Properties

Label 9652.35
Modulus $9652$
Conductor $9652$
Order $126$
Real no
Primitive yes
Minimal yes
Parity odd

Related objects

Learn more

Show commands: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(9652, base_ring=CyclotomicField(126))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([63,28,76]))
 
pari: [g,chi] = znchar(Mod(35,9652))
 

Basic properties

Modulus: \(9652\)
Conductor: \(9652\)
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 9652.iz

\(\chi_{9652}(35,\cdot)\) \(\chi_{9652}(215,\cdot)\) \(\chi_{9652}(275,\cdot)\) \(\chi_{9652}(519,\cdot)\) \(\chi_{9652}(587,\cdot)\) \(\chi_{9652}(707,\cdot)\) \(\chi_{9652}(1031,\cdot)\) \(\chi_{9652}(1859,\cdot)\) \(\chi_{9652}(1923,\cdot)\) \(\chi_{9652}(1947,\cdot)\) \(\chi_{9652}(2303,\cdot)\) \(\chi_{9652}(2327,\cdot)\) \(\chi_{9652}(2399,\cdot)\) \(\chi_{9652}(2771,\cdot)\) \(\chi_{9652}(2791,\cdot)\) \(\chi_{9652}(3235,\cdot)\) \(\chi_{9652}(3455,\cdot)\) \(\chi_{9652}(3931,\cdot)\) \(\chi_{9652}(4735,\cdot)\) \(\chi_{9652}(4983,\cdot)\) \(\chi_{9652}(5291,\cdot)\) \(\chi_{9652}(5343,\cdot)\) \(\chi_{9652}(5383,\cdot)\) \(\chi_{9652}(5495,\cdot)\) \(\chi_{9652}(6039,\cdot)\) \(\chi_{9652}(6051,\cdot)\) \(\chi_{9652}(6067,\cdot)\) \(\chi_{9652}(6211,\cdot)\) \(\chi_{9652}(7047,\cdot)\) \(\chi_{9652}(7283,\cdot)\) ...

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

\((4827,7621,8893)\) → \((-1,e\left(\frac{2}{9}\right),e\left(\frac{38}{63}\right))\)

Values

\(-1\)\(1\)\(3\)\(5\)\(7\)\(9\)\(11\)\(13\)\(15\)\(17\)\(21\)\(23\)
\(-1\)\(1\)\(e\left(\frac{125}{126}\right)\)\(e\left(\frac{2}{63}\right)\)\(e\left(\frac{25}{126}\right)\)\(e\left(\frac{62}{63}\right)\)\(e\left(\frac{23}{126}\right)\)\(e\left(\frac{17}{21}\right)\)\(e\left(\frac{1}{42}\right)\)\(e\left(\frac{1}{7}\right)\)\(e\left(\frac{4}{21}\right)\)\(e\left(\frac{13}{14}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 9652 }(35,a) \;\) at \(\;a = \) e.g. 2