Properties

Label 3724.143
Modulus $3724$
Conductor $3724$
Order $126$
Real no
Primitive yes
Minimal yes
Parity odd

Related objects

Learn more

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(3724, base_ring=CyclotomicField(126))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([63,93,119]))
 
pari: [g,chi] = znchar(Mod(143,3724))
 

Basic properties

Modulus: \(3724\)
Conductor: \(3724\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(126\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: yes
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 3724.eu

\(\chi_{3724}(143,\cdot)\) \(\chi_{3724}(299,\cdot)\) \(\chi_{3724}(383,\cdot)\) \(\chi_{3724}(395,\cdot)\) \(\chi_{3724}(439,\cdot)\) \(\chi_{3724}(507,\cdot)\) \(\chi_{3724}(675,\cdot)\) \(\chi_{3724}(831,\cdot)\) \(\chi_{3724}(915,\cdot)\) \(\chi_{3724}(927,\cdot)\) \(\chi_{3724}(971,\cdot)\) \(\chi_{3724}(1039,\cdot)\) \(\chi_{3724}(1363,\cdot)\) \(\chi_{3724}(1447,\cdot)\) \(\chi_{3724}(1459,\cdot)\) \(\chi_{3724}(1503,\cdot)\) \(\chi_{3724}(1571,\cdot)\) \(\chi_{3724}(1739,\cdot)\) \(\chi_{3724}(1895,\cdot)\) \(\chi_{3724}(2035,\cdot)\) \(\chi_{3724}(2103,\cdot)\) \(\chi_{3724}(2271,\cdot)\) \(\chi_{3724}(2427,\cdot)\) \(\chi_{3724}(2511,\cdot)\) \(\chi_{3724}(2523,\cdot)\) \(\chi_{3724}(2635,\cdot)\) \(\chi_{3724}(2803,\cdot)\) \(\chi_{3724}(3043,\cdot)\) \(\chi_{3724}(3055,\cdot)\) \(\chi_{3724}(3099,\cdot)\) ...

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: $\Q(\zeta_{63})$
Fixed field: Number field defined by a degree 126 polynomial (not computed)

Values on generators

\((1863,3041,3137)\) → \((-1,e\left(\frac{31}{42}\right),e\left(\frac{17}{18}\right))\)

Values

\(-1\)\(1\)\(3\)\(5\)\(9\)\(11\)\(13\)\(15\)\(17\)\(23\)\(25\)\(27\)
\(-1\)\(1\)\(e\left(\frac{65}{126}\right)\)\(e\left(\frac{65}{126}\right)\)\(e\left(\frac{2}{63}\right)\)\(e\left(\frac{5}{14}\right)\)\(e\left(\frac{5}{63}\right)\)\(e\left(\frac{2}{63}\right)\)\(e\left(\frac{113}{126}\right)\)\(e\left(\frac{55}{126}\right)\)\(e\left(\frac{2}{63}\right)\)\(e\left(\frac{23}{42}\right)\)
value at e.g. 2