Properties

Label 8016.613
Modulus $8016$
Conductor $2672$
Order $332$
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(8016)
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,83,0,224]))
 
pari: [g,chi] = znchar(Mod(613,8016))
 

Basic properties

Modulus: \(8016\)
Conductor: \(2672\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(332\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{2672}(613,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 8016.bs

\(\chi_{8016}(61,\cdot)\) \(\chi_{8016}(85,\cdot)\) \(\chi_{8016}(133,\cdot)\) \(\chi_{8016}(157,\cdot)\) \(\chi_{8016}(181,\cdot)\) \(\chi_{8016}(205,\cdot)\) \(\chi_{8016}(229,\cdot)\) \(\chi_{8016}(397,\cdot)\) \(\chi_{8016}(421,\cdot)\) \(\chi_{8016}(517,\cdot)\) \(\chi_{8016}(565,\cdot)\) \(\chi_{8016}(589,\cdot)\) \(\chi_{8016}(613,\cdot)\) \(\chi_{8016}(733,\cdot)\) \(\chi_{8016}(757,\cdot)\) \(\chi_{8016}(805,\cdot)\) \(\chi_{8016}(853,\cdot)\) \(\chi_{8016}(877,\cdot)\) \(\chi_{8016}(901,\cdot)\) \(\chi_{8016}(949,\cdot)\) \(\chi_{8016}(997,\cdot)\) \(\chi_{8016}(1021,\cdot)\) \(\chi_{8016}(1117,\cdot)\) \(\chi_{8016}(1213,\cdot)\) \(\chi_{8016}(1285,\cdot)\) \(\chi_{8016}(1357,\cdot)\) \(\chi_{8016}(1429,\cdot)\) \(\chi_{8016}(1477,\cdot)\) \(\chi_{8016}(1525,\cdot)\) \(\chi_{8016}(1597,\cdot)\) ...

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

\((3007,2005,5345,673)\) → \((1,i,1,e\left(\frac{56}{83}\right))\)

Values

\(-1\)\(1\)\(5\)\(7\)\(11\)\(13\)\(17\)\(19\)\(23\)\(25\)\(29\)\(31\)
\(1\)\(1\)\(e\left(\frac{307}{332}\right)\)\(e\left(\frac{19}{166}\right)\)\(e\left(\frac{47}{332}\right)\)\(e\left(\frac{81}{332}\right)\)\(e\left(\frac{63}{83}\right)\)\(e\left(\frac{293}{332}\right)\)\(e\left(\frac{49}{166}\right)\)\(e\left(\frac{141}{166}\right)\)\(e\left(\frac{317}{332}\right)\)\(e\left(\frac{60}{83}\right)\)
value at e.g. 2

Related number fields

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