Properties

Label 6012.5
Modulus $6012$
Conductor $1503$
Order $498$
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(6012)
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,415,3]))
 
pari: [g,chi] = znchar(Mod(5,6012))
 

Basic properties

Modulus: \(6012\)
Conductor: \(1503\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(498\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{1503}(5,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 6012.bf

\(\chi_{6012}(5,\cdot)\) \(\chi_{6012}(41,\cdot)\) \(\chi_{6012}(101,\cdot)\) \(\chi_{6012}(113,\cdot)\) \(\chi_{6012}(149,\cdot)\) \(\chi_{6012}(245,\cdot)\) \(\chi_{6012}(257,\cdot)\) \(\chi_{6012}(389,\cdot)\) \(\chi_{6012}(401,\cdot)\) \(\chi_{6012}(425,\cdot)\) \(\chi_{6012}(437,\cdot)\) \(\chi_{6012}(473,\cdot)\) \(\chi_{6012}(497,\cdot)\) \(\chi_{6012}(569,\cdot)\) \(\chi_{6012}(581,\cdot)\) \(\chi_{6012}(605,\cdot)\) \(\chi_{6012}(641,\cdot)\) \(\chi_{6012}(713,\cdot)\) \(\chi_{6012}(785,\cdot)\) \(\chi_{6012}(797,\cdot)\) \(\chi_{6012}(821,\cdot)\) \(\chi_{6012}(833,\cdot)\) \(\chi_{6012}(869,\cdot)\) \(\chi_{6012}(905,\cdot)\) \(\chi_{6012}(941,\cdot)\) \(\chi_{6012}(977,\cdot)\) \(\chi_{6012}(1037,\cdot)\) \(\chi_{6012}(1073,\cdot)\) \(\chi_{6012}(1085,\cdot)\) \(\chi_{6012}(1121,\cdot)\) ...

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

\((3007,3341,4681)\) → \((1,e\left(\frac{5}{6}\right),e\left(\frac{1}{166}\right))\)

Values

\(-1\)\(1\)\(5\)\(7\)\(11\)\(13\)\(17\)\(19\)\(23\)\(25\)\(29\)\(31\)
\(1\)\(1\)\(e\left(\frac{43}{249}\right)\)\(e\left(\frac{11}{249}\right)\)\(e\left(\frac{1}{498}\right)\)\(e\left(\frac{143}{498}\right)\)\(e\left(\frac{68}{83}\right)\)\(e\left(\frac{29}{83}\right)\)\(e\left(\frac{190}{249}\right)\)\(e\left(\frac{86}{249}\right)\)\(e\left(\frac{367}{498}\right)\)\(e\left(\frac{52}{249}\right)\)
value at e.g. 2

Related number fields

Field of values: $\Q(\zeta_{249})$
Fixed field: Number field defined by a degree 498 polynomial