Properties

Label 1104.221
Modulus $1104$
Conductor $1104$
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(1104, base_ring=CyclotomicField(44))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,33,22,42]))
 
pari: [g,chi] = znchar(Mod(221,1104))
 

Basic properties

Modulus: \(1104\)
Conductor: \(1104\)
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 1104.bo

\(\chi_{1104}(5,\cdot)\) \(\chi_{1104}(53,\cdot)\) \(\chi_{1104}(125,\cdot)\) \(\chi_{1104}(149,\cdot)\) \(\chi_{1104}(221,\cdot)\) \(\chi_{1104}(245,\cdot)\) \(\chi_{1104}(293,\cdot)\) \(\chi_{1104}(341,\cdot)\) \(\chi_{1104}(365,\cdot)\) \(\chi_{1104}(389,\cdot)\) \(\chi_{1104}(557,\cdot)\) \(\chi_{1104}(605,\cdot)\) \(\chi_{1104}(677,\cdot)\) \(\chi_{1104}(701,\cdot)\) \(\chi_{1104}(773,\cdot)\) \(\chi_{1104}(797,\cdot)\) \(\chi_{1104}(845,\cdot)\) \(\chi_{1104}(893,\cdot)\) \(\chi_{1104}(917,\cdot)\) \(\chi_{1104}(941,\cdot)\)

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

\((415,277,737,97)\) → \((1,-i,-1,e\left(\frac{21}{22}\right))\)

Values

\(-1\)\(1\)\(5\)\(7\)\(11\)\(13\)\(17\)\(19\)\(25\)\(29\)\(31\)\(35\)
\(1\)\(1\)\(e\left(\frac{9}{44}\right)\)\(e\left(\frac{7}{11}\right)\)\(e\left(\frac{37}{44}\right)\)\(e\left(\frac{27}{44}\right)\)\(e\left(\frac{2}{11}\right)\)\(e\left(\frac{25}{44}\right)\)\(e\left(\frac{9}{22}\right)\)\(e\left(\frac{41}{44}\right)\)\(e\left(\frac{8}{11}\right)\)\(e\left(\frac{37}{44}\right)\)
value at e.g. 2