Properties

Label 1840.53
Modulus $1840$
Conductor $1840$
Order $44$
Real no
Primitive yes
Minimal yes
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([0,11,33,38]))
 
pari: [g,chi] = znchar(Mod(53,1840))
 

Basic properties

Modulus: \(1840\)
Conductor: \(1840\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(44\)
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 1840.cf

\(\chi_{1840}(53,\cdot)\) \(\chi_{1840}(157,\cdot)\) \(\chi_{1840}(237,\cdot)\) \(\chi_{1840}(293,\cdot)\) \(\chi_{1840}(373,\cdot)\) \(\chi_{1840}(477,\cdot)\) \(\chi_{1840}(557,\cdot)\) \(\chi_{1840}(613,\cdot)\) \(\chi_{1840}(773,\cdot)\) \(\chi_{1840}(797,\cdot)\) \(\chi_{1840}(957,\cdot)\) \(\chi_{1840}(1253,\cdot)\) \(\chi_{1840}(1413,\cdot)\) \(\chi_{1840}(1437,\cdot)\) \(\chi_{1840}(1493,\cdot)\) \(\chi_{1840}(1597,\cdot)\) \(\chi_{1840}(1653,\cdot)\) \(\chi_{1840}(1677,\cdot)\) \(\chi_{1840}(1813,\cdot)\) \(\chi_{1840}(1837,\cdot)\)

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: Number field defined by a degree 44 polynomial

Values on generators

\((1151,1381,737,1201)\) → \((1,i,-i,e\left(\frac{19}{22}\right))\)

Values

\(-1\)\(1\)\(3\)\(7\)\(9\)\(11\)\(13\)\(17\)\(19\)\(21\)\(27\)\(29\)
\(1\)\(1\)\(e\left(\frac{9}{11}\right)\)\(e\left(\frac{29}{44}\right)\)\(e\left(\frac{7}{11}\right)\)\(e\left(\frac{1}{44}\right)\)\(e\left(\frac{1}{11}\right)\)\(e\left(\frac{35}{44}\right)\)\(e\left(\frac{9}{44}\right)\)\(e\left(\frac{21}{44}\right)\)\(e\left(\frac{5}{11}\right)\)\(e\left(\frac{35}{44}\right)\)
value at e.g. 2