Properties

Label 2304.11
Modulus $2304$
Conductor $2304$
Order $192$
Real no
Primitive yes
Minimal yes
Parity even

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(2304)
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([96,63,32]))
 
pari: [g,chi] = znchar(Mod(11,2304))
 

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: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 2304.cd

\(\chi_{2304}(11,\cdot)\) \(\chi_{2304}(59,\cdot)\) \(\chi_{2304}(83,\cdot)\) \(\chi_{2304}(131,\cdot)\) \(\chi_{2304}(155,\cdot)\) \(\chi_{2304}(203,\cdot)\) \(\chi_{2304}(227,\cdot)\) \(\chi_{2304}(275,\cdot)\) \(\chi_{2304}(299,\cdot)\) \(\chi_{2304}(347,\cdot)\) \(\chi_{2304}(371,\cdot)\) \(\chi_{2304}(419,\cdot)\) \(\chi_{2304}(443,\cdot)\) \(\chi_{2304}(491,\cdot)\) \(\chi_{2304}(515,\cdot)\) \(\chi_{2304}(563,\cdot)\) \(\chi_{2304}(587,\cdot)\) \(\chi_{2304}(635,\cdot)\) \(\chi_{2304}(659,\cdot)\) \(\chi_{2304}(707,\cdot)\) \(\chi_{2304}(731,\cdot)\) \(\chi_{2304}(779,\cdot)\) \(\chi_{2304}(803,\cdot)\) \(\chi_{2304}(851,\cdot)\) \(\chi_{2304}(875,\cdot)\) \(\chi_{2304}(923,\cdot)\) \(\chi_{2304}(947,\cdot)\) \(\chi_{2304}(995,\cdot)\) \(\chi_{2304}(1019,\cdot)\) \(\chi_{2304}(1067,\cdot)\) ...

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

Values on generators

\((1279,2053,1793)\) → \((-1,e\left(\frac{21}{64}\right),e\left(\frac{1}{6}\right))\)

Values

\(-1\)\(1\)\(5\)\(7\)\(11\)\(13\)\(17\)\(19\)\(23\)\(25\)\(29\)\(31\)
\(1\)\(1\)\(e\left(\frac{31}{192}\right)\)\(e\left(\frac{43}{96}\right)\)\(e\left(\frac{107}{192}\right)\)\(e\left(\frac{145}{192}\right)\)\(e\left(\frac{11}{16}\right)\)\(e\left(\frac{3}{64}\right)\)\(e\left(\frac{89}{96}\right)\)\(e\left(\frac{31}{96}\right)\)\(e\left(\frac{101}{192}\right)\)\(e\left(\frac{11}{24}\right)\)
value at e.g. 2

Related number fields

Field of values: $\Q(\zeta_{192})$
Fixed field: Number field defined by a degree 192 polynomial