Properties

Modulus 3234
Conductor 1617
Order 210
Real no
Primitive no
Minimal yes
Parity even
Orbit label 3234.cf

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(3234)
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([105,205,126]))
 
pari: [g,chi] = znchar(Mod(1307,3234))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Modulus = 3234
Conductor = 1617
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 210
Real = no
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = no
Minimal = yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = even
Orbit label = 3234.cf
Orbit index = 58

Galois orbit

sage: chi.galois_orbit()
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

\(\chi_{3234}(5,\cdot)\) \(\chi_{3234}(47,\cdot)\) \(\chi_{3234}(59,\cdot)\) \(\chi_{3234}(185,\cdot)\) \(\chi_{3234}(257,\cdot)\) \(\chi_{3234}(269,\cdot)\) \(\chi_{3234}(311,\cdot)\) \(\chi_{3234}(383,\cdot)\) \(\chi_{3234}(467,\cdot)\) \(\chi_{3234}(647,\cdot)\) \(\chi_{3234}(719,\cdot)\) \(\chi_{3234}(731,\cdot)\) \(\chi_{3234}(773,\cdot)\) \(\chi_{3234}(845,\cdot)\) \(\chi_{3234}(929,\cdot)\) \(\chi_{3234}(971,\cdot)\) \(\chi_{3234}(983,\cdot)\) \(\chi_{3234}(1181,\cdot)\) \(\chi_{3234}(1193,\cdot)\) \(\chi_{3234}(1235,\cdot)\) \(\chi_{3234}(1307,\cdot)\) \(\chi_{3234}(1433,\cdot)\) \(\chi_{3234}(1445,\cdot)\) \(\chi_{3234}(1571,\cdot)\) \(\chi_{3234}(1643,\cdot)\) \(\chi_{3234}(1655,\cdot)\) \(\chi_{3234}(1769,\cdot)\) \(\chi_{3234}(1853,\cdot)\) \(\chi_{3234}(1895,\cdot)\) \(\chi_{3234}(1907,\cdot)\) ...

Values on generators

\((1079,199,2059)\) → \((-1,e\left(\frac{41}{42}\right),e\left(\frac{3}{5}\right))\)

Values

-115131719232529313741
\(1\)\(1\)\(e\left(\frac{22}{105}\right)\)\(e\left(\frac{57}{70}\right)\)\(e\left(\frac{32}{105}\right)\)\(e\left(\frac{29}{30}\right)\)\(e\left(\frac{25}{42}\right)\)\(e\left(\frac{44}{105}\right)\)\(e\left(\frac{19}{70}\right)\)\(e\left(\frac{13}{30}\right)\)\(e\left(\frac{46}{105}\right)\)\(e\left(\frac{33}{35}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{105})\)