Properties

Label 4410.97
Modulus $4410$
Conductor $315$
Order $12$
Real no
Primitive no
Minimal yes
Parity even

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(4410)
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([8,3,6]))
 
pari: [g,chi] = znchar(Mod(97,4410))
 

Basic properties

Modulus: \(4410\)
Conductor: \(315\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(12\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{315}(97,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 4410.ca

\(\chi_{4410}(97,\cdot)\) \(\chi_{4410}(1273,\cdot)\) \(\chi_{4410}(2743,\cdot)\) \(\chi_{4410}(3037,\cdot)\)

sage: chi.galois_orbit()
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Values on generators

\((3431,2647,1081)\) → \((e\left(\frac{2}{3}\right),i,-1)\)

Values

\(-1\)\(1\)\(11\)\(13\)\(17\)\(19\)\(23\)\(29\)\(31\)\(37\)\(41\)\(43\)
\(1\)\(1\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{7}{12}\right)\)\(-i\)\(1\)\(e\left(\frac{1}{12}\right)\)\(e\left(\frac{1}{6}\right)\)\(e\left(\frac{5}{6}\right)\)\(i\)\(e\left(\frac{5}{6}\right)\)\(e\left(\frac{5}{12}\right)\)
value at e.g. 2

Related number fields

Field of values: \(\Q(\zeta_{12})\)
Fixed field: 12.12.9891413435408203125.1