Properties

Label 1840.41
Modulus $1840$
Conductor $184$
Order $22$
Real no
Primitive no
Minimal no
Parity even

Related objects

Learn more

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(1840, base_ring=CyclotomicField(22))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,11,0,12]))
 
pari: [g,chi] = znchar(Mod(41,1840))
 

Basic properties

Modulus: \(1840\)
Conductor: \(184\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(22\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{184}(133,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 1840.bz

\(\chi_{1840}(41,\cdot)\) \(\chi_{1840}(121,\cdot)\) \(\chi_{1840}(361,\cdot)\) \(\chi_{1840}(441,\cdot)\) \(\chi_{1840}(601,\cdot)\) \(\chi_{1840}(761,\cdot)\) \(\chi_{1840}(841,\cdot)\) \(\chi_{1840}(1001,\cdot)\) \(\chi_{1840}(1481,\cdot)\) \(\chi_{1840}(1641,\cdot)\)

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: \(\Q(\zeta_{11})\)
Fixed field: 22.22.14741666340843480753092741810452692992.1

Values on generators

\((1151,1381,737,1201)\) → \((1,-1,1,e\left(\frac{6}{11}\right))\)

Values

\(-1\)\(1\)\(3\)\(7\)\(9\)\(11\)\(13\)\(17\)\(19\)\(21\)\(27\)\(29\)
\(1\)\(1\)\(e\left(\frac{5}{22}\right)\)\(e\left(\frac{4}{11}\right)\)\(e\left(\frac{5}{11}\right)\)\(e\left(\frac{9}{22}\right)\)\(e\left(\frac{3}{22}\right)\)\(e\left(\frac{9}{11}\right)\)\(e\left(\frac{15}{22}\right)\)\(e\left(\frac{13}{22}\right)\)\(e\left(\frac{15}{22}\right)\)\(e\left(\frac{7}{22}\right)\)
value at e.g. 2