Properties

Label 8034.1441
Modulus $8034$
Conductor $1339$
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(8034)
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,7,6]))
 
pari: [g,chi] = znchar(Mod(1441,8034))
 

Basic properties

Modulus: \(8034\)
Conductor: \(1339\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(12\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{1339}(102,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 8034.cd

\(\chi_{8034}(1441,\cdot)\) \(\chi_{8034}(3295,\cdot)\) \(\chi_{8034}(4531,\cdot)\) \(\chi_{8034}(6385,\cdot)\)

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

\((5357,1237,5773)\) → \((1,e\left(\frac{7}{12}\right),-1)\)

Values

\(-1\)\(1\)\(5\)\(7\)\(11\)\(17\)\(19\)\(23\)\(25\)\(29\)\(31\)\(35\)
\(1\)\(1\)\(-i\)\(e\left(\frac{5}{12}\right)\)\(e\left(\frac{7}{12}\right)\)\(e\left(\frac{1}{6}\right)\)\(e\left(\frac{11}{12}\right)\)\(e\left(\frac{5}{6}\right)\)\(-1\)\(e\left(\frac{1}{3}\right)\)\(-i\)\(e\left(\frac{1}{6}\right)\)
value at e.g. 2

Related number fields

Field of values: \(\Q(\zeta_{12})\)
Fixed field: 12.12.2139933234248197407397573.1