Properties

Label 1380.127
Modulus $1380$
Conductor $460$
Order $44$
Real no
Primitive no
Minimal yes
Parity even

Related objects

Learn more

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(1380, base_ring=CyclotomicField(44))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([22,0,11,40]))
 
pari: [g,chi] = znchar(Mod(127,1380))
 

Basic properties

Modulus: \(1380\)
Conductor: \(460\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(44\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{460}(127,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 1380.bt

\(\chi_{1380}(127,\cdot)\) \(\chi_{1380}(163,\cdot)\) \(\chi_{1380}(187,\cdot)\) \(\chi_{1380}(223,\cdot)\) \(\chi_{1380}(307,\cdot)\) \(\chi_{1380}(403,\cdot)\) \(\chi_{1380}(427,\cdot)\) \(\chi_{1380}(463,\cdot)\) \(\chi_{1380}(487,\cdot)\) \(\chi_{1380}(547,\cdot)\) \(\chi_{1380}(583,\cdot)\) \(\chi_{1380}(607,\cdot)\) \(\chi_{1380}(703,\cdot)\) \(\chi_{1380}(763,\cdot)\) \(\chi_{1380}(823,\cdot)\) \(\chi_{1380}(883,\cdot)\) \(\chi_{1380}(1087,\cdot)\) \(\chi_{1380}(1267,\cdot)\) \(\chi_{1380}(1327,\cdot)\) \(\chi_{1380}(1363,\cdot)\)

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: 44.44.6031750835043748183809156500949648298478534300530340661248000000000000000000000000000000000.1

Values on generators

\((691,461,277,1201)\) → \((-1,1,i,e\left(\frac{10}{11}\right))\)

Values

\(-1\)\(1\)\(7\)\(11\)\(13\)\(17\)\(19\)\(29\)\(31\)\(37\)\(41\)\(43\)
\(1\)\(1\)\(e\left(\frac{1}{44}\right)\)\(e\left(\frac{15}{22}\right)\)\(e\left(\frac{21}{44}\right)\)\(e\left(\frac{27}{44}\right)\)\(e\left(\frac{7}{11}\right)\)\(e\left(\frac{19}{22}\right)\)\(e\left(\frac{21}{22}\right)\)\(e\left(\frac{15}{44}\right)\)\(e\left(\frac{10}{11}\right)\)\(e\left(\frac{35}{44}\right)\)
value at e.g. 2