Properties

Label 2304.43
Modulus $2304$
Conductor $2304$
Order $192$
Real no
Primitive yes
Minimal yes
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(192))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([96,183,128]))
 
pari: [g,chi] = znchar(Mod(43,2304))
 

Basic properties

Modulus: \(2304\)
Conductor: \(2304\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(192\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: yes
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 2304.cc

\(\chi_{2304}(43,\cdot)\) \(\chi_{2304}(67,\cdot)\) \(\chi_{2304}(115,\cdot)\) \(\chi_{2304}(139,\cdot)\) \(\chi_{2304}(187,\cdot)\) \(\chi_{2304}(211,\cdot)\) \(\chi_{2304}(259,\cdot)\) \(\chi_{2304}(283,\cdot)\) \(\chi_{2304}(331,\cdot)\) \(\chi_{2304}(355,\cdot)\) \(\chi_{2304}(403,\cdot)\) \(\chi_{2304}(427,\cdot)\) \(\chi_{2304}(475,\cdot)\) \(\chi_{2304}(499,\cdot)\) \(\chi_{2304}(547,\cdot)\) \(\chi_{2304}(571,\cdot)\) \(\chi_{2304}(619,\cdot)\) \(\chi_{2304}(643,\cdot)\) \(\chi_{2304}(691,\cdot)\) \(\chi_{2304}(715,\cdot)\) \(\chi_{2304}(763,\cdot)\) \(\chi_{2304}(787,\cdot)\) \(\chi_{2304}(835,\cdot)\) \(\chi_{2304}(859,\cdot)\) \(\chi_{2304}(907,\cdot)\) \(\chi_{2304}(931,\cdot)\) \(\chi_{2304}(979,\cdot)\) \(\chi_{2304}(1003,\cdot)\) \(\chi_{2304}(1051,\cdot)\) \(\chi_{2304}(1075,\cdot)\) ...

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: $\Q(\zeta_{192})$
Fixed field: Number field defined by a degree 192 polynomial (not computed)

Values on generators

\((1279,2053,1793)\) → \((-1,e\left(\frac{61}{64}\right),e\left(\frac{2}{3}\right))\)

Values

\(-1\)\(1\)\(5\)\(7\)\(11\)\(13\)\(17\)\(19\)\(23\)\(25\)\(29\)\(31\)
\(-1\)\(1\)\(e\left(\frac{55}{192}\right)\)\(e\left(\frac{67}{96}\right)\)\(e\left(\frac{35}{192}\right)\)\(e\left(\frac{25}{192}\right)\)\(e\left(\frac{11}{16}\right)\)\(e\left(\frac{27}{64}\right)\)\(e\left(\frac{17}{96}\right)\)\(e\left(\frac{55}{96}\right)\)\(e\left(\frac{173}{192}\right)\)\(e\left(\frac{11}{24}\right)\)
value at e.g. 2