Properties

Label 1104.1043
Modulus $1104$
Conductor $1104$
Order $44$
Real no
Primitive yes
Minimal yes
Parity even

Related objects

Learn more

Show commands: 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([22,33,22,12]))
 
pari: [g,chi] = znchar(Mod(1043,1104))
 

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.br

\(\chi_{1104}(35,\cdot)\) \(\chi_{1104}(59,\cdot)\) \(\chi_{1104}(131,\cdot)\) \(\chi_{1104}(179,\cdot)\) \(\chi_{1104}(347,\cdot)\) \(\chi_{1104}(371,\cdot)\) \(\chi_{1104}(395,\cdot)\) \(\chi_{1104}(443,\cdot)\) \(\chi_{1104}(491,\cdot)\) \(\chi_{1104}(515,\cdot)\) \(\chi_{1104}(587,\cdot)\) \(\chi_{1104}(611,\cdot)\) \(\chi_{1104}(683,\cdot)\) \(\chi_{1104}(731,\cdot)\) \(\chi_{1104}(899,\cdot)\) \(\chi_{1104}(923,\cdot)\) \(\chi_{1104}(947,\cdot)\) \(\chi_{1104}(995,\cdot)\) \(\chi_{1104}(1043,\cdot)\) \(\chi_{1104}(1067,\cdot)\)

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

\((415,277,737,97)\) → \((-1,-i,-1,e\left(\frac{3}{11}\right))\)

Values

\(-1\)\(1\)\(5\)\(7\)\(11\)\(13\)\(17\)\(19\)\(25\)\(29\)\(31\)\(35\)
\(1\)\(1\)\(e\left(\frac{23}{44}\right)\)\(e\left(\frac{2}{11}\right)\)\(e\left(\frac{9}{44}\right)\)\(e\left(\frac{3}{44}\right)\)\(e\left(\frac{9}{22}\right)\)\(e\left(\frac{37}{44}\right)\)\(e\left(\frac{1}{22}\right)\)\(e\left(\frac{29}{44}\right)\)\(e\left(\frac{3}{22}\right)\)\(e\left(\frac{31}{44}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 1104 }(1043,a) \;\) at \(\;a = \) e.g. 2