Properties

Label 6012.107
Modulus $6012$
Conductor $2004$
Order $166$
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([83,83,92]))
 
pari: [g,chi] = znchar(Mod(107,6012))
 

Basic properties

Modulus: \(6012\)
Conductor: \(2004\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(166\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{2004}(107,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 6012.w

\(\chi_{6012}(107,\cdot)\) \(\chi_{6012}(179,\cdot)\) \(\chi_{6012}(215,\cdot)\) \(\chi_{6012}(251,\cdot)\) \(\chi_{6012}(359,\cdot)\) \(\chi_{6012}(395,\cdot)\) \(\chi_{6012}(431,\cdot)\) \(\chi_{6012}(467,\cdot)\) \(\chi_{6012}(503,\cdot)\) \(\chi_{6012}(539,\cdot)\) \(\chi_{6012}(755,\cdot)\) \(\chi_{6012}(863,\cdot)\) \(\chi_{6012}(899,\cdot)\) \(\chi_{6012}(935,\cdot)\) \(\chi_{6012}(1079,\cdot)\) \(\chi_{6012}(1187,\cdot)\) \(\chi_{6012}(1223,\cdot)\) \(\chi_{6012}(1295,\cdot)\) \(\chi_{6012}(1331,\cdot)\) \(\chi_{6012}(1367,\cdot)\) \(\chi_{6012}(1511,\cdot)\) \(\chi_{6012}(1547,\cdot)\) \(\chi_{6012}(1619,\cdot)\) \(\chi_{6012}(1655,\cdot)\) \(\chi_{6012}(1691,\cdot)\) \(\chi_{6012}(1727,\cdot)\) \(\chi_{6012}(1763,\cdot)\) \(\chi_{6012}(2015,\cdot)\) \(\chi_{6012}(2051,\cdot)\) \(\chi_{6012}(2195,\cdot)\) ...

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

\((3007,3341,4681)\) → \((-1,-1,e\left(\frac{46}{83}\right))\)

Values

\(-1\)\(1\)\(5\)\(7\)\(11\)\(13\)\(17\)\(19\)\(23\)\(25\)\(29\)\(31\)
\(1\)\(1\)\(e\left(\frac{9}{166}\right)\)\(e\left(\frac{149}{166}\right)\)\(e\left(\frac{43}{83}\right)\)\(e\left(\frac{7}{83}\right)\)\(e\left(\frac{145}{166}\right)\)\(e\left(\frac{107}{166}\right)\)\(e\left(\frac{72}{83}\right)\)\(e\left(\frac{9}{83}\right)\)\(e\left(\frac{105}{166}\right)\)\(e\left(\frac{63}{166}\right)\)
value at e.g. 2

Related number fields

Field of values: $\Q(\zeta_{83})$
Fixed field: Number field defined by a degree 166 polynomial