Properties

Label 2672.613
Modulus $2672$
Conductor $2672$
Order $332$
Real no
Primitive yes
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(2672)
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,83,224]))
 
pari: [g,chi] = znchar(Mod(613,2672))
 

Basic properties

Modulus: \(2672\)
Conductor: \(2672\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(332\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: yes
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 2672.w

\(\chi_{2672}(21,\cdot)\) \(\chi_{2672}(29,\cdot)\) \(\chi_{2672}(61,\cdot)\) \(\chi_{2672}(77,\cdot)\) \(\chi_{2672}(85,\cdot)\) \(\chi_{2672}(93,\cdot)\) \(\chi_{2672}(133,\cdot)\) \(\chi_{2672}(141,\cdot)\) \(\chi_{2672}(157,\cdot)\) \(\chi_{2672}(173,\cdot)\) \(\chi_{2672}(181,\cdot)\) \(\chi_{2672}(189,\cdot)\) \(\chi_{2672}(205,\cdot)\) \(\chi_{2672}(221,\cdot)\) \(\chi_{2672}(229,\cdot)\) \(\chi_{2672}(261,\cdot)\) \(\chi_{2672}(293,\cdot)\) \(\chi_{2672}(317,\cdot)\) \(\chi_{2672}(341,\cdot)\) \(\chi_{2672}(365,\cdot)\) \(\chi_{2672}(381,\cdot)\) \(\chi_{2672}(397,\cdot)\) \(\chi_{2672}(421,\cdot)\) \(\chi_{2672}(461,\cdot)\) \(\chi_{2672}(509,\cdot)\) \(\chi_{2672}(517,\cdot)\) \(\chi_{2672}(525,\cdot)\) \(\chi_{2672}(533,\cdot)\) \(\chi_{2672}(549,\cdot)\) \(\chi_{2672}(557,\cdot)\) ...

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

\((335,2005,673)\) → \((1,i,e\left(\frac{56}{83}\right))\)

Values

\(-1\)\(1\)\(3\)\(5\)\(7\)\(9\)\(11\)\(13\)\(15\)\(17\)\(19\)\(21\)
\(1\)\(1\)\(e\left(\frac{57}{332}\right)\)\(e\left(\frac{307}{332}\right)\)\(e\left(\frac{19}{166}\right)\)\(e\left(\frac{57}{166}\right)\)\(e\left(\frac{47}{332}\right)\)\(e\left(\frac{81}{332}\right)\)\(e\left(\frac{8}{83}\right)\)\(e\left(\frac{63}{83}\right)\)\(e\left(\frac{293}{332}\right)\)\(e\left(\frac{95}{332}\right)\)
value at e.g. 2

Related number fields

Field of values: $\Q(\zeta_{332})$
Fixed field: Number field defined by a degree 332 polynomial