Properties

Label 8033.407
Modulus $8033$
Conductor $277$
Order $138$
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(8033)
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,47]))
 
pari: [g,chi] = znchar(Mod(407,8033))
 

Basic properties

Modulus: \(8033\)
Conductor: \(277\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(138\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{277}(130,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 8033.cb

\(\chi_{8033}(407,\cdot)\) \(\chi_{8033}(871,\cdot)\) \(\chi_{8033}(1306,\cdot)\) \(\chi_{8033}(1973,\cdot)\) \(\chi_{8033}(2002,\cdot)\) \(\chi_{8033}(2031,\cdot)\) \(\chi_{8033}(2060,\cdot)\) \(\chi_{8033}(2263,\cdot)\) \(\chi_{8033}(2408,\cdot)\) \(\chi_{8033}(2582,\cdot)\) \(\chi_{8033}(2959,\cdot)\) \(\chi_{8033}(3133,\cdot)\) \(\chi_{8033}(3336,\cdot)\) \(\chi_{8033}(3394,\cdot)\) \(\chi_{8033}(3510,\cdot)\) \(\chi_{8033}(3626,\cdot)\) \(\chi_{8033}(3684,\cdot)\) \(\chi_{8033}(3713,\cdot)\) \(\chi_{8033}(3742,\cdot)\) \(\chi_{8033}(3829,\cdot)\) \(\chi_{8033}(4177,\cdot)\) \(\chi_{8033}(4351,\cdot)\) \(\chi_{8033}(4409,\cdot)\) \(\chi_{8033}(4699,\cdot)\) \(\chi_{8033}(4815,\cdot)\) \(\chi_{8033}(4931,\cdot)\) \(\chi_{8033}(5163,\cdot)\) \(\chi_{8033}(5192,\cdot)\) \(\chi_{8033}(5569,\cdot)\) \(\chi_{8033}(5627,\cdot)\) ...

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

\((5541,1944)\) → \((1,e\left(\frac{47}{138}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(5\)\(6\)\(7\)\(8\)\(9\)\(10\)\(11\)
\(1\)\(1\)\(e\left(\frac{3}{46}\right)\)\(e\left(\frac{2}{69}\right)\)\(e\left(\frac{3}{23}\right)\)\(e\left(\frac{47}{138}\right)\)\(e\left(\frac{13}{138}\right)\)\(e\left(\frac{34}{69}\right)\)\(e\left(\frac{9}{46}\right)\)\(e\left(\frac{4}{69}\right)\)\(e\left(\frac{28}{69}\right)\)\(e\left(\frac{53}{138}\right)\)
value at e.g. 2

Related number fields

Field of values: $\Q(\zeta_{69})$
Fixed field: Number field defined by a degree 138 polynomial