Properties

Label 1840.87
Modulus $1840$
Conductor $920$
Order $44$
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(44))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([22,22,11,24]))
 
pari: [g,chi] = znchar(Mod(87,1840))
 

Basic properties

Modulus: \(1840\)
Conductor: \(920\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(44\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{920}(547,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 1840.co

\(\chi_{1840}(87,\cdot)\) \(\chi_{1840}(167,\cdot)\) \(\chi_{1840}(407,\cdot)\) \(\chi_{1840}(423,\cdot)\) \(\chi_{1840}(487,\cdot)\) \(\chi_{1840}(583,\cdot)\) \(\chi_{1840}(647,\cdot)\) \(\chi_{1840}(807,\cdot)\) \(\chi_{1840}(823,\cdot)\) \(\chi_{1840}(887,\cdot)\) \(\chi_{1840}(903,\cdot)\) \(\chi_{1840}(1047,\cdot)\) \(\chi_{1840}(1143,\cdot)\) \(\chi_{1840}(1223,\cdot)\) \(\chi_{1840}(1383,\cdot)\) \(\chi_{1840}(1527,\cdot)\) \(\chi_{1840}(1543,\cdot)\) \(\chi_{1840}(1623,\cdot)\) \(\chi_{1840}(1687,\cdot)\) \(\chi_{1840}(1783,\cdot)\)

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: \(\Q(\zeta_{44})\)
Fixed field: 44.44.25298996654427333182343480348559113656901710330851609956835131392000000000000000000000000000000000.1

Values on generators

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

Values

\(-1\)\(1\)\(3\)\(7\)\(9\)\(11\)\(13\)\(17\)\(19\)\(21\)\(27\)\(29\)
\(1\)\(1\)\(e\left(\frac{21}{44}\right)\)\(e\left(\frac{5}{44}\right)\)\(e\left(\frac{21}{22}\right)\)\(e\left(\frac{10}{11}\right)\)\(e\left(\frac{39}{44}\right)\)\(e\left(\frac{3}{44}\right)\)\(e\left(\frac{15}{22}\right)\)\(e\left(\frac{13}{22}\right)\)\(e\left(\frac{19}{44}\right)\)\(e\left(\frac{9}{11}\right)\)
value at e.g. 2