(e\left(\frac{25}{32}\right)\)\(-i\)
value at e.g. 2