Properties

Label 6012.25
Modulus $6012$
Conductor $1503$
Order $249$
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([0,166,3]))
 
pari: [g,chi] = znchar(Mod(25,6012))
 

Basic properties

Modulus: \(6012\)
Conductor: \(1503\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(249\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{1503}(25,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 6012.y

\(\chi_{6012}(25,\cdot)\) \(\chi_{6012}(49,\cdot)\) \(\chi_{6012}(61,\cdot)\) \(\chi_{6012}(85,\cdot)\) \(\chi_{6012}(97,\cdot)\) \(\chi_{6012}(121,\cdot)\) \(\chi_{6012}(133,\cdot)\) \(\chi_{6012}(157,\cdot)\) \(\chi_{6012}(169,\cdot)\) \(\chi_{6012}(205,\cdot)\) \(\chi_{6012}(229,\cdot)\) \(\chi_{6012}(265,\cdot)\) \(\chi_{6012}(337,\cdot)\) \(\chi_{6012}(409,\cdot)\) \(\chi_{6012}(421,\cdot)\) \(\chi_{6012}(481,\cdot)\) \(\chi_{6012}(517,\cdot)\) \(\chi_{6012}(529,\cdot)\) \(\chi_{6012}(565,\cdot)\) \(\chi_{6012}(589,\cdot)\) \(\chi_{6012}(601,\cdot)\) \(\chi_{6012}(625,\cdot)\) \(\chi_{6012}(697,\cdot)\) \(\chi_{6012}(733,\cdot)\) \(\chi_{6012}(745,\cdot)\) \(\chi_{6012}(805,\cdot)\) \(\chi_{6012}(841,\cdot)\) \(\chi_{6012}(853,\cdot)\) \(\chi_{6012}(877,\cdot)\) \(\chi_{6012}(889,\cdot)\) ...

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

\((3007,3341,4681)\) → \((1,e\left(\frac{2}{3}\right),e\left(\frac{1}{83}\right))\)

Values

\(-1\)\(1\)\(5\)\(7\)\(11\)\(13\)\(17\)\(19\)\(23\)\(25\)\(29\)\(31\)
\(1\)\(1\)\(e\left(\frac{86}{249}\right)\)\(e\left(\frac{22}{249}\right)\)\(e\left(\frac{1}{249}\right)\)\(e\left(\frac{143}{249}\right)\)\(e\left(\frac{53}{83}\right)\)\(e\left(\frac{58}{83}\right)\)\(e\left(\frac{131}{249}\right)\)\(e\left(\frac{172}{249}\right)\)\(e\left(\frac{118}{249}\right)\)\(e\left(\frac{104}{249}\right)\)
value at e.g. 2

Related number fields

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