Properties

Label 1840.719
Modulus $1840$
Conductor $460$
Order $22$
Real no
Primitive no
Minimal yes
Parity odd

Related objects

Learn more

Show commands: 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([11,0,11,18]))
 
pari: [g,chi] = znchar(Mod(719,1840))
 

Basic properties

Modulus: \(1840\)
Conductor: \(460\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(22\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{460}(259,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 1840.bq

\(\chi_{1840}(239,\cdot)\) \(\chi_{1840}(399,\cdot)\) \(\chi_{1840}(639,\cdot)\) \(\chi_{1840}(719,\cdot)\) \(\chi_{1840}(959,\cdot)\) \(\chi_{1840}(1039,\cdot)\) \(\chi_{1840}(1199,\cdot)\) \(\chi_{1840}(1359,\cdot)\) \(\chi_{1840}(1439,\cdot)\) \(\chi_{1840}(1599,\cdot)\)

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: 22.0.351468714257323283030813737164800000000000.1

Values on generators

\((1151,1381,737,1201)\) → \((-1,1,-1,e\left(\frac{9}{11}\right))\)

Values

\(-1\)\(1\)\(3\)\(7\)\(9\)\(11\)\(13\)\(17\)\(19\)\(21\)\(27\)\(29\)
\(-1\)\(1\)\(e\left(\frac{1}{11}\right)\)\(e\left(\frac{6}{11}\right)\)\(e\left(\frac{2}{11}\right)\)\(e\left(\frac{19}{22}\right)\)\(e\left(\frac{21}{22}\right)\)\(e\left(\frac{5}{22}\right)\)\(e\left(\frac{17}{22}\right)\)\(e\left(\frac{7}{11}\right)\)\(e\left(\frac{3}{11}\right)\)\(e\left(\frac{8}{11}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 1840 }(719,a) \;\) at \(\;a = \) e.g. 2