Properties

Conductor 539
Order 210
Real no
Primitive no
Minimal yes
Parity even
Orbit label 3234.ck

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
 
sage: H = DirichletGroup_conrey(3234)
 
sage: chi = H[61]
 
pari: [g,chi] = znchar(Mod(61,3234))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 539
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.ck
Orbit index = 63

Galois orbit

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

\(\chi_{3234}(61,\cdot)\) \(\chi_{3234}(73,\cdot)\) \(\chi_{3234}(145,\cdot)\) \(\chi_{3234}(271,\cdot)\) \(\chi_{3234}(283,\cdot)\) \(\chi_{3234}(409,\cdot)\) \(\chi_{3234}(481,\cdot)\) \(\chi_{3234}(523,\cdot)\) \(\chi_{3234}(535,\cdot)\) \(\chi_{3234}(733,\cdot)\) \(\chi_{3234}(745,\cdot)\) \(\chi_{3234}(787,\cdot)\) \(\chi_{3234}(871,\cdot)\) \(\chi_{3234}(943,\cdot)\) \(\chi_{3234}(985,\cdot)\) \(\chi_{3234}(997,\cdot)\) \(\chi_{3234}(1069,\cdot)\) \(\chi_{3234}(1249,\cdot)\) \(\chi_{3234}(1333,\cdot)\) \(\chi_{3234}(1405,\cdot)\) \(\chi_{3234}(1447,\cdot)\) \(\chi_{3234}(1459,\cdot)\) \(\chi_{3234}(1531,\cdot)\) \(\chi_{3234}(1657,\cdot)\) \(\chi_{3234}(1669,\cdot)\) \(\chi_{3234}(1711,\cdot)\) \(\chi_{3234}(1867,\cdot)\) \(\chi_{3234}(1909,\cdot)\) \(\chi_{3234}(1921,\cdot)\) \(\chi_{3234}(1993,\cdot)\) ...

Values on generators

\((1079,199,2059)\) → \((1,e\left(\frac{11}{42}\right),e\left(\frac{9}{10}\right))\)

Values

-115131719232529313741
\(1\)\(1\)\(e\left(\frac{41}{210}\right)\)\(e\left(\frac{19}{35}\right)\)\(e\left(\frac{68}{105}\right)\)\(e\left(\frac{13}{15}\right)\)\(e\left(\frac{20}{21}\right)\)\(e\left(\frac{41}{105}\right)\)\(e\left(\frac{1}{70}\right)\)\(e\left(\frac{7}{30}\right)\)\(e\left(\frac{19}{105}\right)\)\(e\left(\frac{22}{35}\right)\)
value at  e.g. 2

Related number fields

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