Properties

Label 1110.bh
Modulus $1110$
Conductor $555$
Order $12$
Real no
Primitive no
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(1110, base_ring=CyclotomicField(12))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([6,3,8]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(47,1110))
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(1110\)
Conductor: \(555\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(12\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 555.bi
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Related number fields

Field of values: \(\Q(\zeta_{12})\)
Fixed field: 12.12.5001167034977361328125.1

Characters in Galois orbit

Character \(-1\) \(1\) \(7\) \(11\) \(13\) \(17\) \(19\) \(23\) \(29\) \(31\) \(41\) \(43\)
\(\chi_{1110}(47,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{12}\right)\) \(-1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(i\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(-i\)
\(\chi_{1110}(137,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(-1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(i\) \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(-i\)
\(\chi_{1110}(713,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(-1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(-i\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(i\)
\(\chi_{1110}(803,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{12}\right)\) \(-1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(-i\) \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(i\)