Properties

Label 3724.29
Modulus $3724$
Conductor $931$
Order $126$
Real no
Primitive no
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([0,54,119]))
 
pari: [g,chi] = znchar(Mod(29,3724))
 

Basic properties

Modulus: \(3724\)
Conductor: \(931\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(126\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{931}(29,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 3724.er

\(\chi_{3724}(29,\cdot)\) \(\chi_{3724}(281,\cdot)\) \(\chi_{3724}(337,\cdot)\) \(\chi_{3724}(421,\cdot)\) \(\chi_{3724}(477,\cdot)\) \(\chi_{3724}(561,\cdot)\) \(\chi_{3724}(813,\cdot)\) \(\chi_{3724}(869,\cdot)\) \(\chi_{3724}(925,\cdot)\) \(\chi_{3724}(953,\cdot)\) \(\chi_{3724}(1009,\cdot)\) \(\chi_{3724}(1093,\cdot)\) \(\chi_{3724}(1345,\cdot)\) \(\chi_{3724}(1401,\cdot)\) \(\chi_{3724}(1457,\cdot)\) \(\chi_{3724}(1485,\cdot)\) \(\chi_{3724}(1541,\cdot)\) \(\chi_{3724}(1625,\cdot)\) \(\chi_{3724}(1877,\cdot)\) \(\chi_{3724}(1933,\cdot)\) \(\chi_{3724}(1989,\cdot)\) \(\chi_{3724}(2017,\cdot)\) \(\chi_{3724}(2073,\cdot)\) \(\chi_{3724}(2409,\cdot)\) \(\chi_{3724}(2465,\cdot)\) \(\chi_{3724}(2521,\cdot)\) \(\chi_{3724}(2605,\cdot)\) \(\chi_{3724}(2689,\cdot)\) \(\chi_{3724}(2997,\cdot)\) \(\chi_{3724}(3053,\cdot)\) ...

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

\((1863,3041,3137)\) → \((1,e\left(\frac{3}{7}\right),e\left(\frac{17}{18}\right))\)

Values

\(-1\)\(1\)\(3\)\(5\)\(9\)\(11\)\(13\)\(15\)\(17\)\(23\)\(25\)\(27\)
\(-1\)\(1\)\(e\left(\frac{89}{126}\right)\)\(e\left(\frac{34}{63}\right)\)\(e\left(\frac{26}{63}\right)\)\(e\left(\frac{10}{21}\right)\)\(e\left(\frac{109}{126}\right)\)\(e\left(\frac{31}{126}\right)\)\(e\left(\frac{10}{63}\right)\)\(e\left(\frac{11}{63}\right)\)\(e\left(\frac{5}{63}\right)\)\(e\left(\frac{5}{42}\right)\)
value at e.g. 2